\[
\newcommand{\ltwonorm}{L^2}
\newcommand{\degree}[1]{p = #1}
\newcommand{\Degree}[1]{\mathcal{P}^{#1}}
\]
Objective
Verify that internal material-cell boundaries do not materially change the response of a homogeneous trimmed solid, including where multiple planar interface faces meet along longitudinal edges or at cross-section corners. Six partitioned square cross-sections are compared with an unpartitioned monolithic beam using identical elastic properties in every material definition. The quantities of interest are the relative differences in tip displacement and in displacement and stress profiles sampled along the beam and across its section.
Geometry
The specimen is a prismatic cantilever with square cross-section \(b \times b\) and length \(L\) . Every internal cross-section boundary is extruded through the full beam length, producing planar material-interface faces parallel to the beam axis. Figure 1 shows the monolithic reference and the six partition patterns.
The first three partitions exercise rectangular inclusions that respectively touch one exterior face, touch two exterior faces, or remain completely enclosed. The zig-zag and nested-L partitions divide the square into equal-area cells and introduce non-collinear interface planes. The Tetris partition uses a \(3 \times 3\) construction: two equal four-square L cells surround a one-square central cell, so three materials meet at the central square’s corners.
Material
The partitioned models use distinct Abaqus material and solid-section definitions for each colored cell: two definitions in the first five cases and three in the Tetris case. Every definition has the same isotropic, linear-elastic properties, so the internal boundaries are physically invisible in the continuum problem.
Loading & boundary conditions
The \(z=0\) end face is pinned in all three translational directions. A uniform surface traction of magnitude \(t_y\) acts in the negative \(y\) direction over every cell face at \(z=L\) . Applying the same traction to the full partitioned end face produces resultant shear force \(P=t_y b^2\) and exercises bending and transverse shear without introducing density as another material parameter.
Mesh & discretization
Each model uses the same immersed rectilinear background grid, outer geometry, grid origin, and \(h/p\) coordinates. The background element sizes are \((5,5,10)/2^k\) in \((x,y,z)\) for \(k=0,\ldots,3\) , at degrees \(p=1\) , \(2\) , and \(3\) with maximum continuity \(C^{p-1}\) . Only the retained internal cell topology changes between the monolithic and partitioned models. The complete study contains 84 independently schedulable simulations: seven cross-sections, four refinement levels, and three degrees. The following views look along the beam axis and use the \(p=2\) results databases. Retained cells are colored categorically by part_id using the Coreform primary palette in index order; each 2-by-2 figure progresses from the coarsest to the finest cross-sectional background mesh.
Monolithic reference
Figure 2: Monolithic reference cross-section meshes.
Bottom-centered one-third square
Figure 3: Bottom-centered one-third-square partition meshes.
Bottom-left one-half square
Figure 4: Bottom-left one-half-square partition meshes.
Centered one-third square
Figure 5: Centered one-third-square partition meshes.
Zig-zag interface
Figure 6: Zig-zag partition meshes.
Nested L interface
Figure 7: Nested-L partition meshes.
Tetris partition
Figure 8: Three-cell Tetris partition meshes.
Reference & accepted solutions
The primary numerical reference for every partitioned result is the monolithic beam at the identical degree, refinement level, background-grid placement, loading, and material properties. This same-\(h\) , same-\(p\) pairing removes ordinary discretization error from the comparison and isolates the effect of creating and coupling retained material cells.
Six response differences are recorded for every pairing: tip \(u_y\) ; relative \(L^2\) differences in \(u_y\) along an axial line; and relative \(L^2\) differences in \(\sigma_{zz}\) and \(\tau_{yz}\) along vertical and horizontal midspan probes. The study-level CTest takes the maximum of those six quantities at the finest level and enforces the calibrated acceptance tolerance. The homogeneous Euler–Bernoulli cantilever solution [1]
Results
Each partition geometry below is presented independently. The case-tabbed table reports the measured partitioned response, the same-\(h\) , same-\(p\) monolithic reference response, and their relative difference for every mesh size and degree. For the tip displacement these are scalar values. For each line probe the measured and reference values are the profile \(L^2\) norms, while the relative difference is the \(L^2\) norm of the pointwise profile difference normalized by the reference norm. The three probe figures use one subfigure per degree and overlay every partitioned mesh size against the finest matching-degree monolithic result; the final figure tracks the maximum same-mesh relative difference across all six verification quantities under refinement.
Bottom-centered one-third square
h=10, p=1 h=5, p=1 h=2.5, p=1 h=1.25, p=1 h=10, p=2 h=5, p=2 h=2.5, p=2 h=1.25, p=2 h=10, p=3 h=5, p=3 h=2.5, p=3 h=1.25, p=3
Tip displacement \(u_y\)
\(-1.89 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(9.44\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(9.28 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(9.26\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.25\) \(0.279\) \(10.4\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(11.9\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(48.4 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(9.76\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(38.9 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(8.09\%\)
Tip displacement \(u_y\)
\(-3.32 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(2.67\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(16.2 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(2.63\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.457\) \(0.471\) \(2.96\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(30.9 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(6.39\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(91.0 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(3.64\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(43.9 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(0.967\%\)
Tip displacement \(u_y\)
\(-3.87 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.238\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.236\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.531\) \(0.533\) \(0.46\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(1.08\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.108\) \(0.108\) \(0.292\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.6 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.375\%\)
Tip displacement \(u_y\)
\(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.036\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.0361\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.544\) \(0.544\) \(0.219\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.936\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(90.1 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(0.0398\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.7 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.0783\%\)
Tip displacement \(u_y\)
\(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.00453\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0079\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.162\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(26.5 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(2.69\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.6 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(0.83\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(37.5 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(0.291\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00549\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00672\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0237\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(2.64\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.7 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0817\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(45.2 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.0854\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(341 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(427 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00854\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.223\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.8 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0278\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.133\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(335 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(403 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00519\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.228\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(395 \times 10^{-6}\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.00364\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00555\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00642\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.147\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.0 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(2.41\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.7 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.248\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.4 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(1.53\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(85.8 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(121 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0153\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0333\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.00664\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.147\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(903 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00107\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00818\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.146\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0246\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.0 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0148\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(274 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(328 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(198 \times 10^{-6}\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0455\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.00405\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.00211\%\)
Download data (CSV)
Centerline displacement profile
Figure 9: Bottom-centered one-third square: centerline displacement profiles under mesh refinement.
Transverse normal-stress profile
Figure 10: Bottom-centered one-third square: transverse normal-stress profiles under mesh refinement.
Transverse shear-stress profile
Figure 11: Bottom-centered one-third square: transverse shear-stress profiles under mesh refinement.
Relative differences under refinement
Bottom-left one-half square
h=10, p=1 h=5, p=1 h=2.5, p=1 h=1.25, p=1 h=10, p=2 h=5, p=2 h=2.5, p=2 h=1.25, p=2 h=10, p=3 h=5, p=3 h=2.5, p=3 h=1.25, p=3
Tip displacement \(u_y\)
\(-1.95 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(6.52\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(9.59 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(6.26\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.256\) \(0.279\) \(8.35\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.0 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(7.75\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(45.4 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(18.6\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(37.9 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(5.92\%\)
Tip displacement \(u_y\)
\(-3.34 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(2.13\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(16.2 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(2.1\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.459\) \(0.471\) \(2.74\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.1 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(8.78\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(87.2 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(10.2\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(43.7 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(2.8\%\)
Tip displacement \(u_y\)
\(-3.87 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.186\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.184\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.531\) \(0.533\) \(0.429\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.828\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.104\) \(0.108\) \(6.01\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.7 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.698\%\)
Tip displacement \(u_y\)
\(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.0198\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.0197\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.544\) \(0.544\) \(0.119\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.48\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(88.6 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(2.29\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.6 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.43\%\)
Tip displacement \(u_y\)
\(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.0227\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0278\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0297\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(26.6 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(4.83\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.5 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(0.793\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(38.2 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(5.28\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00958\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0116\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0357\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(2.17\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.0 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.306\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(45.3 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.663\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(750 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(915 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0309\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.357\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.079\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.261\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(177 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(210 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00386\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.149\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.00786\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.124\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00183\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0021\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.201\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.0 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(0.802\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.6 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.602\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.6 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(1.35\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00134\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00157\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.028\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0406\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.135\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.0564\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(227 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(269 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00916\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.114\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0458\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0515\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(317 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(378 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(651 \times 10^{-6}\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0171\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0092\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.00986\%\)
Download data (CSV)
Centerline displacement profile
Figure 13: Bottom-left one-half square: centerline displacement profiles under mesh refinement.
Transverse normal-stress profile
Figure 14: Bottom-left one-half square: transverse normal-stress profiles under mesh refinement.
Transverse shear-stress profile
Figure 15: Bottom-left one-half square: transverse shear-stress profiles under mesh refinement.
Relative differences under refinement
Centered one-third square
h=10, p=1 h=5, p=1 h=2.5, p=1 h=1.25, p=1 h=10, p=2 h=5, p=2 h=2.5, p=2 h=1.25, p=2 h=10, p=3 h=5, p=3 h=2.5, p=3 h=1.25, p=3
Tip displacement \(u_y\)
\(-1.94 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(7.1\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(9.54 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(6.79\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.253\) \(0.279\) \(9.47\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.9 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(9.98\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(48.6 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(9.46\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(38.7 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(7.61\%\)
Tip displacement \(u_y\)
\(-3.17 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(7.06\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(15.4 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(6.99\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.434\) \(0.471\) \(7.85\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.0 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(3.11\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(87.2 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(7.72\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(44.1 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(1.8\%\)
Tip displacement \(u_y\)
\(-3.87 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.293\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.291\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.531\) \(0.533\) \(0.424\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(1.59\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.108\) \(0.108\) \(0.561\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.8 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.401\%\)
Tip displacement \(u_y\)
\(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.0566\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.0567\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.544\) \(0.544\) \(0.306\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(1.13\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(90.1 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(0.161\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.7 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.101\%\)
Tip displacement \(u_y\)
\(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.00316\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00114\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.114\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(26.7 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(2.16\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.4 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(0.631\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(37.5 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(0.514\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00213\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00275\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0171\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(0.782\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.1 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.422\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(45.2 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.792\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(126 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(144 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.016\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.364\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.8 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0359\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.281\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(87.5 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(107 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00561\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.329\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0216\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.0618\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00122\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(388 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.126\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(1.24\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.8 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.221\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.607\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(554 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(647 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0285\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.112\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.0 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.175\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.183\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(120 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(134 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0157\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.226\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0879\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.0 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0327\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(83.5 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(101 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00336\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0211\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.00912\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0118\%\)
Download data (CSV)
Centerline displacement profile
Figure 17: Centered one-third square: centerline displacement profiles under mesh refinement.
Transverse normal-stress profile
Figure 18: Centered one-third square: transverse normal-stress profiles under mesh refinement.
Transverse shear-stress profile
Figure 19: Centered one-third square: transverse shear-stress profiles under mesh refinement.
Relative differences under refinement
Zig-zag interface
h=10, p=1 h=5, p=1 h=2.5, p=1 h=1.25, p=1 h=10, p=2 h=5, p=2 h=2.5, p=2 h=1.25, p=2 h=10, p=3 h=5, p=3 h=2.5, p=3 h=1.25, p=3
Tip displacement \(u_y\)
\(-1.99 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(4.56\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(9.79 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(4.33\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.264\) \(0.279\) \(5.48\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.6 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(4.29\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(50.7 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(6.81\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(37.2 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(3.22\%\)
Tip displacement \(u_y\)
\(-3.34 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(2.18\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(16.2 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(2.14\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.459\) \(0.471\) \(2.75\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(30.9 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(6.14\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(92.8 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(3.48\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(44.6 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(4.02\%\)
Tip displacement \(u_y\)
\(-3.87 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.192\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.19\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.532\) \(0.533\) \(0.295\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(1.13\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.107\) \(0.108\) \(2.02\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.6 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.627\%\)
Tip displacement \(u_y\)
\(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.0271\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.0269\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.544\) \(0.544\) \(0.133\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(1.16\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(90.1 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(0.838\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.6 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.499\%\)
Tip displacement \(u_y\)
\(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.0283\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0335\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0635\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(26.2 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(7.17\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.3 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(1.14\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(37.3 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(2.15\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00223\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00296\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00625\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(1.22\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.0 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.294\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(45.0 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.807\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(645 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(751 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0114\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.139\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0528\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.8 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.561\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(456 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(543 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00128\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.142\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.044\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.0546\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00742\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00885\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0519\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(1.15\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.0 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.254\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.2 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(1.44\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00261\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00306\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0168\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.415\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.8 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.147\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.459\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(422 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(506 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0063\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.193\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.058\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.0 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.269\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(217 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(256 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(620 \times 10^{-6}\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.46\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.00508\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.265\%\)
Download data (CSV)
Centerline displacement profile
Figure 21: Zig-zag interface: centerline displacement profiles under mesh refinement.
Transverse normal-stress profile
Figure 22: Zig-zag interface: transverse normal-stress profiles under mesh refinement.
Transverse shear-stress profile
Figure 23: Zig-zag interface: transverse shear-stress profiles under mesh refinement.
Relative differences under refinement
Nested L interface
h=10, p=1 h=5, p=1 h=2.5, p=1 h=1.25, p=1 h=10, p=2 h=5, p=2 h=2.5, p=2 h=1.25, p=2 h=10, p=3 h=5, p=3 h=2.5, p=3 h=1.25, p=3
Tip displacement \(u_y\)
\(-1.97 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(5.7\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(9.67 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(5.46\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.259\) \(0.279\) \(7.17\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.7 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(6.61\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(49.8 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(8.16\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(37.9 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(5.33\%\)
Tip displacement \(u_y\)
\(-3.27 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(4.25\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(15.9 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(4.2\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.451\) \(0.471\) \(4.5\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.1 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(2.72\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(91.7 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(5.81\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(44.2 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(3.01\%\)
Tip displacement \(u_y\)
\(-3.87 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.236\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.235\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.531\) \(0.533\) \(0.268\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(2.08\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.108\) \(0.108\) \(1.21\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.6 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.705\%\)
Tip displacement \(u_y\)
\(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.042\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.0421\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.544\) \(0.544\) \(0.153\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.394\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(90.1 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(0.22\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.7 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.145\%\)
Tip displacement \(u_y\)
\(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.00611\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00721\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.106\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(26.4 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(5.02\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.4 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(0.896\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(39.1 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(8.02\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00741\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00917\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.11\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(3.45\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.1 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.459\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(45.2 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.832\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(348 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(361 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0146\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(1.01\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0821\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.8 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.546\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(174 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(198 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00781\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.147\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0388\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.0578\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00109\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00126\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0291\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(0.992\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.0 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.433\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(1.38\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00197\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00234\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0299\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.229\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.8 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.191\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.392\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(500 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(597 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00985\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0595\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.1\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0749\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(230 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(271 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00192\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0289\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0136\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0194\%\)
Download data (CSV)
Centerline displacement profile
Figure 25: Nested L interface: centerline displacement profiles under mesh refinement.
Transverse normal-stress profile
Figure 26: Nested L interface: transverse normal-stress profiles under mesh refinement.
Transverse shear-stress profile
Figure 27: Nested L interface: transverse shear-stress profiles under mesh refinement.
Relative differences under refinement
Tetris partition
h=10, p=1 h=5, p=1 h=2.5, p=1 h=1.25, p=1 h=10, p=2 h=5, p=2 h=2.5, p=2 h=1.25, p=2 h=10, p=3 h=5, p=3 h=2.5, p=3 h=1.25, p=3
Tip displacement \(u_y\)
\(-1.93 \times 10^{-9}\) \(-2.09 \times 10^{-9}\) \(7.42\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(9.50 \times 10^{-9}\) \(10.2 \times 10^{-9}\) \(7.21\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.255\) \(0.279\) \(8.83\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.7 \times 10^{-3}\) \(31.3 \times 10^{-3}\) \(12.1\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(48.9 \times 10^{-3}\) \(53.6 \times 10^{-3}\) \(8.97\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(38.9 \times 10^{-3}\) \(36.1 \times 10^{-3}\) \(8.2\%\)
Tip displacement \(u_y\)
\(-3.17 \times 10^{-9}\) \(-3.41 \times 10^{-9}\) \(7.15\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(15.4 \times 10^{-9}\) \(16.6 \times 10^{-9}\) \(7.08\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.435\) \(0.471\) \(7.83\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.2 \times 10^{-3}\) \(30.6 \times 10^{-3}\) \(4.9\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(87.0 \times 10^{-3}\) \(94.4 \times 10^{-3}\) \(8.27\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(43.8 \times 10^{-3}\) \(43.9 \times 10^{-3}\) \(1.5\%\)
Tip displacement \(u_y\)
\(-3.86 \times 10^{-9}\) \(-3.88 \times 10^{-9}\) \(0.394\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(18.8 \times 10^{-9}\) \(18.8 \times 10^{-9}\) \(0.392\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.531\) \(0.533\) \(0.616\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(1.35\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.107\) \(0.108\) \(1.1\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.8 \times 10^{-3}\) \(46.8 \times 10^{-3}\) \(0.0943\%\)
Tip displacement \(u_y\)
\(-3.97 \times 10^{-9}\) \(-3.97 \times 10^{-9}\) \(0.0768\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.3 \times 10^{-9}\) \(19.3 \times 10^{-9}\) \(0.077\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.544\) \(0.544\) \(0.311\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(1.13\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(90.1 \times 10^{-3}\) \(90.1 \times 10^{-3}\) \(0.223\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.7 \times 10^{-3}\) \(46.7 \times 10^{-3}\) \(0.107\%\)
Tip displacement \(u_y\)
\(-3.99 \times 10^{-9}\) \(-3.99 \times 10^{-9}\) \(0.0142\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.0161\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0597\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(26.5 \times 10^{-3}\) \(26.7 \times 10^{-3}\) \(4.67\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.8 \times 10^{-3}\) \(95.0 \times 10^{-3}\) \(0.635\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(37.0 \times 10^{-3}\) \(37.5 \times 10^{-3}\) \(2.77\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00511\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00635\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0158\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(30.8 \times 10^{-3}\) \(30.8 \times 10^{-3}\) \(0.922\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.6 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.348\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(45.4 \times 10^{-3}\) \(45.2 \times 10^{-3}\) \(0.666\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(139 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(194 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0138\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(31.8 \times 10^{-3}\) \(31.8 \times 10^{-3}\) \(0.349\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.8 \times 10^{-3}\) \(94.8 \times 10^{-3}\) \(0.0555\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.155\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(447 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(538 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.00531\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.1 \times 10^{-3}\) \(0.335\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0253\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(46.9 \times 10^{-3}\) \(46.9 \times 10^{-3}\) \(0.0473\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00818\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00971\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0348\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.1 \times 10^{-3}\) \(32.0 \times 10^{-3}\) \(1.89\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(95.0 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.155\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.953\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(0.00187\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(0.00225\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0112\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.175\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.102\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.0 \times 10^{-3}\) \(47.0 \times 10^{-3}\) \(0.0945\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(788 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(936 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0184\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.366\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.0806\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.017\%\)
Tip displacement \(u_y\)
\(-4.00 \times 10^{-9}\) \(-4.00 \times 10^{-9}\) \(267 \times 10^{-6}\%\)
Centerline displacement \(\lVert u_y\rVert_{L^2}\)
\(19.4 \times 10^{-9}\) \(19.4 \times 10^{-9}\) \(320 \times 10^{-6}\%\)
Vertical normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(0.548\) \(0.548\) \(0.0033\%\)
Vertical shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(32.2 \times 10^{-3}\) \(32.2 \times 10^{-3}\) \(0.0264\%\)
Horizontal normal stress \(\lVert\sigma_{zz}\rVert_{L^2}\)
\(94.9 \times 10^{-3}\) \(94.9 \times 10^{-3}\) \(0.011\%\)
Horizontal shear stress \(\lVert\tau_{yz}\rVert_{L^2}\)
\(47.1 \times 10^{-3}\) \(47.1 \times 10^{-3}\) \(0.0148\%\)
Download data (CSV)
Centerline displacement profile
Figure 29: Tetris partition: centerline displacement profiles under mesh refinement.
Transverse normal-stress profile
Figure 30: Tetris partition: transverse normal-stress profiles under mesh refinement.
Transverse shear-stress profile
Figure 31: Tetris partition: transverse shear-stress profiles under mesh refinement.
Relative differences under refinement
Discussion
Because all material definitions are identical, the exact continuum response is independent of the internal cell decomposition. Differences from the monolithic result therefore measure numerical sensitivity to retained interfaces, including closed inclusions, re-entrant partition corners, diagonal interfaces, and three-material junctions. The full refinement history is retained so that a passing finest-level result can be distinguished from a coarse-grid coincidence and so regressions at individual interface topologies remain visible.
References
[1]
J. M. Gere and S. P. Timoshenko, Mechanics of materials , 4th ed. Boston: PWS Publishing Company, 1997.
Appendix
Capabilities exercised
The table is generated from current passing simulation and study artifacts. Each row must satisfy the linked capability card’s evidence contract; declaring a capability in a test does not, by itself, create evidence.
Download artifacts
Download all verification artifacts (ZIP)
Geometry CAD files
No separate CAD file is required for this problem; the geometry is fully defined in the Abaqus/CAE journal files.
Abaqus/CAE journal files
84 generated Abaqus/CAE journals are available.
Show 84 individual journals
Supported Abaqus keywords
The deck below is reproduced from the monolithic \(h_0p_2\) test with comments stripped and instance-specific names redacted.
*Heading *Preprint , echo =NO , model =NO , history =NO , contact =NO *Include , input = <iga-mesh-inp> *System *Material , name = <material> *Elastic *User Output Variables *Boundary <node-set> , PINNED*Step , name = <step> , nlgeom =NO *Static *Restart , write, frequency =0 *Output , field *Node Output *Element Output , position =AVERAGED AT NODES , directions =YES *Output , history, variable =PRESELECT *End Step
Provenance
The records below identify the execution environment and verification basis for every simulation and study CTest reported on this page.
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 11:29:21
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 11:45:18
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:14:51
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:46:33
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:29:55
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:46:57
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:15:12
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:46:52
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:30:13
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:49:56
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:16:15
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:48:24
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 11:30:10
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 11:57:52
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:16:09
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:50:05
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:30:26
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:01:21
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:17:18
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:52:34
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:30:34
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:04:24
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:17:43
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:54:18
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 11:30:41
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 12:04:21
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:18:15
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:53:24
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:30:51
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:05:24
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:18:53
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:54:21
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:31:04
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:05:36
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:19:33
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:58:50
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 11:27:52
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 11:44:36
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:13:11
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:42:54
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:28:06
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:44:54
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:13:55
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:43:14
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:29:09
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:45:00
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:14:17
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:45:19
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 11:31:36
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 12:06:45
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:21:37
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 13:07:56
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:31:47
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:07:04
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:22:28
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 13:08:40
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:32:01
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:07:22
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:23:08
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 13:11:28
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 11:32:05
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 12:07:36
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:23:37
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 13:15:09
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:32:20
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:07:58
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:24:25
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 13:19:56
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:32:31
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:08:23
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:25:16
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 13:22:59
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 11:31:07
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (0 positive)
Test date 26-Aug-2026 12:06:19
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:19:58
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:57:10
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:31:21
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:06:03
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:20:39
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:57:42
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 11:31:30
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:06:35
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:21:18
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Record-only diagnostic
CTest result Passed (Release)
Verification result Not asserted — 1 record-only check (1 positive)
Test date 26-Aug-2026 12:59:51
Operating system Ubuntu 26.04 LTS
Coreform IGA version 2026.8-dev+tewk_1787764370
Source revision bb2d69b00831
Abaqus version Abaqus 6.26-4
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 26-Aug-2026 19:29:55 UTC
Operating system —
Coreform IGA version Not applicable — postprocessing-only CTest
Source revision bb2d69b00831
Abaqus version Not applicable — postprocessing-only CTest
