NAFEMS P18 T1: membrane with a circular hot spot

1 Objective

Verify the stress produced by the discontinuous thermal strain in Test T1 of The Standard NAFEMS Benchmarks [1]. The automated study compares an immersed Coreform/Abaqus IGA discretization with the published solution.

2 Geometry

Two symmetry planes reduce the \(20\ \text{mm} \times 20\ \text{mm}\) membrane to the \(10\ \text{mm} \times 10\ \text{mm} \times 0.25\ \text{mm}\) quarter model in Figure 1. The quarter-circle of radius \(1\ \text{mm}\) is a second material region, not a hole. Point D lies at \((x,y)=(1,0)\ \text{mm}\) on the interface.

Figure 1: Quarter-symmetry model for NAFEMS P18 T1.

3 Material

Both regions are isotropic and linear elastic with \(E=100{,}000\ \text{MPa}\) and \(\nu=0.3\). The circular region receives a uniform thermal strain of \(1\times10^{-3}\), while the surrounding membrane has zero thermal strain.

4 Loading & boundary conditions

Symmetry conditions impose \(u_x=0\) on \(x=0\) and \(u_y=0\) on \(y=0\). The two cells belong to one multi-cell part and use different Abaqus material sections, so the thermal expansion changes discontinuously while displacement remains continuous. The reported \(\sigma_{yy}\) is sampled at D on the surrounding-material side.

5 Mesh & discretization

The immersed model uses a linear, \(C^0\) spline space constructed from a uniform \(44\times44\times1\) background grid. The in-plane cell size is \(0.227\ \text{mm}\), and no local or hierarchical refinement is used. The three-dimensional formulation constrains \(u_z\) and applies the constitutive transformation required to reproduce plane stress.

Figure 2: Exact background grid used for both immersed material regions.

6 Reference & accepted solutions

The accepted value is \(\sigma_{yy}(D)=50.0\ \text{MPa}\) [1]. The Coreform IGA test enforces a 4% relative-error limit.

7 Results

7.1 Stress at point D

Table 1: NAFEMS P18 T1 verification results.
Discretization \(\sigma_{yy}(D)\) (MPa) Relative error Limit
Immersed Coreform/Abaqus IGA 48.503 2.99% 4%
Figure 3: Immersed Coreform/Abaqus IGA stress field near the circular interface.

8 Discussion

The immersed result satisfies the accepted value and verifies displacement continuity across the multi-cell material interface together with the discontinuous thermal-strain assignment.

References

[1]
The standard NAFEMS benchmarks. NAFEMS.

Appendix

8.1 Download artifacts

Download all verification artifacts (ZIP)

8.1.1 Geometry CAD files

8.1.2 Abaqus/CAE journal files

1 generated Abaqus/CAE journal is available.

Show 1 individual journal

8.2 Provenance

The record below identifies the Coreform/Abaqus verification evidence used by this page.

Parameter Value
Evidence type Numerical verification
CTest result Passed (Release)
Verification result Passed — 1/1 enforced criterion passed
Test date 10-Sep-2026 15:59:15
Operating system Ubuntu 22.04.4 LTS
Coreform IGA version 2026.9+69838
Source revision d88163e59ac0
Abaqus version Abaqus 6.26-4