T1: Plane stress elements—membrane with hot-spot

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

This page discusses:

ProductsAbaqus/Standard

Elements tested

CPS3

CPS4

CPS4I

CPS4R

CPS6

CPS6M

CPS8

CPS8R

Problem description



Material:

Linear elastic, Young's modulus = 100 GPa, Poisson's ratio = 0.3.

Boundary conditions:

A quarter-section is modeled with the symmetry conditions uy=​ 0 along y=​ 0 and ux=​ 0 along x=​ 0.

Loading:

Within the hot-spot, thermal strain (α⁢T) = 1.0 × 10−3. Outside the hot-spot, thermal strain (α⁢T) = 0.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test T1 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Target solution: σy⁢y at point D (outside the hot-spot) = 50.0 MPa.

Results and discussion

The results are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.

Elementσy⁢y at D
CPS3 54.25 MPa (8.4%)
CPS4 50.94 MPa (1.9%)
CPS4I 46.29 MPa (−7.4%)
CPS4R 23.65 MPa (−52.7%)*
CPS6 54.46 MPa (8.9%)
CPS6M 54.25 MPa (8.5%)
CPS8 51.53 MPa (3.1%)
CPS8R 44.06 MPa (−11.9%)*

*A comparison of the results for reduced-integration and full-integration elements indicates that the full-integration elements perform significantly better for problems with stress concentrations of this type.