4.3.1 T1: Plane stress elements—membrane with hot-spot

Product: ABAQUS/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 0 along 0 and 0 along 0.

Loading:

Within the hot-spot, thermal strain () = 1.0 × 10^–3. Outside the hot-spot, thermal strain () = 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: 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.

Element	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.