4.2.1 LE1: Plane stress elements

4.2.1 LE1: Plane stress elements—elliptic membrane

Products: ABAQUS/Standard ABAQUS/Explicit

Elements tested

CPS3 CPS4 CPS4I CPS4R CPS6 CPS6M CPS8 CPS8R

Problem description

Model:

Plane stress problem with shape defined by ABCD. Functions defining the curves BC and AD are given above.

Mesh:

A coarse and a fine mesh are tested for each element. In addition, a very fine mesh is tested for each element in the explicit dynamic analysis.

Material:

Linear elastic, Young's modulus = 210 GPa, Poisson's ratio = 0.3, density = 7800 kg/m³.

Boundary conditions:

along edge AB, along edge CD.

Loading:

Uniform outward pressure of 10 MPa at outer edge BC. In the explicit dynamic analysis the loading is applied such that a quasi-static solution is obtained.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test LE1 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Target solution: Tangential edge stress () at D is 92.7 MPa.

Results and discussion

The results are shown in Table 4.2.1–1 and Table 4.2.1–2. The values enclosed in parentheses are percentage differences with respect to the reference solution.

Table 4.2.1–1 ABAQUS/Standard analysis.

Element	Coarse Mesh	Fine Mesh
CPS3	51.04 MPa (–45%)	71.26 MPa (–23%)
CPS4	66.73 MPa (–28%)	84.54 MPa (–9%)
CPS4I	58.82 MPa (–37%)	78.21 MPa (–16%)
CPS4R*	40.48 MPa (–56%)	56.18 MPa (–39%)
CPS6	89.10 MPa (–4%)	94.01 MPa (1%)
CPS6M	85.88 MPa (–7%)	93.71 MPa (1%)
CPS8	84.54 MPa (–9%)	92.81 MPa (0.12%)
CPS8R	85.80 MPa (–7%)	90.07 MPa (–3%)

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

Table 4.2.1–2 ABAQUS/Explicit analysis.

Element	Coarse Mesh	Fine Mesh	Very Fine Mesh
CPS3	51.2 MPa (–45%)	71.5 MPa (–23%)	85.7 MPa (–8%)
CPS4R	39.6 MPa (–57%)	55.7 MPa (–40%)	87.3 MPa (–6%)
CPS6M	86.12 MPa (–7%)	92.93 MPa (–0.2%)	—