4.2.6 LE6: Skew plate under normal pressure

Products: ABAQUS/Standard ABAQUS/Explicit

Elements tested

S4R S4RS S4RSW S8R5 S9R5

Problem description

Model:

Skew plate under normal pressure.

Mesh:

A coarse (2 × 2) and a fine (4 × 4) are tested for each element. In addition, a very fine (8 × 8) 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 edges AB, BC, CD, and AD. 0 at point A and at point B to prevent rigid body motion.

Loading:

Uniform pressure of –7.0 kPa in the vertical -direction. 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 LE6 from NAFEMS Publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Target solution: Maximum principal stress = 0.802 MPa on the lower surface at point E.

Results and discussion

The results are shown in Table 4.2.6–1 and Table 4.2.6–2. The values enclosed in parentheses are percentage differences with respect to the reference solution.

Table 4.2.6–1 ABAQUS/Standard analysis.

Element	Coarse Mesh	Fine Mesh
S8R5	1.156 MPa (+44.1%)	0.862 MPa (+7.5%)
S9R5	1.156 MPa (+44.1%)	0.862 MPa (+7.5%)

Table 4.2.6–2 ABAQUS/Explicit analysis.

Element	Coarse Mesh	Fine Mesh	Very Fine Mesh
S4R	0.338 MPa (–58%)	0.703 MPa (–12.3%)	0.765 MPa (–4.61%)
S4RS	0.343 MPa (–57%)	0.745 MPa (–7.11%)	0.8021 MPa (+0.01%)
S4RSW	0.341 MPa (–57%)	0.674 MPa (–16.0%)	0.8034 MPa (+0.17%)