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 z-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.

ElementCoarse MeshFine Mesh
S8R51.156 MPa (+44.1%)0.862 MPa (+7.5%)
S9R51.156 MPa (+44.1%)0.862 MPa (+7.5%)

Table 4.2.6–2 ABAQUS/Explicit analysis.

ElementCoarse MeshFine MeshVery Fine Mesh
S4R0.338 MPa (–58%)0.703 MPa (–12.3%)0.765 MPa (–4.61%)
S4RS0.343 MPa (–57%)0.745 MPa (–7.11%)0.8021 MPa (+0.01%)
S4RSW0.341 MPa (–57%)0.674 MPa (–16.0%)0.8034 MPa (+0.17%)

Remarks

The skew sensitivity of shell elements is discussed in Skew sensitivity of shell elements, Section 2.3.4.

Input files

ABAQUS/Standard input files

Coarse mesh tests:


nle6x58c.inp

S8R5 elements.

nle6x59c.inp

S9R5 elements.

Fine mesh tests:


nle6x58f.inp

S8R5 elements.

nle6x59f.inp

S9R5 elements.

ABAQUS/Explicit input files

Coarse mesh tests:


le6_c.inp

S4R elements.

le6_c_s4rs.inp

S4RS elements.

le6_c_s4rsw.inp

S4RSW elements.

Refined mesh tests:


le6_f.inp

S4R elements.

le6_f_s4rs.inp

S4RS elements.

le6_f_s4rsw.inp

S4RSW elements.

Very refined mesh tests:


le6_vf.inp

S4R elements.

le6_vf_s4rs.inp

S4RS elements.

le6_vf_s4rsw.inp

S4RSW elements.