OS-V: 0010 Elliptic Membrane

Test No. LE1 The model is a thin plate of thickness 0.1m subjected to a uniform pressure for linear static analysis. OptiStruct examines the direct stress $σ_{y y}$ at the point on inside the ellipse on the x-axis.

Benchmark Model

Second order Hexahedral, Penta, Tetra, Quad and Tria elements are used to create the coarse and fine mesh. A uniform outward pressure of 10 MPa is applied on the outer face. The pressure is converted to force and is applied to the nodes for Quad8 and Tria6 elements.

The material properties are:

Material Properties: Value
Young's Modulus: 210 x 10³ MPa
Poisson's Ratio: 0.3

Linear Static Analysis Results

All results are normalized with the target value (92.7 MPa).

	Direct Stress $σ_{y y}$ at Point D (MPa)	Normalized with the Target Value
Solid Hexahedral:
Hex8 coarse	63.15	1.467933492
Hex20 coarse	87.46	1.059913103
Hex8 fine	79.8	1.161654135
Hex20 fine	91.01	1.018569388
Solid Wedges:
Penta6 coarse	48.68	1.904272802
Penta15 coarse	95.21	0.973637223
Penta6 fine	67.3	1.377414562
Penta15 fine	94.28	0.983241409
Solid Tetrahedral:
Tetra4 coarse	53.34	1.737907762
Tetra10 coarse	95.96	0.966027511
Tetra4 fine	66.56	1.392728365
Tetra10 fine	95.28	0.972921914
Quad Shells:
Quad4 coarse	61.83	1.499272198
Quad8 coarse	86.67	1.069574247
Quad4 fine	79.7	1.163111669
Quad8 fine	91.48	1.013336248
Triangular Shells:
Tria3 coarse	54.06	1.714761376
Tria6 coarse	97.07	0.954980942
Tria3 fine	74.21	1.249157795
Tria6 fine	96.64	0.959230132

Model Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this problem include:

LE1Hex8C.fem
LE1Hex20C.fem
LE1Hex8F.fem
LE1Hex20F.fem
LE1Pen6C.fem
LE1Pen15C.fem
LE1Pen6F.fem
LE1Pen15F.fem
LE1Tet4C.fem
LE1Tet10C.fem
LE1Tet4F.fem
LE1Tet10F.fem
LE1Quad4C.fem
LE1Quad8C.fem
LE1Quad4F.fem
LE1Quad8F.fem
LE1Tria3C.fem
LE1Tria6C.fem
LE1Tria3F.fem
LE1Tria6F.fem

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis