FV15: Clamped thin rhombic plate

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

This page discusses:

ProductsAbaqus/Standard

Elements tested

S8R5

STRI65

Problem description



Material:

Young's modulus = 200 GPa, Poisson's ratio = 0.3, density = 8000 kg/m3.

Boundary conditions:

ux=uy=ϕz=0 at all nodes. vz=ϕx=ϕy=0 along all edges.

General:

Gauss integration is used for the shell cross-section for element STRI65.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test FV15 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Mode shapes predicted by Abaqus



The contour plots were generated by setting the maximum and minimum contour levels close to zero. Where contour levels coincided with the element boundaries, the maximum contour level was increased and the minimum contour level was decreased appropriately.

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.

 Mode
123456
NAFEMS 7.938 12.835 17.941 19.133 24.009 27.922
S8R5 7.902 (−0.45) 12.884 (0.38) 18.027 (0.48) 18.989 (−0.75) 24.119 (0.46) 28.234 (1.12)
STR165 7.935 (−0.04) 12.804 (−0.24) 18.095 (0.86) 19.267 (−0.70) 24.428 (1.75) 27.945 (0.08)