Test 13: Simply supported thin square plate: frequency extraction

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:

Elements tested
Problem description
Reference solution
Mode shapes predicted by Abaqus
Results and discussion
Input files

ProductsAbaqus/Standard

Elements tested

S8R5

Problem description

Model:

Plate thickness = 0.05 m.

Material:

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

Boundary conditions:

$u_{x} = u_{y} = ϕ_{z} = 0$ at all nodes. $u_{z} = 0$ along all four edges. $ϕ_{x} = 0$ along edges $x = 0$ and $x = 10$ , $ϕ_{y} = 0$ along edges $y = 0$ and $y = 10$ .

Frequency extraction is performed in Step 1.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 13 from NAFEMS “Selected Benchmarks for Forced Vibration,” R0016, March 1993.

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.


Mode	Abaqus result	NAFEMS reference result	% Difference
1	2.377	2.377	0.00
2, 3	5.961	5.942	0.32
4	9.483	9.507	−0.25
5, 6	12.133	11.884	2.10
7, 8	15.468	15.449	0.12

Input files

nfm1358x.inp: S8R5 elements.