Benchmark C5

VMC5
Simply-Supported Solid Square Plate

Overview

Reference:

NAFEMS, "The Standard NAFEMS Benchmarks", Rev. No. TSNB, National Engineering Laboratory, E. Kilbride, Glasgow, UK, August, 1989, Test No. FV52 (modified).

Analysis Type(s):

Mode-frequency Analysis (ANTYPE = 2)

Element Type(s):

3D 8-Node Structural Solid Elements (SOLID185)

3D 10-Node Tetrahedral Structural Solid Elements (SOLID187)

Input Listing:

vmc5.dat

Test Case

A simply-supported rectangular solid of thickness t is analyzed to determine the first P = 10 natural frequencies (the first three of which are rigid body modes). Determine the natural frequencies and mode shapes using the Block Lanczos eigenvalue extraction method for both element types.

Figure 595: Solid Square Plate Problem Sketch

Material Properties

Geometric Properties

Parameter Definitions

E = 200 x 10⁹ N/m²

υ = 0.3

ρ = 8000 kg/m³

a = 10.0 m

t = 1.0 m

At Z = 0 UZ = 0 along 4 edges

N1 = No. elements along edges

N2 = No. elements through thickness

Target Solution

Modes 1-3 are rigid body modes (zero frequency).

Mode	4	5	6	7	8	9	10
Frequency (Hz)	45.897	109.44	109.44	167.89	193.59	206.19	206.19

Results Comparison

			Frequency Ratio
ETYP	N1	N2	4	5	6	7	8	9	10
185	8	3	0.987	1.041	1.041	1.032	1.016	1.016	1.016
187	6	1	0.970	0.992	0.992	0.988	1.000	1.000	1.000

Figure 596: Representative Mesh Options

Figure 597: Graphical Results - Mode Shapes

Assumptions, Modeling Notes, and Solution Comments

The problem is designed to test the calculation of rigid body modes, coincident frequencies, and associated mode shapes.
The plate is simply supported on the bottom plate edges only (not at the midplane).
Three rigid body modes are correctly predicted in every test case analyzed.