Simply Supported Rectangular Plate

Description

Calculate the deflection at the center of a simply supported isotropic plate subjected to:
  • Concentrated load F = 400 lbs, and
  • Uniform pressure q = 1 psi.

Dimensions of the plate are as follows: h = 1 in, a = b = 40 in.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Static_1.SLDPRT and open the file.

Study Type

Static.

Mesh Type

Shell mesh.

Shell Parameters

Shell thickness is 1" - Thin formulation.

Material Properties

Modulus of elasticity = 3 X 107 psi, Poisson's ratio = 0.3.

Meshing Parameters

Use the default Global Size for Study A and 1/2 the Global Size (left-most position on the slider) for Study B.

Modeling Hints

Due to double symmetry in geometry and loads, only a quarter of the plate is modeled.

Results

The deflection at the center of the plate is calculated and compared to analytical solution.

Case X (in) Y (in) Deflection at the center (UY), in
Theory SOLIDWORKS Simulation
Maximum Study A 20 20 0.00270230 0.00270293
Maximum Study B 20 20 0.00378327 0.00378550

Analytical Solution

Study A: UY = (0.0116 * F * b2) / D

D = (E * h3) / (12* (1 - v2))

Study B: UY = ( 0.00406 * q * b4) / D

where:

  • F: Concentrated load
  • q: Uniform pressure
  • b: Plate side
  • E: Modulus of Elasticity
  • v: Poisson's ratio
  • h: Plate thickness

Reference

Timoshenko, S. P. and Woinowsky-Krieger, “Theory of Plates and Shells,” McGraw-Hill Book Co., 2nd edition. pp. 120, 143, 1962.