Circular Plate Under a Concentrated Load

Description

A circular thick plate of radius 5" is subjected to a load of 4 lb at its center. The plate is clamped at its boundary. Determine the transverse displacement along the radius r.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Static_10.SLDPRT and open the file.

Study Type

Static.

Mesh Type

Shell mesh.

Shell Parameters

Shell thickness = 2 in - Thick formulation.

Meshing Parameters

Use a Global Size of 1 in.

Material Properties

Modulus of elasticity = 1.09 X 106 psi, Poisson's ratio = 0.3.

Modeling Hints

s

Due to axial symmetry of the model, only a quarter of the plate is modeled.

Results

Distance from the plate center, r (in)

Analytical

SOLIDWORKS Simulation
0.0 --- 5.465E-06
1.0 3.53748E-06 3.566E-06
2.0 2.19719E-06 2.225E-06
3.0 1.14364E-06 1.152E-06
4.0 3.88628E-07 3.913E-07
5.0 0 0.00E+00

The following formula was used to generate the analytical results:

U(r) = PR2 [1-(r/R)2-2(r/R)2 ln(R/r)-8D ln(r/R)/(KGtR2)]/16πD

where:

  • U(r): The displacement at distance r from the plate center
  • R: The radius of the plate
  • P: The force value
  • D: EX t3/12*(1-NUXY2), where EX and NUXY are the modulus of elasticity and the Poisson's ratio of the plate and t is the thickness of the plate
  • G: EX /2*(1+NUXY)
  • K: 0.8333 (shear correction factor)

Reference

Hughes, T. J. R., Taylor, R. L., and Kanoknukulchai, W. A., “Simple and Efficient Finite Element for Plate Bending,” I.J.N.M.E., 11, 1529-1543, 1977.