Bending of a Circular Plate with a Center Hole

Description

A circular plate with a center hole is fixed along the inner edge. The outer edge of the plate is subjected to bending by a moment M = 10 in-lb/in. Determine the maximum deflection and the maximum slope of the plate. The plate thickness is 0.25" and the outer and inner radii of the plate are 30" and 10" respectively. Due to symmetry of the problem, a 10º wedge is modeled. The applied moment is equivalent to applying a moment of 52.359 lb-in per 10º segment.

File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Static_9.SLDPRT and open the file.

Study Type

Static.

Mesh Type

Shell mesh.

Shell Parameters

Shell thickness = 0.25 in - Thin formulation.

Meshing Parameters

Use a Global Size of 1 in.

Material Properties

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

Results

 

Theory

SOLIDWORKS Simulation
Maximum deflection (UZ), inch 0.04906 0.04786
Maximum rotation (RY), rad 0.0045089 0.004519

Analytical Solution

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

C1 = ( 2 * rout2 * M ) / D * ( rout2 * (1+ v ) + rin2 * (1 - v ) )

C2 = - (rout2 * rin2 * M ) / D * ( rout2 * (1+ v ) + rin2 * (1 - v ) )

Maximum rotation: RY = C1* x / 2 + C2 / x , for x = rout

Maximum deflection: UZ = C1*( (rout2 - x2) / 4 - C2 * log ( x / rout ) ), for x = rin

where:
  • E: Modulus of elasticity
  • v: Poisson's ratio
  • h: Plate thickness
  • rin: Inner radius
  • rout: Outer radius
  • M: Bending moment per unit length
  • x: Radial distance

Reference

Timoshenko, S., “Strength of Materials, Part II, Advanced Theory and Problems,” 3rd Edition, D. Van Nostrand Co., Inc., New York, l956.