VM15

VM15
Bending of a Circular Plate Using Axisymmetric Elements

Overview

Reference:S. Timoshenko, Strength of Material, Part II, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pp. 96, 97, and 103.
Analysis Type(s):Static Analysis (ANTYPE = 0)
Element Type(s):2-Node Finite Strain Axisymmetric Shell (SHELL208)
Input Listing:vm15.dat

Test Case

A flat circular plate of radius r and thickness t is subject to various edge constraints and surface loadings. Determine the deflection δ at the middle and the maximum stress σmax for each case.

Case 1: Uniform loading P, clamped edge.
Case 2: Concentrated center loading F, clamped edge.
Case 3: Uniform loading P/4, simply supported edge.

Figure 18: Flat Circular Plate Problem Sketch

Flat Circular Plate Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
υ = 0.3
r = 40 in
t = 1 in
P = 6 psi
F = 7,539.82 lb

Analysis Assumptions and Modeling Notes

The stiffness matrix formed in the first load step is automatically reused in the second load step. A new stiffness matrix is automatically formed in the third load step because of changed boundary constraints. The mesh density is biased near the centerline and outer edge to recover stress values near those points.

Results Comparison

 TargetMechanical APDL [1]Ratio
Case 1Deflection, in-0.08736-0.087641.003
Stressmax , psi7200.7040.3730.978
Case 2Deflection, in-0.08736-0.088271.010
Stressmax , psi[2]3600.3568.2720.991
Case 3Deflection, in-0.08904-0.089111.001
Stressmax , psi2970.2966.4550.999

  1. Theoretical σmax occurs at a node location; Mechanical APDL results, taken from element solution printout, are at the centroid of the nearest element.

  2. This result is at the edge of the plate since point loading causes (theoretically) infinite stresses at the point of load application.

Figure 19: Displaced Geometry Displays

Displaced Geometry Displays
Window 1: Uniform Loading, Clamped Edge
Window 2: Concentrated Loading, Clamped Edge
Window 3: Uniform Loading Simply-supported Edge