VM-WB-MECH-051

VM-WB-MECH-051
Bending of a Circular Plate Using Axisymmetric Elements

Overview

Reference:

Timoshenko, S. (1956). Strength of Material, Part II: Elementary Theory and Problems (3rd ed., pp. 96, 97, & 103). New York, NY: D. Van Nostrand Co., Inc.

Solver(s):Ansys Mechanical
Analysis Type(s):Static Structural Analysis
Element Type(s):Axisymmetric Shell Element

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

Figure 65: Schematic

Schematic

Material PropertiesGeometric PropertiesLoading
E = 3e7 psi
ν = 0.3
r = 40 in
t = 1 in
Case 1:
P = 6 psi
Case 2:
F = -7539.82 lb (y direction)

Analysis Assumptions and Modeling Notes for Ansys Mechanical

Because the geometry and loading are symmetric about the y-axis, the above problem can be analyzed as an axisymmetric problem.

Figure 66: Schematic for Ansys Mechanical

Case 1:
Schematic for Ansys Mechanical
Case 2:
Schematic for Ansys Mechanical

Results Comparison for Ansys Mechanical

ResultsTargetMechanicalError (%)
Case 1:Deflection (in)-0.08736-0.087114-0.282
Stressmax (psi)7200.07212.80.178
Case 2:Deflection (in)-0.08736-0.0880250.761
Stressmax (psi)3600.03607.90.219