VM-WB-MECH-086

VM-WB-MECH-086
Stress Concentration at a Hole in a Plate

Overview

Reference:

Roark.R.J. (1965). Formulas for Stress and Strain (4th Edition). New York, NY: McGraw-Hill Book Co., Inc.

Solver(s):

Ansys Mechanical

Analysis Type(s):Static Structural, Submodeling (2D-2D)
Element Type(s):Solid

Test Case

Determine the maximum stress at a circular hole cut into a rectangular plate loaded with uniform tension P.

This problem is also presented in

VM142

in the Mechanical APDL Verification Manual.

Figure 113: Plate Problem Sketch

Plate Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
υ = 0.3
L = 12 in
d = 1 in
t = 1 in
P = 1000 psi

Analysis Assumptions and Modeling Notes

Due to symmetry, only a quarter sector of the plate is modeled. The reference result is from an infinitely long plate. Using a transferred load from the coarse model, the submodel result closely approximates the fine model.

Results Comparison

Note:  Submodeling has proven to be the quickest and most accurate approach to solving the test case. Fine and Coarse Model results have been included for comparison.

2D-2D Results

ResultsTargetMechanicalError (%)
Fine ModelEquivalent Stress - Max3018.03006.30.388
Coarse ModelEquivalent Stress - Max3018.02939.9-2.588
SubmodelEquivalent Stress - Max3018.03015.8-0.073

Figure 114: 2D-2D Coarse Model Equivalent Stress

2D-2D Coarse Model Equivalent Stress

Figure 115: 2D-2D Submodel Equivalent Stress

2D-2D Submodel Equivalent Stress