VM142

VM142
Stress Concentration At a Hole in a Plate

Overview

Reference:

R. J. Roark, Formulas for Stress and Strain, 4th Edition, McGraw-Hill Book Co., Inc., New York, NY, 1965, pg. 384.

Analysis Type(s):

Static Analysis (ANTYPE = 0), Submodeling

Element Type(s):

2D 4-Node Structural Solid Elements (PLANE182)

2D 8-Node Structural Solid Elements (PLANE183)

Input Listing:

vm142.dat

Test Case

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

Figure 196: Plate Problem Sketch

Material Properties

Geometric Properties

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. Mesh generation is used for node and element creation. The area around the hole is remodeled with a fine mesh and boundary conditions are interpolated from the first model by use of the cut-boundary interpolation capability (CBDOF) in POST1.

Results Comparison

		Target	Mechanical APDL	Ratio
Coarse Model	stress_x max PLANE183	3018	2721	0.902
Submodel	stress_x max PLANE182	3018	2975	0.986

Max σ_x based on estimated bounds due to discretization error for the coarse model and submodel are 2855. and 3076. respectively.

The coarse PLANE183 model is offered for comparison with the submodel. Coarse PLANE183 results may vary across platforms.

Figure 197: Stress Concentration in Coarse Model

Figure 198: Stress Concentration in Fine Model