Plane Elastic-Plastic Analysis of Perforated Plates based on Complex Stress Functions

Abstract

The problem of stress distribution around a hole or a crack belongs to the very important one in the field of fracture mechanics. In this paper, the problem of an infinite plate with a circular or elliptic hole under simple tension was investigated.
Basic equations were derived from complex stress functions introduced by E. Goursat and developed by N. I. Muskhelishvili and S. Moriguchi. As a first step, stress function F^X (x, y;x₀, y₀) for a unit force in x-direction valid for a infinite plate without any discontinuity was derived. Then, by the use of principle of reflection (proposed by S. Moriguchi), the stress function F^X_H (x, y;x₀, y₀) for a plate with a hole was deduced.
Two dimensional elastic-plastic analysis was conducted by using the “Modified Initial Strain Method” introduced by T. Fujimoto in the field of welding dynamics.
In order to derive stress function F^εx* (x, y;x₀, y₀) for unit initial strain ε^*_x atpoint (x₀, y₀), the concept of thermo-elastic theory was used.
The calculated results show that the applied analytical method is more useful in stress calculation than F. E. M.