A comparative study of numerical methods of elastic-plastic analysis.

TLDR: In this article, a comparison between the elastic-plastic stress-strain analysis of continuous solid bodies and the tangent modulus method has been made, where the load is applied in increments, and at each stage, a new set of coefficients are obtained for the equilibrium equations.

Abstract: WO general methods have been developed for the elasticplastic analysis of continuous solid bodies. The method of "thermal" or "initial strains"1 is based on the idea of modifying the elastic equations of equilibrium to compensate for the fact that the plastic strains do not cause any change in stress. On the other hand, the tangent modulus method2 is based on the linearity of the incremental laws of plasticity. The load is applied in increments, and at each stage, a new set of coefficients are obtained for the equilibrium equations. Both methods have been used in conjunction with finite element theory. The matrix equations for finite element analysis using the method of initial strains were developed in Refs. 3-5, whereas the equations for the tangent modulus method were developed in Refs. 6-8. Since both methods solve the same problem, there should be a close relation between them, and perhaps a comparison could lead to a better understanding of the original problem. This note addresses itself to such a comparison. II. Elastic-Plastic Stress-Strain Relations The linear relation between the increments of stress and strain developed in Marcal and King8 is taken here as the point of departure. With the definition of the elastic components of the strain increments,