Optimization-Based Elastic-Plastic Analysis of Steel Frames by Volumetric Plasticity Concept

Abstract

Structures composed of physical nonlinear finite elements under bending and compression or tension are considered in this paper. Material nonlinearity is considered as linearly hardened. In case of material hardening, plastic strains do not concentrate in one point but distribute in the certain volumes of finite element. Volumes of plastic strains zones in frame structure elements impact on elasticity modules of these elements sections by decreasing them. Technique of such elasticity modules decrease in finite elements sections is suggested. To realize such structure analysis, a treatment of strains in mathematical model is changed. Now strains are treated not as rotation angles and elongations of finite elements, but as longitudinal strains. Mathematical model including above mentioned modifications is presented. Solving algorithm based on a modified Newton-Raphson method is particularly explained and employed for numerical example.