Quasi-static and dynamic inelastic buckling and failure of plate structures using the finite strip method

Abstract

©Civil-Comp Press, 2015. The main aim of this paper is the presentation of the inelastic stability analysis of uniformly compressed plated structures using the finite strip method (FSM). Such structures fail by first developing local buckles which change into local plastic mechanisms and failure. The nonlinear behavior of the material is invoked using the rheological-dynamical analogy (RDA). According to this analogy, a very complicated nonlinear problem in the visco-elastic-plastic (VEP) range of strains may be solved as a simple linear dynamic one. Since the development of micro cracks induces a reduction in the stiffness of materials and structures, the damage state is characterized by the RDA modulus. After presentation of the theory for uniaxial problems, an extended and more general theoretical framework for threedimensional continua is presented. Although quasi-static relations are derived for isotropic material, different stress components induce orthotropy in the material through the RDA modulus stress dependence. This leads to the orthotropic constitutive relations for multiaxial VEP flow and failure. A new modulus iterative method for the solution of nonlinear orthotropic equations is presented. In order to illustrate the application, provide a validation and demonstrate the capabilities of the presented theory, inelastic bifurcation stability analysis of uniformly compressed rectangular slabs is carried out for quasi-static and dynamic loading using the FSM.