Abstract
In this paper a total incremental method for solving nonlinear system equation due to plasticity of shear deformable plates is presented. The material is assumed to undergo small strains. The von Mises criterion is used to evaluate the plastic zone and elastic perfectly plastic material behaviour is assumed. An initial stress formulation is used to formulate the boundary integral equations. The domain integral due to material nonlinearity is evaluated using a cell discretization technique. Several examples are presented and comparisons are made to demonstrate the validity and the accuracy of the total incremental method to solve the nonlinear system of equation due to plasticity.
Highlights
Nonlinear analysis of plate bending can be divided into two categories e.i. geometrical and material nonlinearity
The classical plate theory neglects the shear deformation through the plate thickness whereas the shear deformable theory takes into account the shear deformation and the transverse normal stresses through the plate thickness
This paper presents the application of the total incremental method to solve the nonlinear system of equation due plasticity in boundary element method (BEM)
Summary
Nonlinear analysis of plate bending can be divided into two categories e.i. geometrical and material nonlinearity. Wen, Aliabadi and Young (2004) proposed the total incremental method to solve the nonlinear system of equation due to large deflection in which the iterative process is neglected. This paper presents the application of the total incremental method to solve the nonlinear system of equation due plasticity in BEM. Somigliana’s identity for displacements in elastoplastics shear deformable plate bending problems states that the rate of the displacements (two rotations and one deflection) at any points X’ [ w& i(X’)] that belong to domain (X’a V) to the boundary values of displacement rates [ w& j(x)] and traction rates [ p& j(x)] can be expressed as (Karam, 1998):. Solution Algorithm The total incremental method solves the nonlinear system of equations of equation (10) based on the incremental load to be applied on the structure.
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