A discrete element stress and displacement analysis of elastoplasticplates

Abstract

A displacement method of analysis for elastoplastie plates is presented with particular emphasis on accurate stress results. The Hencky-Nadai stress-strain law is assumed and a discretized potential energy function is formed using bicubic Hermite displacement functions. To achieve interelement continuous stress fields, bicubic spline constraints are introduced that produce interelement curvature continuity. The planar variation in material properties caused by plastic strains is approximated using additional nodes that uniformly subdivide the element planform into four quadrants. Integration of the strain energy through the plate thickness is accomplished using gaussian quadrature. Solutions of the nonlinear discretized equilibrium equations are obtained by energy minimization using the conjugate gradient algorithm. Results in the elastic range indicate the displacements converge with the fourth power of the grid size and the stresses converge with the grid size squared. These convergence rates were obtained with both bicubic Hermite and spline displacement functions. Elastoplastic results are presented that compare well with both deformation and incremental theory solutions. Stress results are also presented that demonstrate an elastic compressibility effect in elastoplastie plates.