Enforcement Techinque of Essential Bounary Conditions for Nonlinear Plate Bending Problem employing Reproducing Kernel Approximation

Abstract

The authors have performed nonlinear plate bending analyses using meshfree/particle method. Reproducing kernel approximation is used to approximate the in-plane deformation and out-of-plane deformation. Stabilized conforming nodal integration is adopted to integrate the tangent stiffness matrix to impose so-called integration constraint condition. Total Lagrangian formulation is adopted for solving plate bending problems with geometrical non-linearity. In this paper, an enforcement technique of essential boundary conditions is introduced using Multiple Point Constraint (MPC) method to solve thin-plate buckling problems. As numerical examples, nonlinear plate bending problem and thin-plate bucking problem are analyzed to validate the proposed approach.