Meshless Modelling of Laminate Mindlin Plates under Dynamic Loads

Abstract

Collocation method and Galerkin method have been dominant in the existing meshless methods. A meshless local Petrov-Galerkin (MLPG) method is applied to solve laminate plate problems described by the Reissner-Mindlin theory for transient dynamic loads. The Reissner-Mindlin theory reduces the original three-dimensional (3-D) thick plate problem to a two-dimensional (2-D) problem. The bending moment and the shear force expressions are obtained by integration through the laminated plate for the considered constitutive equations in each lamina. The weak-form on small subdomains with a Heaviside step function as the test functions is applied to derive local integral equations. After performing the spatial MLS approximation, a system of ordinary differential equations of the second order for certain nodal unknowns is obtained. The derived ordinary differential equations are solved by the Houbolt finite-difference scheme as a time-stepping method.