Open Access

ARTICLE

Meshless Local Petrov-Galerkin (MLPG) Method for Laminate Plates under Dynamic Loading

J. Sladek¹, V. Sladek¹, P. Stanak¹, Ch. Zhang²

1 Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia
2 Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany

Computers, Materials & Continua 2010, 15(1), 1-26. https://doi.org/10.3970/cmc.2010.015.001

Abstract

A meshless local Petrov-Galerkin (MLPG) method is applied to solve laminate plate problems described by the Reissner-Mindlin theory. Both stationary and transient dynamic loads are analyzed here. 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 Reissner-Mindlin theory reduces the original three-dimensional (3-D) thick plate problem to a two-dimensional (2-D) problem. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding this node. 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.

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Keywords

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