Communications - Scientific Letters of the University of Zilina 2012, 14(3):24-31 | DOI: 10.26552/com.C.2012.3.24-31

Meshless Modelling of Laminate Mindlin Plates under Dynamic Loads

Milan Zmindak1, Daniel Riecky1
1 Department of Applied Mechanics, Faculty of Mechanical Engineering, University of Zilina, Slovakia

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.

Keywords: local integral equations, Reissner-Mindlin plate theory, MLS approximation, orthotropic material properties

Published: September 30, 2012  Show citation

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Zmindak, M., & Riecky, D. (2012). Meshless Modelling of Laminate Mindlin Plates under Dynamic Loads. Communications - Scientific Letters of the University of Zilina, 14(3), 24-31. doi: 10.26552/com.C.2012.3.24-31
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