The MLPG for Bending of Electroelastic Plates
J. Sladek; V. Sladek; P. Stanak; E. Pan

doi:10.3970/cmes.2010.064.267
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 64, No. 3, pp. 267-298, 2010
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Keywords Local integral equations, Kirchhoff theory, MLS approximation, Houbolt method, piezoelectric material, orthotropic properties
Abstract The plate equations are obtained by means of an appropriate expansion of the mechanical displacement and electric potential in powers of the thickness coordinate in the variational equation of electroelasticity and integration through the thickness. The appropriate assumptions are made to derive the uncoupled equations for the extensional and flexural motion. The present approach reduces the original 3-D plate problem to a 2-D problem, with all the unknown quantities being localized in the mid-plane of the plate. A meshless local Petrov-Galerkin (MLPG) method is then applied to solve the problem. Nodal points are randomly spread in the mid-plane of the plate and each node is surrounded by a circular subdomain. The weak forms for the governing equations on subdomains with appropriate test functions are applied to derive local integral equations. The meshless approximation based on the moving least-squares (MLS) method is employed for the implementation. After performing the spatial MLS approximation, a system of ordinary differential equations for the nodal unknowns is obtained. The corresponding system of ordinary differential equations of the second order resulting from the equations of motion is solved by the Houbolt finite-difference scheme as a time-stepping method.
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