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Application of the MLPG to Thermo-Piezoelectricity

J. Sladek1, V. Sladek1, Ch. Zhang2, P. Solek3
Institute of Construction and Architecture, SlovakAcademy of Sciences, 84503 Bratislava, Slovakia
Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany
Department of Mechanics, Slovak Technical University,Bratislava, Slovakia

Computer Modeling in Engineering & Sciences 2007, 22(3), 217-234. https://doi.org/10.3970/cmes.2007.022.217

Abstract

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of boundary value problems for coupled thermo-electro-mechanical fields. Transient dynamic governing equations are considered here. To eliminate the time-dependence in these equations, the Laplace-transform technique is applied. Material properties of piezoelectric materials are influenced by a thermal field. It is leading to an induced nonhomogeneity and the governing equations are more complicated than in a homogeneous counterpart. Two-dimensional analyzed domain is subdivided into small circular subdomains surrounding nodes randomly spread over the whole domain. A unit step function is used as the test functions in the local weak-form. The derived local integral equations (LIEs) have boundary-domain integral form. The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs. The Stehfest's inversion method is applied to obtain the final time-dependent solutions.

Keywords

Meshless local Petrov-Galerkin method (MLPG), Moving least-squares interpolation, piezoelectric solids, orthotropic properties, transient thermal load, Laplace-transform

Cite This Article

Sladek, J., Sladek, V., Zhang, C., Solek, P. (2007). Application of the MLPG to Thermo-Piezoelectricity. CMES-Computer Modeling in Engineering & Sciences, 22(3), 217–234.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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