Application of the MLPG to Thermo-Piezoelectricity
J. Sladek; V. Sladek; Ch. Zhang; and P. Solek

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 22, No. 3, pp. 217-234, 2007
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Keywords Meshless local Petrov-Galerkin method (MLPG), Moving least-squares interpolation, piezoelectric solids, orthotropic properties, transient thermal load, Laplace-transform
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.
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