Acta Mechanica Slovaca 2010, 14(4):16-27 | DOI: 10.2478/v10147-011-0030-z

Analysis of Thermo-Piezoelectricity Problems by Meshless Method

Jan Sládek1, Vladimír Sládek2, Peter Staňák3
1 Slovak Academy of Sciences
2 Comenius University
3 Institute of Construction and Architecture, Slovak Academy of Sciences

In this paper meshless method based on the local Petrov-Galerkin approach is pesented for the solution of boundary value problems for coupled thermo-electro-mechanical fields. Transient dynamic governing equations are considered in analysis of the problems. 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 compared to a homogeneous counterpart. Two-dimensional analyzed domain is divided into small circular subdomains surrounding nodes that are 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 and afterwards to obtain a system of ordinary differential equations (ODE) for unknown nodal quantities. To solve this system of ODE, Houbolt finite-difference scheme is applied as a time-stepping method.

Keywords: Meshless Local Petrov-Galerkin (MLPG) Method, MLS Interpolation, Piezoelectric Solids, Transient Thermal Load, Houbolt Finite-Difference Scheme, Orthotropic Properties

Published: October 31, 2010  Show citation

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Sládek, J., Sládek, V., & Staňák, P. (2010). Analysis of Thermo-Piezoelectricity Problems by Meshless Method. Acta Mechanica Slovaca, 14(4), 16-27. doi: 10.2478/v10147-011-0030-z
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