Analysis of Thermo-Piezoelectricity Problems by Meshless Method
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.