Abstract
In Chapter 2 Green’s functions in piezoelectric materials were described. Applications of these Green’s functions to the boundary element method (BEM) are discussed in this chapter. In contrast to the finite element method (FEM), BEM involves only discretization of the boundary of the structure due to the governing differential equation being satisfied exactly inside the domain leading to a relatively smaller system size with sufficient accuracy. This is an important advantage over domain-type solutions such as FEM or the finite difference method. During the past two decades several BEM techniques have been successfully developed for analyzing structure performance with piezoelectric materials [1–4]. Lee and Jiang [1] derived the boundary integral equation of piezoelectric media by the method of weighted residuals for plane piezoelectricity. Lu and Mahrenholtz [5] presented a variational boundary integral equation for the same problem. Ding, Wang, and Chen [6] developed a boundary integral formulation that is efficient for analyzing crack problems in piezoelectric material. Rajapakse [7] discussed three boundary element methods (direct boundary method, indirect boundary element method, and fictitious stress-electric charge method) in coupled electroelastic problems.
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Qin, QH. (2009). Boundary Element Method. In: Yang, J. (eds) Special Topics in the Theory of Piezoelectricity. Springer, New York, NY. https://doi.org/10.1007/978-0-387-89498-0_5
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DOI: https://doi.org/10.1007/978-0-387-89498-0_5
Publisher Name: Springer, New York, NY
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