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The numerical analysis of piezoelectric ceramics based on the Hermite-type RPIM. (English) Zbl 1411.74062
Summary: In this paper, the Hermite-type radial point interpolation method (RPIM) is applied to analyze the property of piezoelectric ceramics in order to overcome the defects of finite element method. In this method, the inside and boundary of the problem domain are discreted by a distribution of nodes, and then the interpolation function of nodes are constructed to solve the displacement of the evaluation nodes. Compared with the finite element method, it is easier and faster for the Hermite-type RPIM to accurately achieve solution of the local regions. In contrast with the existing meshless methods, this method would not cause singularity in the process of evaluating the shape function. Furthermore, the shape function of the Hermite-type RPIM has a better stability and it can adapt to any distribution of nodes. In addition, the accuracy and stability of the method are proved by the numerical simulation.

74S30 Other numerical methods in solid mechanics (MSC2010)
74F15 Electromagnetic effects in solid mechanics
78A48 Composite media; random media in optics and electromagnetic theory
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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