Radial basis reproducing kernel particle method for piezoelectric materials.

*(English)*Zbl 1403.74331Summary: To reduce the negative effect of different kernel functions on calculating accuracy, the radial basis function (RBF) is introduced into the reproducing kernel particle method (RKPM), and the radial basis reproducing kernel particle method (RRKPM) is proposed, the corresponding governing equations are derived. The RRKPM is more efficient to solve the local problem domain, and can improve the accuracy and stability of the RKPM. Then the RRKPM is applied to the numerical simulation of piezoelectric materials, the corresponding formulae for piezoelectric materials are derived. The numerical results illustrate the proposed method is more stable and accurate than the RKPM.

##### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |

74F15 | Electromagnetic effects in solid mechanics |

##### Keywords:

meshless methods; piezoelectric materials; radial basis functions; reproducing kernel particle method; numerical simulation
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\textit{T. Zhang} et al., Eng. Anal. Bound. Elem. 92, 171--179 (2018; Zbl 1403.74331)

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