### Abstract

A meshless method based on the local Petrov-Galerkin approach is proposed, to solve boundary and initial value problems of piezoelectric and magnetoelectric-elastic solids with continuously varying material properties. Stationary and transient dynamic 2-D problems are considered in this paper. The mechanical fields are described by the equations of motion with an inertial term. To eliminate the time-dependence in the governing partial differential equations the Laplacetransform technique is applied to the governing equations, which are satisfied in the Laplace-transformed domain in a weak-form on small subdomains. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variation of the displacements and the electric potential are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations, one obtains a system of linear algebraic equations for unknown nodal values. The boundary conditions on the global boundary are satisfied by the collocation of the MLS-approximation expressions for the displacements and the electric potential at the boundary nodal points. The Stehfest's inversion method is applied to obtain the final time-dependent solutions.

Original language | English |
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Pages (from-to) | 273-300 |

Number of pages | 28 |

Journal | CMES - Computer Modeling in Engineering and Sciences |

Volume | 34 |

Issue number | 3 |

State | Published - 2008 |

### Keywords

- Laplace-transform
- Meshless local Petrov-Galerkin method (MLPG)
- Moving least-squares interpolation
- Piezoelectric and piezomagnetic solids
- Stehfest's inversion

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## Cite this

*CMES - Computer Modeling in Engineering and Sciences*,

*34*(3), 273-300.