Modeling of intelligent material systems by the MLPG

J. Sladek, V. Sladek, P. Solek, S. N. Atluri

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26 Scopus citations


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 languageEnglish
Pages (from-to)273-300
Number of pages28
JournalCMES - Computer Modeling in Engineering and Sciences
Issue number3
StatePublished - 2008


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


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