Open Access

ARTICLE

Modeling of Intelligent Material Systems by the MLPG

by J. Sladek¹, V. Sladek², P. Solek¹, S.N. Atluri³

1 Institution of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia, sladek@savba.sk.
2 Department of Mechanics, Slovak Technical University, Bratislava, Slovakia.
3 Department of Mechanical and Aerospace Engineering, University of California, Irvine, USA.

Computer Modeling in Engineering & Sciences 2008, 34(3), 273-300. https://doi.org/10.3970/cmes.2008.034.273

Abstract

A meshless method based on the local Petrov-Galerkin approach is proposed, to solve boundary and initial value problems of piezoelectric and magneto-electric-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 Laplace-transform 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.

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Keywords

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