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Modeling of Intelligent Material Systems by the MLPG

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

Institution of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia,
Department of Mechanics, Slovak Technical University, Bratislava, Slovakia.
Department of Mechanical and Aerospace Engineering, University of California, Irvine, USA.

Computer Modeling in Engineering & Sciences 2008, 34(3), 273-300.


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.


Cite This Article

Sladek, J., Sladek, V., Solek, P., Atluri, S. (2008). Modeling of Intelligent Material Systems by the MLPG. CMES-Computer Modeling in Engineering & Sciences, 34(3), 273–300.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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