@Article{cmes.2008.034.273,
AUTHOR = {J.  Sladek, V.  Sladek, P.  Solek, S.N.  Atluri},
TITLE = {Modeling of Intelligent Material Systems by the MLPG},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {34},
YEAR = {2008},
NUMBER = {3},
PAGES = {273--300},
URL = {http://www.techscience.com/CMES/v34n3/26717},
ISSN = {1526-1506},
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.},
DOI = {10.3970/cmes.2008.034.273}
}