TY - EJOU
AU - Sladek, J.
AU - Sladek, V.
AU - Solek, P.
AU - Atluri, S.N.
TI - Modeling of Intelligent Material Systems by the MLPG
T2 - Computer Modeling in Engineering \& Sciences
PY - 2008
VL - 34
IS - 3
SN - 1526-1506
AB - 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.
KW - Meshless local Petrov-Galerkin method (MLPG)
KW - Moving least-squares interpolation
KW - piezoelectric and piezomagnetic solids
KW - Laplace-transform
KW - Stehfest's inversion
DO - 10.3970/cmes.2008.034.273