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J. Sladek, V. Sladek, H.A. Mang:
"Meshless Local Boundary Integral Equation Method for Plates Resting on Elastic Foundation";
Computer Methods in Applied Mechanics and Engineering, 191 (2002), 51-52; 5943 - 5959.

Simply supported and clamped thin elastic plates resting on a two-parameter foundation are analyzed in the paper. The governing partial differential equation of fourth order for a plate is decomposed into two coupled partial differential equations of second order. One of them is Poisson's equation whereas the other one is Helmholtz's equation. The local boundry integral equation method is used with meshless approximation for both the Poisson and the Helmholtz equation. The moving least square method is employed as the meshless approximation. Independent of the boundary conditions fictitious nodal unknowns used for the approximation of bending moments and deflections are always coupled in the resulting system of algebraic equations. The Winkler foundation model follows from the Pasternak model if the second parameter is equal to zero. Numerical results for a square plate with simply and/or clamped edges are presented to prove the efficiency of the proposed formulation.

Keywords: Pasternak-type foundation, simply supported and clamped pla, coupled Poisson and Helmholtz eq, moving least square approximatio

http://dx.doi.org/10.1016/S0045-7825(02)00505-4