The element free Galerkin method is used to analyze free vibration of thin plates resting on Pasternak elastic foundations with all possible types of classical boundary conditions. Convergence of solution is studied by increasing number of nodes for different boundary conditions and foundation parameters. Upon comparison with available results in literature, it was found that the method converges very fast and has very good accuracy even with small number of nodes. Applicability of the method was shown by solving numerical examples with all possible combinations of boundary conditions and different values of foundation parameters.

The dynamic response of laminated composite beams subjected to distributed moving masses is investigated using the finite element method (FEM) based on the both first-order shear deformation theory (FSDT) and the classical beam theory (CLT). Six and ten degrees of freedom beam elements are used to discretize the CLT and FSDT equations of motion, respectively. The resulting spatially discretized beam governing equations including the effect of inertial, Coriolis, and centrifugal forces due to moving distributed mass are evaluated in time domain by applying Newmark’s scheme. The presented approach is first validated by studying its convergence behavior and comparing the results with those of existing solutions in the literature. Then, the effect of incline angle, mass, and velocity of moving body, layer orientation, load length, and inertial, Coriolis, and centrifugal forces due to the moving distributed mass and friction force between the beam and the moving distributed mass on the dynamic behavior of inclined laminated composite beams are investigated.

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Element Free Galerkin method was used to analyze bending of thin plates with variable thickness resting on one parameter elastic foundation. Thickness of plate is considered as linearly varying in one direction. Formulation could be applied to plates of any shape with general boundary conditions and loadings. Convergence of solution was examined for different number of nodes, thickness variation and foundation parameters. It was found that for deflection good results were achieved even with small number of nodes regardless of boundary condition, thickness variation and foundation parameters. Accuracy of method is checked against available results and good agreements were found. Applicability of method is demonstrated by solving numerical examples with different boundary conditions, thickness and foundation parameters, and loadings.

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