Analysis of plates under the application of moving concentrated loads using a meshfree method with adaptive re-arrangement of nodes

Dynamic behavior of continuous systems, such as beams and plates under the application of moving concentrated loads, is an important issue in engineering. In this study, a meshfree method is presented for the analysis of the dynamic response of thick plates under the influence of concentrated moving loads. The displacement field is based on the third-order shear deformation theory. In this numerical method, the field variables are interpolated only by using nodes distributed purposively in the computational domain. Since there is no conectivity between the nodes, it is possible to add nodes in the areas of application of the force. Another feature of the proposed method is the use of the radial point interpolation method (RPIM) shape functions which possess the Kronecker delta function property and therefore satisfies the essential boundary conditions easily. Also, due to the high density of nodal points in the vicinity of the point of application of the load, the background decomposition method (BDM) is used in order to achieve a high accuracy with appropriate speed. In this paper, nodes are re-arranged in the path of the moving load adaptively which leads to high accuracy and speed of the final solution. To validate the proposed method, the obtained results are compared with the analytical solutions.