FUNCTIONALLY GRADED NONHOMOGENEOUS ANISOTROPIC THICK PLATES. A MESHLESS 3D ANALYSIS
M.S. Nerantzaki (UDC: 624.073.2:539.3)
The meshless analog equation method (MAEM) is employed for 3D analysis of thick functionally graded nonhomogeneous anisotropic plates. In this case the response of the plate is governed by three coupled partial differential equations (PDEs) of second order with variable coefficients in terms of displacements, i.e. the counterpart of the Navier equations for the general nonhomogeneous anisotropic body. The system of equations is solved using the new truly meshless method for solving elliptic PDEs developed by Katsikadelis. This method is based on the concept of the analog equation, which converts the original coupled PDEs into three uncoupled Poisson‘s equations with fictitious sources, under the original boundary conditions. The fictitious sources, unknown in the first instance, are approximated by multiquadrics radial basis functions (MQ-RBFs) series. Integration of the substitute equations allows the approximation of the sought solution by new RBFs, which approximate accurately not only the solution but also its derivatives. This permits a strong formulation of the problem. Thus, inserting the approximate solution in the PDEs and in the boundary conditions (BCs) and collocating at a predefined set of mesh-free nodal points yield a system of linear equations, which permit the evaluation of the expansion coefficients of radial basis series, which represent the solution. Numerical results are given which validate the efficiency and the accuracy of the developed solution procedure.