AN IMPLEMENTATION OF THE METHOD OF FUNDAMENTAL SOLUTIONS FOR THE DYNAMIC RESPONSE OF VON KARMAN NONLINEAR PLATE MODEL

Abstract

The nonlinear plate dynamics is a subject of investigations across many disciplines. Various models have been proposed. In this paper, one of the models derived by von Karman is under consideration. In this case, the initial-boundary value problem of the dynamics of a plate large deflection is described by two nonlinear, coupled partially differential equations of fourth order with two initial conditions and four boundary conditions given at each boundary point. There are various means of simulating the dynamic response of thin nonlinear plate, to various degrees of accuracy. The proposal of this paper is to implement one of the meshfree methods i.e., the method of fundamental solutions (MFS). The problem is solved in discretized time domain. This discretization is done in a conception of the finite difference method. The nonlinearity of the equations, obtained at each time step, is solved by application of Picard iterations. For each iteration step, a boundary value problem is to be solved. Moreover, the equations at each iteration step are inhomogeneous ones. So, the radial basis function approximation is applied and a particular solution of boundary value problems is obtained. The final solution is calculated by implementation of the MFS. The numerical experiment has confirmed that the proposed numerical procedure gives the solutions with demanded accuracy and is a good tool to solve the considered problem.