Numerical solution of the problems for plates on partial internal supports of complicated configurations

Abstract

Very recently in the work "Simple Iterative Method for Solving Problems for Plates with Partial Internal Supports, Journal of Engineering Mathematics, DOI: 10.1007/s10665-013-9652-7 (in press)", we proposed a numerical method for solving some problems of plates on one and two line partial internal supports (LPIS). In the essence they are problems with strongly mixed boundary conditions for biharmonic equation. Using this method we reduced the problems to a sequence of boundary value problems for the Poisson equation with weakly mixed boundary conditions, which are easily solved numerically. The advantages of the method over other ones were shown.In this paper we apply the method to plates on internal supports of more complicated configurations. Namely, we consider the case of three LPIS and the case of the cross support. The convergence of the method is established theoretically and its efficiency is confirmed on numerical experiments.