Numerical solution of the problems for plates on some complex partial internal supports

Abstract

In the recent works, Dang and Truong proposed an iterative method for solving some problems of plates on one, two and three line partial internal supports (LPISs), and a cross internal support. In nature they are problems with strongly mixed boundary conditions for biharmonic equation. For this reason the method combines a domain decomposition technique with the reduction of the order of the equation from four to two.

In this study, the method is developed for plates on internal supports of more complex configurations. Namely, we examine the cases of symmetric rectangular and H-shape supports, where the computational domain after reducing to the first quadrant of the plate is divided into three subdomains. Also, we consider the case of asymmetric rectangular support where the computational domain needs to be divided into 9 subdomains. The problems under consideration are reduced to sequences of weak mixed boundary value problems for the Poisson equation, which are solved by difference method. The performed numerical experiments show the effectiveness of the iterative method.