Comparison of calculation results of flexible plates on the basis of difference equations of successive approximation method and generalized equations of finite difference method

Abstract

In structural engineering, the analysis of plate elements is one of the important problems that based on theory of plates. The analytical solutions using traditional methods and manual calculations are determined in the cases with simple calculation schemes. It will be difficult to solve problems with the complicatedness in loading and boundary conditions. Thereof, the application of numerical methods is necessary to deal with that. The finite difference method and successive approximation method are popular numerical methods to solve relatively thoroughly the plate problems. In addition, with the development of construction technology, the dimensions of the current building projects become greater and lead to increase of building displacements that is required to take into account in analysis. The analysis of plates with non-linear geometrical is relatively complicated and iterative algorithms can help to solve this problem. In this paper, the authors used the difference equations of successive approximation method (MSA) and generalized equations of finite difference method (MFD) to solve the problems of non-linear plates with different boundary conditions and loading. From the comparison of obtained results with Volmir’s analytical results the conclusions and recommendations are proposed.