Rectangular plate calculation algorithm for static loads with geometric nonlinearity

Abstract

The aim of this study is to develop an algorithm for calculating rectangular plates for statistical loads taking into account geometrical nonlinearity on the basis of difference equations of the method of sequential approximations taking into account full and partial contact with elastic base. For our study, we used methods: finite elements method and method of sequential approximations, and theory of plate calculation considering large deflections. Results: a method, algorithm, and calculation algorithm for rectangular plates in the geometrically nonlinear formulation using difference equations of the method of sequential approximations (SEA) taking into account full and partial contact with the elastic base have been developed. Conclusion: An algorithm has been developed for the computation of rectangular plates in geometrically nonlinear formulation using difference equations of the method of sequential approximations. It is recommended to use generalized difference equations of finite difference method when calculating rectangular plates for the action of piecewise distributed transverse loads without taking into consideration interaction with elastic base. Having more compact form of recording, the solution obtained by using them has comparable accuracy as the version using SEA difference equations.

Keywords

• finite element method
• deflection
• stress function
• plate
• differential equations