Application of the successive approximation method to the analysis of bending plates

Radek Gabbasov,Nikita Ryasny,Vladimir Filatov,A Volkov,A Adamtsevich,A Pustovgar

doi:10.1051/matecconf/201825104058

Radek Gabbasov, Nikita Ryasny + Show 4 more

Open Access

https://doi.org/10.1051/matecconf/201825104058

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Abstract

This work presents an algorithm for calculating the bending plates of medium thickness according to the Reissner’. To obtain numerical results, the method of successive approximations (MSA) is used. This method has high accuracy and fast convergence, which was confirmed by the solution of a range of tasks. Publication of the results of the calculation of plates of medium thickness with the boundary conditions revised here is supposed to be in the following articles.

Highlights

One of the important sections of the theory of calculation of plates and shells is a section related to the calculation of plates of medium thickness
In the course of formation the theory of calculation of three-layered anisotropic plates with attached masses in work [4] the assumptions for plates of medium thickness were taken into consideration within the framework of the theory of S
The works [5, 6] are devoted to the formation of the numerical solution based on the finite difference method (FDM) in its classical form

Summary

Introduction

One of the important sections of the theory of calculation of plates and shells is a section related to the calculation of plates of medium thickness. In [2] the solution for bendable rectangular continuous plates of medium thickness was obtained according to the refined theory of B. The works [5, 6] are devoted to the formation of the numerical solution based on the finite difference method (FDM) in its classical form. The difference equations of the method of successive approximations (MSA) are applied in [10,11,12,13] to the calculation of thin bending plates in the form that allows to take into consideration possible discontinuities: of the sought function, its derivatives, and the right-hand side of the initial differential equation. The aim of this work is to apply the difference form of MSA to the calculation of plates of medium thickness according to the Reissner’s theory

Calculation Methodology

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