Mathematical modeling of the solution to the problem of plate bending given various fastenings along the contour and various loads

Serikbay Toibayev,Ayaulym Rakhmatulina,Assemgul Uderbayeva,Zhanar Bidakhmet,Algazy Zhauyt

doi:10.21595/vp.2020.21343

Abstract

The classical equations of plate bending in various fastenings along the contour and various loads are considered. Using the decomposition method, three auxiliary problems are formulated to determine the deflection of the plate. The task is to determine the individual terms of the decomposition coefficients anmi from the individual terms of the load series. Then the system of algebraic equations is obtained to determine anmi. If the plate contour is pivotally fixed along the contour, then the system of equations takes a known form and the expression for the deflection function is explicitly found. Approximate analytical solutions are obtained for the functions of deflections, internal force factors and stresses under various boundary conditions of the plate.

Highlights

In our century, with the increasing complexity of the forms of building structures, the emergence of aircraft manufacturing, and the diverse demands of mechanical engineering, the role of elasticity theory methods has changed dramatically [1]
With the increasing complexity of the forms of building structures, the emergence of aircraft manufacturing, and the diverse demands of mechanical engineering, the role of elasticity theory methods has changed dramatically [1]. They form the basis for constructing practical methods for calculating deformable bodies and systems of bodies of various shapes [2]
The presence of a polymer base gives such a composite material, viscous properties in addition to elasticity, which must be taken into account in the calculations [6]

Summary

Introduction

With the increasing complexity of the forms of building structures, the emergence of aircraft manufacturing, and the diverse demands of mechanical engineering, the role of elasticity theory methods has changed dramatically [1]. They form the basis for constructing practical methods for calculating deformable bodies and systems of bodies of various shapes [2]. Modern calculations take into account the complexity of the body shape and the variety of effects (power, temperature, etc.), and the specificity of the physical properties of the materials from which the bodies are made [3].

Materials and methods

Results and discussion

Conclusions