Mathematical Simulations of Deformation for the Rotation Shells with Variable Wall Thickness

Aleksandr A Dzyuba,Anatoliy P Dzyuba,Inga A Safronova,Larisa D Levitina

doi:10.15421/142105

Abstract

Well-posed boundary value problems are constructed for calculating rotation shells of with a stiffness variable along the meridian in two directions, and also with variable bilateral with respect to the reference surface with the shell wall thickness. Algorithms for the numerical integration of systems of differential equations with variable coefficients are discussed.

Highlights

Shell structures are widely used in the creation of structures for modern mechanical engineering, in the oil and gas, chemical and other industries
This paper presents general information about the exact mathematical models of shells with rigidity, in two directions, as well as with a two-sided change in the shell wall thickness with respect to the reference surface
The use of the Fourier method (and this is possible only in the case when the shell wall thickness changes only in the meridional direction h = h(s), and remains constant in the circumferential direction) makes it possible to reduce the adopted system of equations of state of the shell in partial derivatives to a system of ordinary differential equations with respect to the coefficients expansions in trigonometric series of the main variables of the stress-strain state, which are the coefficients of the expansion of displacements and force factors

Summary

Introduction

Shell structures are widely used in the creation of structures for modern mechanical engineering, in the oil and gas, chemical and other industries. An effective approach to the study of the behavior of such structural elements with irregular parameters remains the direct solution of boundary value problems for systems of differential equations describing their state, where the components of the stress-strain state are unknown In this case, the parameters of non-homogeneity (change in the thickness of the shell wall) are taken into account quite since they turn out to be components of the coefficients of these systems and the computational costs when using this approach are mainly associated only with the need to solve the corresponding boundary value problems [3, 12, 15]. This paper presents general information about the exact mathematical models of shells with rigidity, in two directions, as well as with a two-sided change in the shell wall thickness with respect to the reference surface

Basic Relations

Rotational Shells with a Stiffness Variable Along Meridian

Conclusion