Nonlinear stability analysis of shallow cylindrical shells with initial imperfections

Sergey Trushin,S Jemioło,M Mitew-Czajewska,M Gajewski,M Krzemiński,A Zbiciak

doi:10.1051/matecconf/201711700171

Abstract

The present article describes numerical procedures for geometrically nonlinear stability analysis of shallow flexible cylindrical shells. Computing models are based on the theory of plates with account of transverse shear deformations. The finite difference energy method of discretization is used for reducing the continuum problem to finite dimensional problem. Solution procedures for discrete nonlinear problem are based on initial value formulation. The solution of Cauchy problem is performed using the self-correcting Runge-Kutta method with the constrained equation. For stability analysis of shells with initial imperfections small asymmetric perturbations are introduced in the initial conditions of the Cauchy problem for finding asymmetric shapes of shell equilibrium.

Highlights

In the general case the solution of the stability problem is reduced to the identification of qualitative changes in a behavior of the system at changes in the structure of the system
The stability analysis of a shell structure studies its behavior under small perturbation of parameters including in the energy functional, as well as the initial shape, boundaries and boundary conditions
The developed method for studying the stability of the equilibrium forms of the shell structures were used in the analysis of shallow cylindrical shells under transverse uniformly distributed load with intensity qz (Fig.1)

Summary

Introduction

In the general case the solution of the stability problem is reduced to the identification of qualitative changes in a behavior of the system at changes in the structure of the system. The stability analysis of a shell structure studies its behavior under small perturbation of parameters including in the energy functional, as well as the initial shape, boundaries and boundary conditions. Such a generalization of the concept of stability is important for practical calculations as in real structures it is possible imperfections in the form or a small unbalance in the load and a heterogeneity of the physical properties of material and a deviation from set boundaries and boundary conditions. It allows to obtain the lower estimation of the actual critical load of a real shell

Methods

Results

Conclusion