On stability of cylindrical shells of variable thickness with initial imperfections

Abstract

The paper outlines a numerical method for stability analysis of cylindrical shells with initial imperfections. We solve a nonlinear buckling problem for a cylindrical shell with variable wall thickness under surface pressure. The imperfections of the shell are modeled as the first buckling mode. A probabilistic approach is used to determine the reliability against buckling of the cylindrical shell with the probability density of initial imperfections represented by uniform distribution, triangular distribution, or Gaussian distribution Keywords: cylindrical shell, reliability against buckling, probabilistic approach, initial imperfections Introduction. The current state of the art permits creating highly reliable structures. Thin-walled shells lose their load-carrying capacity by buckling [2-8, 10, 12-15], which characterizes their reliability. In this paper, we propose a numerical method for the stability analysis of cylindrical shells with initial imperfections [5, 6] and use the probabilistic approach developed in [1] and tested in [11] to determine the reliability against buckling of a cylindrical shell with initial imperfections and variable wall thickness under surface pressure.1. Problem Statement. The reliability of structures is known to be strongly dependent on the probabilistic characteristics of the initial imperfections. By defining the probability density of initial imperfections, we can find the probability density of the critical load as a scalar random variable. The functional dependence of the critical load on the initial imperfections permits defining the reliability against buckling as the probability that a structure will not buckle if the load is less than a certain level:

Probabilistic Approach to Determination of Reliability of an Imperfect Supporting Shell

“…Bolotin's approach was also used in numerous publications by Rurdy, Hansen, and Johns (as reviewed in [13]) as well as in our work [14] for the determination of reliability of cylindrical th³n-walled shells with variable wall thickness and initial geometrical imperfections under the action of surface pressure [14]. Using NASTRAN software package and specially developed programs, Shimkovich [15] constructed a finite-element model of an imperfect supporting shell, performed numerical modeling of loading in the form of various combinations of wind load and variable pressure from weight of a liquid-filled tank installed over the supporting shell, carried out a nonlinear stability analysis of an imperfect supporting shell, and derived a surface of critical values of combined loading.…”

Geometrically nonlinear finite-element models for thin shells with geometric imperfections

“…Koiter's method is mainly used to analyze cylindrical and spherical shells, which are characterized by poor agreement between experimental and theoretical results. There are also approaches [4,5,13] that incorporate the initial imperfections of shells into the geometric parameters of the design model and solve the nonlinear problem numerically.The finite-element method is widely used to analyze the stress-strain state and stability of shells [7]. The results of stability analysis of thin shells with real imperfections modeled by buckling modes are presented in [4,5,13].…”

“…There are also approaches [4,5,13] that incorporate the initial imperfections of shells into the geometric parameters of the design model and solve the nonlinear problem numerically.…”

“…Koiter's method is mainly used to analyze cylindrical and spherical shells, which are characterized by poor agreement between experimental and theoretical results. There are also approaches [4,5,13] that incorporate the initial imperfections of shells into the geometric parameters of the design model and solve the nonlinear problem numerically.…”

“…The results of stability analysis of thin shells with real imperfections modeled by buckling modes are presented in [4,5,13]. In studying shells with real imperfections, a shell of canonical geometry is first generated and then imperfections are imposed on its surface.…”