Stability of supported cylindrical shell with geometric imperfections under combined loading

Abstract

A numerical method for investigating stability of the supported cylindrical shell with account for geometric imperfection in the form of its deformation during in-service loading has been developed. The problem of nonlinear stability of the imperfect supported cylindrical shell under combined loading has been solved. The influence of the imperfection amplitude on the critical combination of loads and stability region of the supported shell has been evaluated. Introduction. Supported cylindrical shells find widespread use in many engineering fields such as industrial engineering, food, chemical and other industries. One of the main features required of these structures is the ensuring of their minimum weight with sufficient strength and stability. It can be fulfilled provided that geometric nonlinearity, which is typical of the structures with openings, stiffening rings or ribs on their surface operating under conditions close to boundary ones, is taken into consideration during the investigation of their load-carrying capacity and stability. The problem of evaluation of the influence of geometric imperfection on the stability of shell structures remains topical (1-9). Use of analytical methods involves the form of geometric imperfection of the supported shell to be expressed as trigonometric functions, which considerably narrows the focus of investigations. With the availability of modern calculation systems it is possible to express geometric imperfections arbitrarily (10-13), which enhances the physical understanding of the behaviour of imperfect shells. Despite widespread use of supported shells in engineering practice, the influence of imperfections on stability, especially under combined loading, has not been fully investigated. The paper is devoted to the solution of the problem of stability of the imperfect supported shell under wind loading with account for alternating pressure from the weight of the tank filled with liquid, which is placed at the top. A numerical approach, which is based on the finite element method and nonlinear analysis of stability of the shell with geometric imperfections in the form of its deformation, has been proposed. The limiting values for stress-strain state of the supported shell as well as critical values of combined loading, under which its overall stability conditions are fulfilled, have been determined. The influence of geometric imperfection of the supported shell on the critical values of combined loading and its stability region has been evaluated. Development of the Finite Element Model for the Supported Shell Considering Geometric Imperfection. The shell is a cylinder with two openings, which are reinforced with stiffening ribs. The shell walls are reinforced with vertical stiffening ribs at the top and with lower and upper rings. The shell has the following geometry: diameter D 56 1 . m, height H 53 . m, and wall thickness t 10 mm. The rings take the shape of a plate with width of 200