The influence of geometrical shape on the buckling of thin-walled axisymmetric shells

Abstract

The most economical for long span structures are thin-walled covering consisting of shell elements. These include shells of cylindrical, spherical, conical and other shapes. Buckling analysis of thinwalled structures is important in the design of buildings and structures. In this case, the geometric shape of the shell used has a great effect on the critical load. A comparative analysis of the geometrically nonlinear deformation, buckling, and postbuckling behavior of rotation panels of the same v olume under static thermomechanical loading is carried out. Spherical and conical shells having the same thickness, rise and weight are considered. Preheated shells are loaded with uniform external pressure. The calculation method is based on geometrically nonlinear relations of the three-dimensional theory of thermoelasticity without the use of simplifying hypotheses of shell theory and the use of a moment finite element scheme. A universal 3D isoparametric finite element is used. The element allows you to model shells of stepwise variable thickness, with breaks in the middle surface and with other geometric features in thickness. The problem of nonlinear deformation, buckling, and postbuckling behavior of inhomogeneous shells is solved by a combined algorithm that employs the parameter continuation method, a modified Newton–Kantorovich method, and a procedure for automatic correction of algorithm parameters. The method has been justified numerically in the authors' articles. Research has revealed the behavioral features of the compared shallow panels.