A Method for Analysis of Nonlinear Deformation, Buckling, and Vibrations of Thin Elastic Shells with Inhomogeneous Structures

Abstract

The formulation of the problem and the method of analysis of the stress-strain state, buckling and vibrations of elastic shells with inhomogeneous structure are considered. The modal analysis of the shells is performed at each stage of loading. The method allows one to study the behavior of shells with a complex shape of the middle surface, geometric features throughout the thickness, and a multilayer material structure under thermomechanical loading. We approximate a thin shell with one finite element (FE) over the entire thickness. At the same time, we use spatial FEs of the same type to model shell portions with stepwise-varying thickness. So we apply the universal finite element. It is based on an isoparametric 3D element with polylinear shape functions for coordinates and displacements and has additional parameters. The universal finite element can be transformed (modified) to accurately describe portions of the shell with stepped-variable thickness. This element can be eccentrically displaced relative to the average surface of the shell and change its own thickness. The side edges of neighboring FEs are in continuous contact, and the FE allows simulating sharp bends of the shell. The approach is modern and easy to implement, since it is based on the use of the relations of the three-dimensional geometrically nonlinear theory of thermoelasticity and the application of the moment finite-element scheme. The effectiveness of the method is demonstrated on classical test examples. The convergence, accuracy and reliability of the obtained solutions are investigated. Comparison of the results of calculations obtained by the moment finite-element scheme with the data of other authors shows a good agreement between the solutions.