Generalized Three-Dimensional Theory of Elastic Bodies Stability. Part 1: Finite Deformations
Authors: Dimitrienko Yu.I. | Published: 19.12.2013 |
Published in issue: #4(51)/2013 | |
DOI: | |
Category: Mechanics | |
Keywords: three-dimensional theory of elastic stability, energetic pairs of stress and strain tensors, finite deformations |
A problem of analysis of elastic structure stability is one of main problems in mechanics of deformable solids. Traditional methods of structure stability analysis are based on applying the theory of two-dimensional shell structures, as a rule, the classical Kirchhoff-Love theory. The development of methods for solving threedimensional problems of the stability theory could allow us to expand a range of stability problems which can be solved and to increase the accuracy of obtained solutions. V.V. Novozhilov was one of the first investigators who derived equations of the stability theory from the general nonlinear elasticity theory for the particular case of a continuum. The purpose of the present work is the derivation of generalized three-dimensional equations of the stability theory of nonlinearly elastic bodies with finite deformations for a wide class of nonlinear elasticity models. In order to achieve this aim, two approaches have been applied: the method of a varied configuration (used by A.I. Lurier), which is promising from the viewpoint of generality and universality, as well as the universal method (developed by the author of this paper earlier) for representation of nonlinearly elastic continua models on the basis of energetic pairs ofstress and strain tensors. It is shown that for two ofthe tensor pairs, the stability-theory relationships admit explicit analytical representation without calculation of eigenvalues of the stretch tensor. The results of the study expand the knowledge on fundamental relations of mechanics of deformable continua and represent a theoretical basis for analysis of stability of complex structures including those which are not thin-walled structures.
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