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From:
Norman F. Knight, Jr. (Aerospace Engineering Department, Old Dominion University, Norfolk, VA 23529-0247) “Finite Element Techniques for Nonlinear Postbuckling and Collapse of Elastic Structures”, Chapter 1 in Structural Dynamic Systems: Computational Techniques and Optimization, Edited by Cornelius T. Leondes, Gordon and Breach Science Publishers, 1998
PARTIAL INTRODUCTION: The objectives of this paper are to present a brief overview of the finite element method, to review selected finite element analysis techniques as applied to determining the nonlinear postbuckling and collapse response of elastic structures, and to describe selected application problems. First, some of the fundamental concepts associated with finite element approximations are described. Second, the basic equations of nonlinear solid mechanics are given for the case of small strain, large elastic deformation including a brief discussion of lamination theory for composite structures. Third, different variational formulations are presented along with their finite element models. Then solution techniques for nonlinear systems (both static and dynamic) are discussed. The traditional approach of nonlinear finite element analysis using a Newton-Raphson approach is reviewed. Reduction methods for nonlinear problems such as the global function approach and the reduced basis approach are summarized. Next, selected applications are described, and finally some concluding remarks are made.
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