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The non-linear perturbation analysis of discrete structural systems

Authors
Journal
International Journal of Solids and Structures
0020-7683
Publisher
Elsevier
Publication Date
Volume
4
Issue
8
Identifiers
DOI: 10.1016/0020-7683(68)90054-1

Abstract

Abstract A general form of perturbation analysis for discrete non-linear structural systems is presented. This generates a system of linear equations which can be solved sequentially for the path derivatives in the unloaded state. Each set of linear equations has the same basic non-singular matrix, and the method is thus ideally suitable for use with a digital computer. The general theory is illustrated firstly by an harmonic and secondly by a finite element analysis of a beam suffering large bending deflections, an exact beam formulation being employed and a continuum perturbation analysis being presented for comparison. The first seven path derivatives are evaluated and are observed to converge rapidly in each case to the continuum values which are then used to construct the load-deflection characteristic of the beam: the choice of independent variable in this final construction is seen to be highly significant. Good agreement is achieved with the known non-linear solution, and it is concluded that the perturbation analysis will be a useful tool in problems of moderate non-linearity.

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