A perturbation procedure for the buckling and postbuckling analysis of elastic structures is shown to be well suited to be implemented as an automatic symbolic manipulation procedure. The postbuckling analysis of a circular arch is considered as an example, and the asymptotic description of the bifurcated equilibrium path is given. The main purposes of the automatic procedure are to generate the representation of the Fréchet operator for the strain field and to perform integration by parts. This allows the manipulation of correct expressions of the basic relationships, as the strain-displacement one, without introducing any simplifying assumption or restriction. The perturbation equations are automatically generated and a solution procedure leads to parametric expressions for the coefficients of the asymptotic expansion of the bifurcated path. The symbolic manipulation system used is REDUCE.
Symbolic Manipulation in Buckling and Postbuckling Analysus
TATONE, Amabile
1985-01-01
Abstract
A perturbation procedure for the buckling and postbuckling analysis of elastic structures is shown to be well suited to be implemented as an automatic symbolic manipulation procedure. The postbuckling analysis of a circular arch is considered as an example, and the asymptotic description of the bifurcated equilibrium path is given. The main purposes of the automatic procedure are to generate the representation of the Fréchet operator for the strain field and to perform integration by parts. This allows the manipulation of correct expressions of the basic relationships, as the strain-displacement one, without introducing any simplifying assumption or restriction. The perturbation equations are automatically generated and a solution procedure leads to parametric expressions for the coefficients of the asymptotic expansion of the bifurcated path. The symbolic manipulation system used is REDUCE.Pubblicazioni consigliate
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