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Elastic postbuckling analysis via finite element and perturbation techniques part II: Application to shells of revolution
Author(s) -
Flores Fernando G.,
Godoy Luis A.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620360211
Subject(s) - bifurcation , rotational symmetry , finite element method , discretization , continuation , buckling , numerical continuation , perturbation (astronomy) , mathematics , bifurcation theory , critical load , mathematical analysis , singular perturbation , structural engineering , geometry , physics , engineering , nonlinear system , computer science , quantum mechanics , programming language
The general theory developed in Part 1 of this paper for the finite element stability analysis of structural systems, using perturbation expansions in the vicinity of a critical point, is applied here to the analysis of shells of revolution. The discretization of the shell is performed by means of a semianalytical approximation, and the matrices required for the evaluation of critical points and postcritical equilibrium paths are obtained. Two cases are presented: bifurcation in axisymmetric and in asymmetric buckling modes. The derivatives required for an imperfection analysis are also obtained. A technique of switching between two paths using continuation methods is also discussed, in which the switch is performed using derivatives of the perturbation expansion. Results are presented for bifurcation in axisymmetric and in non‐axisymmetric modes, and compared with known solutions or with results from changing the path using continuation methods; good correlation is shown. For structures displaying unstable bifurcation, the influence of load and geometric imperfections is evaluated.