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Asymptotic-numerical methods and Padé approximants for non-linear elastic structures. (English) Zbl 0805.73076
We apply asymptotic-numerical methods for computing non-linear equilibrium paths of elastic beam, plate and shell structures. The non- linear branches are sought in the form of asymptotic expansions, and they are determined by solving numerically (FEM) several linear problems with a single stiffness matrix. A large number of terms of the series can be easily computed by using recurrence formulas. We show, with some examples, that the choice of the expansion’s parameters and the use of Padé approximants play an important role in the determination of the size of the domain of convergence.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74S05 Finite element methods applied to problems in solid mechanics
74G60 Bifurcation and buckling
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