International Journal for Numerical Methods in Engineering · 1994 · 224 citations · 12 references
EngineeringComputational EngineeringMechanical EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsBeam TheoryConvergence AnalysisElasticity TheoryPlate AnalysisShell AnalysisStructural Finite Element AnalysisAsymptotic ExpansionsBeam Finite Element AnalysisFinite Element Beam FormulationsFinite Element Methods For PlatesFinite Element Methods In ElasticityNonlinear Equilibrium AnalysisPadé ApproximationPlate Finite Element Analysis
Abstract In this paper, 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. In comparison with a more classical step‐by‐step procedure, the method is rapid and automatic. We show, with some examples, that the choice of the expansion's parameter and the use of Padé approximants play an important role in the determination of the size of the domain of convergence.
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