Communications in Numerical Methods in Engineering · 1995 · 62 citations · 11 references
EngineeringComputational EngineeringMechanical EngineeringFinite Element AnalysisFinite Element MethodsStructural AnalysisElastic DeformationElasticity TheoryNonlinear Finite Element AnalysisStrain AnalysisStress-strain BehaviorStructural Finite Element AnalysisEigenvalue Stability AnalysisEigenvaluesElasticityElastoplasticityFinite StrainFinite Strain AnalysisFinite Strain ElementsTangent Stiffness
Abstract The stability of a class of geometrically non‐linear assumed enhanced strain elements is addressed. By means of an eigenvalue analysis of element tangent stiffnesses at finitely deformed configurations, circumstances under which enhanced elements become unstable, with possible development of non‐physical hourglass patterns, are identified. Insight into the influence of spurious eigenvalues on the stability of solution of finite elasticity and elastoplasticity problems is provided by simple numerical tests with a patch of elements. Results of simulations of some practical engineering problems are presented and limitations on the applicability of enhanced strain elements in the finite strain regime are discussed.
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Non-linear elastic deformations
Ray W. Ogden · Engineering Analysis with Boundary Elements · 1984 · 3.5K citations