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Finite element analysis of Saint-Venant torsion problem with exact integration of the elastic-plastic constitutive equations. (English) Zbl 0995.74077

Summary: We study the torsion of prismatic bars considering elastic-plastic material behavior. Based on the presented variational formulation, we develop associated isoparametric finite elements. The unknown warping function is approximated using an isoparametric concept, and the elastic-plastic stresses are obtained by an exact integration of rate equations. Thus the ultimate torque can be calculated in one single load step. This quantity describes the plastic reserve of a bar subjected to torsion. Furthermore, for linear isotropic hardening no local iterations are necessary to compute the stresses at integration points. The numerical results are in good agreement with available analytical solutions for simple geometric shapes. The arbitrarily shaped domains may be simply or multiply connected.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
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References:

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