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Elasto‐plastic stress analysis of prismatic bar under combined bending and torsion
Author(s) -
Ishikawa H.
Publication year - 1973
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19730530104
Subject(s) - torsion (gastropod) , statically indeterminate , bending moment , nonlinear system , cartesian coordinate system , mathematics , isotropy , pure bending , mathematical analysis , plane stress , differential equation , stress–strain curve , geometry , structural engineering , classical mechanics , physics , finite element method , deflection (physics) , engineering , medicine , surgery , quantum mechanics
In this paper, the elasto‐plastic problem of combined bending and torsion of a straight prismatic bar, loaded by a terminal bending couple about the axis of symmetry of the cross section and a twisting couple, is treated analytically for an incompressible isotropic work‐hardening material obeying a nonlinear stress strain law. Evolving a theory so as to satisfy the equilibrium and compatibility condition, the basic nonlinear differential equation in the ordinal Cartesian coordinate system can be linearized, adopting the new parameter in the stress space. Provided that the Ramberg‐Osgood's law is employed as a nonlinear stress strain relation, the linearized basic equation can be reduced to the hypergeometric differential equation. Then, the components of strain and corresponding coordinates can be described in the form of the hypergeometric series. The stress components, the bending and twisting moment can be evaluated by the numerical calculation.