A Theoretical Method for Solving Elasto-Plastic Torsion Problem

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On the elasto-plastic torsion problem, many investigations have been made by following approaches. In the case of perfect-plastic body, the relaxation methods have been used and numerical calculations have been fulfilled adopting the non-linear stress-strain relation.In this paper, authers suggest and analytical method to solve theoretically the elasto-plastic torsion problem. At first, we employ the new parameters (τ', α), where τ' and α are the resultant shear stress derived from Saint-Venant's torsion function and the argument of τ' respectively. Then the basic equation for the elastic torsion problem is reduced to Laplace's equation in term of these parameters (τ', α). Developing the above (τ', α)-theory, a solution for elastoplastic torsin is obtained using the total strain theory of plasticity. At last, we can describe the torsion function (ω) in the form of the hypergeometric series, provided that the Ramberg-Osgood's law is employed as the non-linear stress-strain relation.
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