Abstract
In this paper, a new analytical method in a stress space is suggested to solve the elasto-plastic plane problem that has not been treated analytically even with the total strain theory of plasticity. At first, a general formulation for the elasto-plastic plane theory is established for a compressible isotropic work-hardening material obeying a nonlinear stress-strain law. Then, the basic nonlinear differential equation in ordinary Cartesian coordinate system can be linearized in the system of the stress space, and a complex displacement function, which gives us the solution, can be written in the closed form. Provided that Ramberg-Osgood's law holds as the nonlinear stress-strain relation, the strain component and the corresponding coordinate can be obtained easily and the stress component can be evaluated by the numerical calculation.
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