A Theoretical Method for Solving an Elasto-Plastic Bending Problem

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概要

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• The elasto-plastic stress analysis of a straight prismatic bar bend under the shearing force, is very difficult even for a simple cross section. Such problems have been investigated by an elementarily analytical method, provided that all stress components apart from bending stress are zero. The analytical method for this problem is formulated in this, both for a complete elastic material, and for a compressible isotropic work-hardening material obeying a non-linear stress strain law. Then, the fundamental equation for an elastic bending is reduced to Laplace's equation and on the other hand, one for an elasto-plastic bending, represented as a system of nonlinear, second-order, partial differential equations, can be linearized by adopting new parameters in the system of the stress space. Provided that the Ramberg-Osgood's law is employed as a nonlinear stress strain relation, the linearized governing equation can be reduced to a hypergeometric differential equation.

• 一般社団法人日本機械学会の論文

著者

• Ishikawa Hiromasa

  Faculty Of Engineering Hokkaido Univeristy

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