A Quasi One-Dimensional Approach to Elastic-Plastic Problems of Solid Mechanics.

摘要

A major part of this report is a compilation in rather elementary terms of facts from the theory of elastic, plastic, and elastic-plastic plane solid mechanics, as far as they are useful for a numerical approach. The discussion includes the basic concepts, the question of the continuity of stresses along the elastic-plastic boundary, minimum principles, the theory of characteristics for the stresses, the stress rates and the strain rates in the plastic region, and some facts from plane elasticity theory which allow one to formulate the purely elastic problem as a pair of integral equations in which the unknown functions depend only upon one independent variable, say, the arc length of the boundary of the elastic region. The solution of the differential equations in the plastic region can be found by means of the method of characteristics (provided that the partial differential equations in this region are hyperbolic). On this basis it is possible to devise an algorithm in which the elastic and the plastic region are properly matched.