Extremal Boundary Value Problems in the Theory of Plasticity,
ARMY FOREIGN SCIENCE AND TECHNOLOGY CENTER CHARLOTTESVILLE VA
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In the theory of small deformations, the breaking load for an elastic-plastic body is equivalent to the limiting load for a rigid-plastic body. The problem of the carrying capacity of an elastic-plastic body is solved on this basis, using the limiting equilibrium method. The solution is carried through all the way to the construction of the actual stress fields and displacement. Mathematical programming apparatus is used. The construction of the limiting stress field is carried out by means of regularizing an extremal boundary value problem, which is necessary to resolve the non-uniqueness of the stress field in the limiting equilibrium problem of a rigid-plastic body. The solution of the problem is illustrated on the example of a boundary problem for a generalized plane stressed state.