Mathematical Programming Applications Peculiarities in Shakedown Problem/Matematinio programavimo taikymo konstrukcijų prisitaikymo uždaviniuose ypatumai

The theory of mathematical programming widely spread as a method of a solution of extreme problems. It accompanies the study of plastic theory problem from its posing up to final solution. However, here again from our point of view not all possibilities are realized. Unfortunately, the use of mathematical programming as an instrument of a numerical solution for structural analysis frequently is also restricted by that. The possibilities of mechanical interpretation of optimality criteria of applied algorithms are not uncovered. The global solution of the problem of mathematical programming exists, if Kuhn-Tucker conditions are satisfied. These conditions do not depend on the applied algorithm of a problem solution. The identity of Kuhn-Tucker conditions with a optimality criteria of Rosen algorithm is finding out in this research. The role of a design matrix for the creating of strain compatibility equations is clarified. The Kuhn-Tucker conditions mean the residual strain compatibility equations in analysis of elastic-plastic systems. It is proved in the article that for problems of limiting equilibrium the Kuhn-Tucker conditions include the dependences of the associated law of plastic flow. The Kuhn-Tucker conditions together with limitations of a source problem of account represent a complete set of dependences of the theory of shakedown. The correct mathematical and mechanical interpretation of the Kuhn-Tucker conditions allows to refuse a direct solution of a dual problem of mathematical programming. It makes easier the solution of optimization problems of structures at shakedown.

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