Shakedown of Elastic-Plastic Structures by Jan A. König

By Jan A. König

During this publication, the writer has accrued present details at the research of elastic-plastic constructions subjected to variable repeated lots and to variable temperature fields. He offers the rules of the speculation and its purposes to the shakedown research of buildings of varied forms and to computational algorithms. The publication presents necessary and fascinating fabric for college students of civil and mechanical engineering, working towards engineers with a great mathematical history and likewise scientists fascinated by the research of inelastic constructions.

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4) In some practical applications a special case may occur in which the magnitudes of some loads are constant and the problem consists in evaluating safe limits of variation of the remaining ones. All the above problems are directly or indirectly connected with the evaluation of a safety factor for a given structure. The problems presented below are of completely different nature. (5) Given a load factors domain Q. g. cost) attains a minimum. This is one of the problems of optimum structural design and the computations are tedious even in simple cases [46, 56, 124, 159, 168].

4508 ^ a/b ^ 1. 1. 46 THE CLASSICAL SHAKEDOWN THEORY CH. 1 First yield, shakedown and collapse pressures of a thick-walled tube. 4. 7) (for fi -+ 1) if the left-hand side assumes its maximum possible value and, if simultaneously, the right-hand side reaches its minimum. In principle, such an optimization process can be done in two steps, First, for a given plastic strain history eu(x91), one determines an optimum elastic stress history afj(x, t\ then, an optimum plastic strain path ëu(x, t) is determined.

2. 12) since, for the actual stress state, we have f(au) ^ k. 3). Thus, remembering that Y ^ 0 one can conclude that y(0) ^ Y{t) for / > 0 and r ( 0 -> 0, y ( 0 -> const for t -> oo. 3) we also see that which, after some rearrangements, gives (fi-VOijkfj ^ piOij-ofj-QijYeu = PiQij-QuYtfjAfter integrating over the body volume one obtains Integration with respect to time leads to t \ \ a^jàVàt ^ - 0 - [Y(0)-Y(t)] < - / — n O ) •J J 0 V i " VL — 1 ' Lt ^ 1 y This proves the boundedness of the total energy dissipated.

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