Abstract
In previous papers [1,2], a procedure was described for the evaluation of limit loads and shakedown limits for a body subjected to cyclic loading. The procedure was based upon the “Elastic Compensation” method [9,10] where a sequence of linear problems are solved with spatially varying linear moduli. In [1] it was demonstrated that the method may be interpreted as a nonlinear programming method where the local gradient of the upper bound functional and the potential energy of the linear problem are matched at a current strain rate or during a strain rate history. This interpretation may be used to formulate a very general method for evaluating minimum upper bound solutions. Provided certain convexity conditions are satisfied, it is possible to define a sequence of linear problems where the functional monotonically reduces. The sequence then converges to the solution which corresponds to the absolute minimum of the functional, subject to constraints imposed by the class of strain rate histories under consideration. The theoretical basis for the method and convergence proofs are discussed in ref. [3,4].
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Ponter, A.R.S., Engelhardt, M. (2000). Shakedown Limits for a General Yield Condition: Implementation and Application for a Von Mises Yield Condition. In: Weichert, D., Maier, G. (eds) Inelastic Analysis of Structures under Variable Loads. Solid Mechanics and Its Applications, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9421-4_2
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DOI: https://doi.org/10.1007/978-94-010-9421-4_2
Publisher Name: Springer, Dordrecht
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