A New Starting Point Strategy for Shakedown Analysis
Shakedown analysis is currently implemented by the coupling of finite element methods with techniques of computational optimization. Engineering structures problems contain a large number of variables and constraints, leading to large-scale nonlinear programming problems, since, usually, nonlinear yield criteria are preferred. The respective algorithms use iterative techniques to solve the problem at hand and the selection of a starting point is of crucial importance for their performance. To this goal the elastic limit solution could be applied, which yields a feasible point, since the zero residual stress identically satisfies the null space conditions. The present study proposes a mechanically motivated, simple technique to obtain an initial feasible point with nonzero residual stresses starting from the plastic shakedown analysis. The residual stresses obtained by this problem are generally infeasible and they are projected into the null space of the equilibrium conditions in order to yield a feasible set of self-equilibrating nonzero stresses. Next, this feasible point is completed by a safety factor, obtained from a one-dimensional optimization problem of elastic limit type. The applicability and appropriateness of this approach is studied by numerical comparisons.
The first author would like to thank DAAD for granting a short stay research scholarship at the Institute of General Mechanics (IAM) of RWTH-Aachen University, IAM for the hospitality and especially the head of IAM Prof. B. Markert for financially supporting the trip to Italy. Special thanks to Dr. Hachemi, Dr. Chen and MSc G.Chen from IAM and Dr Skordeli from Aristotle University Thessaloniki, for the fruitful discussions.
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