Keywords: limit load/shakedown analysis, structural analysis and design, random model parameters, robust decisions, quadratic loss functions, deterministic substitute problems, stochastic nonlinear programming.

Problems from plastic analysis and optimal plastic design are based on the convex, linear or linearised yield/ strength condition and the linear equilibrium equation for the stress (state) vector. In practice one has to take into account stochastic variations of the model parameters (e.g. yield stresses, plastic capacities, external load factors, cost factors, etc.), see e.g. [2,3,4]. Hence, in order to get robust optimal load factors, robust optimal designs, resp., the basic plastic analysis or optimal plastic design problem with random parameters must be replaced by an appropriate deterministic substitute problem, cf. [1]. Instead of calculating approximatively the probability of failure/survival based on a certain choice of (approximate) failure modes, a direct approach is proposed based on the primary costs (weight, volume, costs of construction, costs for missing carrying capacity, etc.) and the recourse costs (e.g. costs for repair, compensation for weakness within the structure, damage, failure, etc.). Based on the mechanical survival conditions of plasticity theory, a quadratic error/loss criterion is developed. The minimum recourse costs can be determined then by solving an optimisation problem having a quadratic objective function and linear constraints. For each vector a=a(w) of model parameters and each design vector x one obtains then an explicit representation of the "best" internal load distribution F*. Moreover, also the expected recourse costs can be determined explicitly. The expected recourse function may be represented by means of a "generalised stiffness matrix". Hence, corresponding to an elastic approach, the expected recourse function can be interpreted here as a "generalised expected compliance function". Based on the minimisation of the expected primary costs subject to constraints for the expected recourse costs ("generalised compliance") or the minimisation of the expected total primary and recourse costs, explicit finite dimensional parameter optimisation problems result - as deterministic substitute problems - for finding robust optimal design x*, a maximal load factor, respectively. The analytical properties of the resulting programming problem are discussed, and applications, such as limit load/shakedown analysis, are considered.

1

K. Marti, "Stochastic Optimization Methods", Springer-Verlag, Berlin-Heidelberg-New York, 2005.

2

K. Marti, I. Kaymaz, "Reliability analysis for elastoplastic mechanical structures under stochastic uncertainty", ZAMM, Vol. 86, No. 5, 358-384, 2006. doi:10.1002/zamm.200410246

3

I. Kaymaz, K. Marti, "Reliability-based design optimization for elastoplastic mechanical structures", to appear 2007 in "Computers & Structures". doi:10.1016/j.compstruc.2006.08.076

4

K. Marti, "Computation of probabilities of survival/failure of technical, economic systems/structures by means of piecewise linearization of the performance function", to appear 2007 in "Structural and Multidisciplinary Optimization (SMO)". doi:10.1007/s00158-007-0108-4

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £75 +P&P)