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Stochastic linear programming methods in limit load analysis and optimal plastic design under stochastic uncertainty
Author(s) -
Marti K.,
Stoeckl G.
Publication year - 2004
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200410148
Subject(s) - mathematics , linear programming , mathematical optimization , discretization , stochastic programming , probability distribution , convex optimization , regular polygon , mathematical analysis , statistics , geometry
The basic mechanical conditions in optimal plastic design are the convex, linear or linearized yield/strength condition and the linear equilibrium equation for the generic stress (state) vector. Moreover, based on the mechanical survival conditions, the failure costs may be represented by the minimum value of a convex and often linear program. The basic optimal plastic design problem must be replaced by an appropriate deterministic substitute problem, if stochastic variations of the model parameters (e.g. yield stresses, plastic capacities) and external loadings have to be taken into account. Then the total expected costs are minimized subject to the remaining deterministic constraints. A stochastic convex optimization problem is obtained. A “Stochastic Linear Program (SLP) with complete fixed recourse” results when working with linearized yield/strength conditions. In case of a discretely distributed probability distribution or after the discretization of a more general probability distribution of the random structural parameters and loadings as well as certain random cost factors one has a linear program (LP) with a so‐called “dual decomposition data” structure. Some numerical examples are considered to demonstrate the solution procedures.