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Reliability-based design optimization for elastoplastic mechanical structures

COMPUTERS & STRUCTURES 2007年第10期85卷 615-625页

作者： Kaymaz, Irfan Marti, Kurt Ataturk Univ Dept Mech Engn TR-25240 Erzurum Turkey Fed Armed Forces Univ Munich Aero Space Engn & Technol D-85577 Munich Germany

In this paper, two special formulations to carry out a reliability-based design optimization of elastoplastic mechanical structures are introduced. The first approach is based on a well-known two-level method where the first level involves the optimization for the design parameters whereas the evaluation of the probabilistic constraints is carried out in a sub-optimization level. Because the evaluation of the probabilistic constraints in a sub-optimization level causes non-convergence behavior for some problems as indicated in the literature, an alternative formulation based on one-level is developed considering the optimality conditions of the beta-computation by which the probabilistic constraint appears in the first level reliability-based design optimization formulation. In both approaches, an explicit parameter optimization problem is proposed for the computation of a design point z*(x) for elastoplastic structures. Three examples in this paper demonstrate that the one-level reliability-based design optimization formulation is superior in terms of convergence to an optimal design than the two-level reliability-based design optimization formulation. (c) 2006 Civil-Comp Ltd. and Elsevier Ltd. All rights reserved.

关键词： reliability-based design optimization reliability analysis elastoplastic mechanical structures direct computation of the beta-point

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Reliability analysis for elastoplastic mechanical structures under stochastic uncertainty

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ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 2006年第5期86卷 358-384页

作者： Marti, K. Kaymaz, I. Fed Armed Forces Univ Munich D-85577 Neubiberg Munich Germany Ataturk Univ Fac Engn Dept Mech Engn TR-25240 Erzurum Turkey

Problems from plastic limit load or shakedown analysis and optimal plastic design are based on the convex yield criterion and the linear equilibrium equation for the generic stress (state) vector a. Having to take into account, in practice, stochastic variations of the vector y = y(omega) of model parameters, e.g. yield stresses, external loadings, cost coefficients, etc., the basic stochastic plastic analysis or optimal plastic design problem must be replaced - in order to get robust optimal designs/load factors - by an appropriate deterministic substitute problem. For this purpose, the existence of a statically admissible (safe) stress state vector is described first by means of an explicit scalar state function s* = s* (y, x) depending on the parameter vector y and the design vector x. The state or performance function s* (y, x) is defined by the minimum value function of a convex or linear program based on the basic safety conditions of plasticity theory: A safe (stress) state exists then if and only if s* < 0, and a safe stress state cannot be guaranteed if and only if s* >= 0. Hence, the probability of survival can be represented by p(s) = P (s* (y (omega), x) < 0). Using FORM, the probability of survival is approximated then by the well-known formula p(s) similar to Phi(parallel to z(x)*parallel to) where parallel to z(x)*parallel to X denotes the length of a so-called beta-point, hence, a projection of the origin 0 to the failure domain (transformed to the space of normal distributed model parameters z(omega) = T(y(omega))). Moreover, Phi = Phi(t) denotes the distribution function of the standard N(0,1) normal distribution. Thus, the basic reliability condition, used e.g. in reliability-based optimal plastic design or in limit load analysis problems, reads parallel to z(x)*parallel to >= Phi(-1) (alpha(s)) > with a prescribed minimum probability alpha(s). While in general the computation of the projection z(x)* is very difficult, in the present case of elast

关键词： reliability analysis FORM probability of survival/failure elastoplastic mechanical structures optimizational representations of state functions direct computation of the beta-point Response Surface Methods (RSM)

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