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Reliability analysis for elastoplastic mechanical structures under stochastic uncertainty

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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