Approximation and derivatives of probabilities of survival in structural analysis and design

Yield stresses, allowable stresses, moment capacities (plastic moments), external loadings, manufacturing errors,... are not given fixed quantities in practice, but have to be modelled as random variables with a certain joint probability distribution. Hence, problems from limit (collapse) load analysis or plastic analysis and from plastic and elastic design of structures are treated in the framework of stochastic optimization. Using especially reliability-oriented optimization methods, the behavioral constraints are quantified by means of the corresponding probability p_s of survival. Lower bounds for p_s are obtained by selecting certain redundants in the vector of internal forces/bending-moments; moreover, upper bounds for p_s are constructed by considering a pair of dual linear proprams for the optimizational representation of the yield or safety constraints. Whereas the probability p_s can be computed e.g. by sampling methods or by asymptotic expansion techniques based on Laplace integral representations of certain multiple integrals, efficient techniques for the computation of the sensitivities (of various orders) of p_s with respect to input or design variables X and load factors #lambda# have yet to be developed. Hence, several new techniques (e.g. Transformation Method, Stochastic Completion Technique) are suggested for the numerical computation of derivatives of p_s with respect to (X, #lambda#). (orig.)Available from TIB Hannover: F96B754 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman