8 th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability PMC2000-081 Weber, Hartmann, Faber & Niemann 1 PROCESS ANALYSIS AND RELIABILITY ESTIMATION FOR STRUCTURAL OPTIMIZATION H. Weber, D. Hartmann, O. Faber & H.-J. Niemann Ruhr-University Bochum hw@inf.bi.ruhr-uni-bochum.de , hartus@inf.bi.ruhr-uni-bochum.de , olaf.faber@aib.ruhr-uni-bochum.de , h.niemann@aib.ruhr-uni-bochum.de Abstract A prime problem in optimizing dynamically loaded structures with respect to reliability is the enormous effort of the computations required. The entire computation can be partitioned into five distinct steps, i.) a dynamic structural analysis, ii.) a counting method by which the stress amplitudes are enumerated, iii.) the evaluation of the damages, iv.) the reliability analysis and v.) the optimization of the structure. In particular, the dynamic structural analysis incorporated in the inner nucleus of the solution has to be accomplished in an efficient manner. By making use of the ideas of system theory a covariance analysis is applied containing a shaping filter that describes the loading in association with a structural filter, represented by a finite element analysis. By example, the wind load of a frame structure made of steel is investigated. The wind process is represented through a black box parameter model which is realized in terms of a singular value decomposition (SVD) of sample data. The results of this approach are statistical parameters which describe the probability density function of the stress amplitudes analytically. Subsequently, a damage accumulation rule is applied which allows an estimation of the life time of the structure. Hereby, the reliability is computed using a simulation technique. Finally, the optimization of the structure will be carried out in an outer shell. Two separate ways are possible in the optimization: first, the reliability may be used as an objective, second weight may be minimized and the reliability is linked to the constraints. Introduction Most of the dynamic loading of a structure (e.g. turbulent wind, service load of a crane, etc.) can sufficiently be described as intermittent continuous processes. Such processes are given as continuous processes in a micro-time scale. Each storm event in this micro time scale causes a partial damage which can be determined by a dynamic computation in association with a cycle counting method. The micro-time description, however, must be embedded in a macro-time domain. Here, all loading recurrences are regarded throughout the whole lifetime whereat the partial damages are being accumulated. In the real world, all attributes of design relevant variables, both loading and resistance, have a stochastic character. For load processes dynamic computations would have to be carried out, but they are very time consuming. If the repeated structural analysis could be avoided this would be a decisive step ahead. In this context a possible way is to use a system theory based description both for loading and structure. Then, the expensive solution of the differential equation can be replaced by an algebraic equation and statistical parameters of the structure vibrations are computable.