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Abstract
Real-life analysis and design problems involve uncertainties. Quantification of the uncertainties in a system's response is important and requires a probabilistic analysis of the system. A main challenge in probabilistic analysis of large structural systems is the high computational effort due to the multiple repeated analyses involved. The combined approximations (CA) method, which combines the strengths of both local and global approximations, can be used for efficient probabilistic analysis of structures. The CA method is a combination of binomial series (local) approximations (also called Neumann expansion approximations) and reduced basis (global) approximations. An efficient method is presented for probabilistic analysis of structural systems using the CA method. The effectiveness of this method is demonstrated on analysis of mistuned bladed disk assemblies and systems with progressive collapse using Monte Carlo simulation. It is shown that the method can predict accurately the probability distribution function of the responses of these systems at a considerably lower cost than a method using finite element analysis in each cycle of Monte Carlo simulation.
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