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A. GENERAL REMARKS During the last century, probabilistic methods for design and analysis of engineering systems have assumed a prominent place as an engineering tool. No longer do engineers naively believe that all problems can be analyzed with deterministic methods; but rather, it has been recognized that, due to unc- tainties in the model and the excitation, it may only be possible to describe the state of a system in terms of some random measure. Thus, with the need to address safety and design issues adequately and simultaneously to minimize the cost of a system, much attention has been given to the development of probabilistic criteria which can be applied in a systematic manner [l]t. These techniques allow for uncertainties in the parameters of the model as well as for uncertainties in both the static and dynamic loadings to be considered and therefore give a better measure of the reliability of a system. Widespread application of probabilistic methods can be found in disciplines ranging from civil, mechanical and electrical engineering to biology, economics and political science.
Sommario
I. Introduction.- A. General Remarks.- B. Literature Review.- C. Objective and Scope.- II. Problem Definition and Formulation.- A. The Modified-Bouc Hysteresis Model.- B. Formulation of the First Passage Problem.- III. Numerical Solution of the First Passage Problem.- A. A Petrov-Galerkin Finite Element Method for Three-Dimensional Convection-Diffusion Problems.- B. Solution of the Generalized Pontriagin-Vitt Equation for the Ordinary Moments of Time to First Passage.- C. Solution of the Initial-Boundary Value Problem for Oscillator Reliability.- IV. Validation of Results.- A. Demonstration of the Consistency Between the Steady State and Transient First Passage Formulations.- B. Monte Carlo Simulation of the Failure Process.- C. Comparison of the Finite Element Results with the Simulation.- V. Estimating Oscillator Reliability Using Ordinary Moments.- A. The Maximum Entropy Distributions.- B. Estimating Reliability of the Hysteretic Oscillator.- VI. Conclusions and Recommendations.- I. Derivative Moments.- II. Derivation of the Finite Element Matrices.- III. Derivation of Spectral Density for a Rectangular Pulse Excitation.- IV. Maximum Entropy Distribution Algorithm.- Appendices.- References.
