Stochastic Methods in Engineering

Due to the increasing industrial demand for reliable quantification and management of uncertainty in product performance, engineers must employ probabilistic models in analysis and design in order to account for the random fluctuation of the properties of actual systems. Considerable research and development is therefore being done in this field.

"Stochastic Methods in Engineering" covers computational stochastic analysis and optimization. It begins by introducing concepts and then outlines computational approaches to specific classes of problems. Emanating from the author's courses at the Faculty of Aerospace Engineering at the University of Stuttgart, the book is intended to make the reader familiar with the stochastic point of view, exploring and quantifying random system variability, its source and sensitivity. It also develops methods of stochastic analysis and optimization based on deterministic knowledge, serving as a guide in the transition from determinism to stochastics.

The book begins by introducing concepts of stochastic analysis and design optimization, outlining computational approaches to specific classes of problems, referring first to elastic structures, geometric nonlinearities and elastoplasticity. Two fundamentally different methods are considered in this context and are developed on the basis of the finite element formalism: the analytical Taylor expansion approach and the synthetic Monte Carlo technique. In fact, the single volume is unique in presenting tutorials on essential probabilistics and statistics, recent finite element methods, and Monte Carlo simulation techniques. The considerations are extended to the important issue of system reliability, time variant phenomena and material deformation processes. Supplementary, statistical assessment and comparison of systems is exposed, which is of interest also when validating analysis models by laboratory testing.