Non-Destructive Testing

This book consists of a collection of 27 articles dealing with the subject of probabilistic engineering mechanics with special emphasis on the ensuing computational issues. The book has two parts. The first part is meant as a tutorial on the basic aspects of probabilistic mechanics, whereas the second part is an overview of some of the applications that rely on probabilistic concepts for their treatment. The tutorial part starts with two expository chapters covering both basic and advanced concepts of structural reliability theory. Chapter 2, in particular, gives a clear and concise presentation of the first-order and second-order reliability methods, (FORM/ SORM), as well as a thorough exposition of the various Monte Carlo simulation schemes that have proven to be useful in the context of structural reliability analysis. Chapters 3 and 4 present certain computational aspects associated with the analysis of structural systems with uncertain parameters. Chapter 3 deals with the dynamic analysis of such systems, whereas Chapter 4 treats them in the context of a perturbation-based stochastic finite element method. Chapter 5 is an attempt to couple the boundary element with a perturbation expansion for applying it to uncertain systems. In Chapter 6, a Neumann expansion is used to obtain statistics of the amplitude and frequency of uncertain vibratory systems. Useful truncation and convergence criteria associated with the expansion are also presented. The advanced mean value method for efficient estimation of the CDF is presented in Chapter 7. The NESSUS probabilistic finite element program is also reviewed in this chapter. The perturbation approach is again demonstrated in Chapter 8 through its application to the transient analysis of structures with uncertain damping. An improved perturbation approach is presented in Chapter 9. Here, an iterative perturbation scheme is reviewed that aims at improving the efficiency of the perturbation approach for the analysis of uncertain systems. Brief and sketchy presentations of directional simulation and importance sampling are presented in Chapter 10. The efficacy of these two methods in the reliability analysis of structural systems is indicated. Chapter 11 presents the coupling of the perturbation approach with the response surface approach for the reliability analysis of structural systems. The response surface approach is presented in Chapter 12 where it is applied to the analysis to uncertain nonlinear continua. A central composite design for the response surface is