2 Outline

Abstract

The monograph is structured as follows:

Part I including Chapts. 3–6 reviews briefly the theoretical background of the deterministic methods and procedures as used in subsequent chapters. From the proposed procedures, particularly from the mathematical point of view, the so-called spectral theorem is most important. It is particularly useful when dealing with finite dimensional operators. Part II comprises probabilistic methods and procedures relevant for the practical applications shown in Part III. Starting with a general chapter on the rational treatment of uncertainties in computational stochastic mechanics (Chap. 7), the focus of Chapt. 8 lies on the discrete version of the Karhunen-Loève expansion. Well known tools in computational stochastic mechanics such as the Monte Carlo simulation technique and equivalent statistical linearization are treated in Chapts. 9 and 10. Chapter 11 describes an efficient procedure for the calculation of statistical second moment characteristics of large linear and non-linear finite element systems subjected to stochastic dynamic loading. Some practical applications of the procedures treated in Part I and II are shown in Part III. Chapter 12 concentrates on the uncertainty assessment of large non-linear imperfection sensitive finite element systems, special emphasis is given to the stability analysis of axially compressed cylindrical shells. Chapt. 13 is devoted to random vibration problems, in particular to the calculation of the response of a large 6-story office building subjected to dynamic stochastic loading. The monograph is concluded with Part IV. Appendix A describes briefly an imperfection database, which provided the basis for the estimation of the second moment properties of geometric and boundary imperfections, respectively, of cylindrical shells. For the sake of completeness, the fundamentals of the Lyapunov matrix differential equation are shown in Appendix B.