Springer Structural Optimization with Uncertainties: 162 (Solid Mechanics and Its Applications, 162)

This text details new ways to formulate problems of structural optimization with incomplete information and solution techniques. It is mostly devoted to the minimax approach using worst case scenario, but it also covers mixed probabilistic guaranteed approach. Review From the reviews:“The monograph consists of three parts and 17 chapters. … The book is intended for graduate and post graduate students, specialists in mechanics and applied mathematics, engineers, university professors, etc.” (Bojidar Cheshankov, Zentralblatt MATH, Vol. 1182, 2010) From the Back Cover This monograph is devoted to the exposition of new ways of formulating problems of structural optimization with incomplete information and techniques of solution. Research results concerning the optimum shape and structural properties of the bodies subjected to external loadings are recapitulated. Problems of optimal design with incomplete information, accounting for the interaction between the structure and its environment, properties of materials, existence of initial damages and damage accumulation are studied. This volume treats overcoming the corresponding mathematical difficulties caused by raising local functionals. Most of the book is devoted to the minimax approach using worst case scenarios, i.e. the so-called guaranteed approach. However, the probabilistic approach, that does not guarantee the result, is also described in the monograph, because it gives more “optimistic” results. Also, the mixed probabilistic guaranteed approach is discussed and applied for the solution of structural optimization problems with uncertainties.