Structural Optimization with Uncertainties

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.

Zusammenfassung
Structural optimization is currently attracting considerable attention. Interest in - search in optimal design has grown in connection with the rapid development of aeronautical and space technologies, shipbuilding, and design of precision mach- ery. A special ?eld in these investigations is devoted to structural optimization with incomplete information (incomplete data). The importance of these investigations is explained as follows. The conventional theory of optimal structural design - sumes precise knowledge of material parameters, including damage characteristics and loadings applied to the structure. In practice such precise knowledge is seldom available. Thus, it is important to be able to predict the sensitivity of a designed structure to random ?uctuations in the environment and to variations in the material properties. To design reliable structures it is necessary to apply the so-called gu- anteed approach, based on a worst case scenario or a more optimistic probabilistic approach, if we have additional statistical data. Problems of optimal design with incomplete information also have consid- able theoretical importance. The introduction and investigations into new types of mathematical problems are interesting in themselves. Note that some ga- theoretical optimization problems arise for which there are no systematic techniques of investigation. This monograph is devoted to the exposition of new ways of formulating and solving problems of structural optimization with incomplete information. We recall some research results concerning the optimum shape and structural properties of bodies subjected to external loadings.

Inhalt
Prototype Problems.- Guaranteed Approaches.- Probabilistic Uncertainties.- Optimization in Frame of Guaranteed Approach.- Uncertainties and Worst Case Scenarios.- Optimal Design of Beams and Plates with Uncertainties.- Uncertainties in Fracture Mechanics and Optimal Design Formulations.- Beams and Plates with Brittle-Fracture Constraints.- Optimization of Axisymmetric Shells Against Brittle Fracture.- Shape and Thickness Distribution of Pressure Vessels.- Brittle and Quasi-Brittle Materials.- Gravity Forces and Snow Loading.- Damage Characteristics and Longevity Constraints.- Optimization of Shells Under Cyclic Crack Growth.- Uncertainties in Material Characteristics.- Probabilistic and Mixed Probabilistic Guaranteed Approaches.- Some Basic Notions of Probability Theory.- Probabilistic Approaches for Incomplete Information.- Optimization Under Longevity Constraint.- Mixed Probabilistic-Guaranteed Optimal Design.