Ebook: 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.

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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.

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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.

Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Guaranteed Approaches....Pages 3-12
Probabilistic Uncertainties....Pages 13-19
Front Matter....Pages 22-22
Uncertainties and Worst Case Scenarios....Pages 23-35
Optimal Design of Beams and Plates with Uncertainties....Pages 37-53
Uncertainties in Fracture Mechanics and Optimal Design Formulations....Pages 55-64
Beams and Plates with Brittle-Fracture Constraints....Pages 65-73
Optimization of Axisymmetric Shells Against Brittle Fracture....Pages 75-89
Shape and Thickness Distribution of Pressure Vessels....Pages 91-102
Brittle and Quasi-Brittle Materials....Pages 103-113
Gravity Forces and Snow Loading....Pages 115-123
Damage Characteristics and Longevity Constraints....Pages 125-134
Optimization of Shells Under Cyclic Crack Growth....Pages 135-155
Uncertainties in Material Characteristics....Pages 157-170
Front Matter....Pages 172-172
Some Basic Notions of Probability Theory....Pages 173-184
Probabilistic Approaches for Incomplete Information....Pages 185-195
Optimization Under Longevity Constraint....Pages 197-211
Mixed Probabilistic-Guaranteed Optimal Design....Pages 213-220
Back Matter....Pages 221-233

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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.

Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Guaranteed Approaches....Pages 3-12
Probabilistic Uncertainties....Pages 13-19
Front Matter....Pages 22-22
Uncertainties and Worst Case Scenarios....Pages 23-35
Optimal Design of Beams and Plates with Uncertainties....Pages 37-53
Uncertainties in Fracture Mechanics and Optimal Design Formulations....Pages 55-64
Beams and Plates with Brittle-Fracture Constraints....Pages 65-73
Optimization of Axisymmetric Shells Against Brittle Fracture....Pages 75-89
Shape and Thickness Distribution of Pressure Vessels....Pages 91-102
Brittle and Quasi-Brittle Materials....Pages 103-113
Gravity Forces and Snow Loading....Pages 115-123
Damage Characteristics and Longevity Constraints....Pages 125-134
Optimization of Shells Under Cyclic Crack Growth....Pages 135-155
Uncertainties in Material Characteristics....Pages 157-170
Front Matter....Pages 172-172
Some Basic Notions of Probability Theory....Pages 173-184
Probabilistic Approaches for Incomplete Information....Pages 185-195
Optimization Under Longevity Constraint....Pages 197-211
Mixed Probabilistic-Guaranteed Optimal Design....Pages 213-220
Back Matter....Pages 221-233
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