Banichuk / Neittaanmäki Structural Optimization with Uncertainties

1. Auflage 2009
ISBN: 978-90-481-2518-0
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 233 Seiten

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.

Autoren/Hrsg.

Banichuk, N.V.

Neittaanmäki, Pekka

Inhaltsverzeichnis

1;Structural Optimization with Uncertainties;1
1.1;Part I Prototype Problems;12
1.1.1;1 Guaranteed Approaches;13
1.1.1.1;1.1 Prototype Problem 1;13
1.1.1.2;1.2 Prototype Problem 2 Illustrating Nonexistenceof a Worst Load;18
1.1.2;2 Probabilistic Uncertainties;23
1.1.2.1;2.1 Prototype Problem 3: Moment Constraints;23
1.1.2.2;2.2 Prototype Problem 4: Optimization with Direct Probabilistic Constraints;27
1.2;Part II Optimization in Frame of Guaranteed Approach;30
1.2.1;3 Uncertainties and Worst Case Scenarios;31
1.2.1.1;3.1 Transformation Schemes;31
1.2.1.2;3.2 Uncertainties in Loading Conditions;33
1.2.1.3;3.3 Some Optimal Solutions;35
1.2.1.4;3.4 Optimal Design with Uncertainties Versus Optimal Multipurpose Design;37
1.2.2;4 Optimal Design of Beams and Plates with Uncertainties;44
1.2.2.1;4.1 Beams Having the Smallest Weight with Constraints on Strength;44
1.2.2.2;4.2 Some Rigidity Optimization Problems for Elastic Beams and Plates;53
1.2.2.2.1;4.2.1 Minimization of Elastic Deflection;54
1.2.2.2.2;4.2.2 Rigidity Estimation for Thin-Walled Elastic Structures and Worst Case Loading;58
1.2.3;5 Uncertainties in Fracture Mechanics and Optimal Design Formulations;61
1.2.3.1;5.1 Basic Relations of Fracture Mechanics;62
1.2.3.2;5.2 Model Assumptions and Optimization Problems;66
1.2.4;6 Beams and Plates with Brittle-Fracture Constraints;71
1.2.4.1;6.1 Optimization of Beams;71
1.2.4.2;6.2 Optimum Shapes of Holes in Elastic Plates;73
1.2.4.3;6.3 Optimal Design of Bimaterial Layered Beams;74
1.2.5;7 Optimization of Axisymmetric Shells Against Brittle Fracture;80
1.2.5.1;7.1 Basic Relations of the Membrane Shell Model;80
1.2.5.2;7.2 Some Problems of Optimal Thickness Distribution ;85
1.2.5.2.1;7.2.1 Thickness Distribution for Toroidal Shell;86
1.2.5.2.2;7.2.2 Thickness Distribution for Conical Shell;86
1.2.5.2.3;7.2.3 Thickness Distribution for Spherical Shell;88
1.2.5.3;7.3 Some Examples with Prescribed Middle Surfaces;90
1.2.6;8 Shape and Thickness Distribution of Pressure Vessels;95
1.2.6.1;8.1 Optimizing the Shape of a Shell of Revolution;95
1.2.6.2;8.2 The Search for the Shape and Thickness Distribution of an Optimal Shell;97
1.2.6.3;8.3 Some Properties of the Optimal Solution;105
1.2.7;9 Brittle and Quasi-Brittle Materials;107
1.2.7.1;9.1 Mass Effectiveness and Its Maximization;107
1.2.7.2;9.2 Analytical Solution and Convexity Properties;110
1.2.8;10 Gravity Forces and Snow Loading;118
1.2.8.1;10.1 Equilibrium of Shells Under Gravity Forces;118
1.2.8.2;10.2 Weight Minimization;119
1.2.8.3;10.3 Shape and Thickness Optimization by Genetic Algorithm;122
1.2.9;11 Damage Characteristics and Longevity Constraints;127
1.2.9.1;11.1 Transformations of the Longevity Constraint;127
1.2.9.2;11.2 Investigation of Optimal Design;130
1.2.9.3;11.3 Loader Crane Optimization with Longevity Constraints;132
1.2.9.3.1;11.3.1 First Example;133
1.2.9.3.2;11.3.2 Second Example;134
1.2.9.3.3;11.3.3 Third Example;135
1.2.10;12 Optimization of Shells Under Cyclic Crack Growth;137
1.2.10.1;12.1 Basic Relations and Optimization Modeling;137
1.2.10.2;12.2 Optimal Thickness Distribution for Shells of Given Geometry;143
1.2.10.3;12.3 Shape Optimization of Axisymmetric Shells;145
1.2.10.4;12.4 Simultaneous Optimization of the Meridian Shape and the Thickness Distribution of the Shell;149
1.2.10.4.1;12.4.1 Optimum Shells of Positive Gaussian Curvature;150
1.2.10.4.2;12.4.2 Optimum Shells of Negative Gaussian Curvature;154
1.2.10.4.3;12.4.3 Some Properties of Optimal Solution;157
1.2.11;13 Uncertainties in Material Characteristics;158
1.2.11.1;13.1 Discrete Sets of Materials with Uncertain Properties;158
1.2.11.1.1;13.1.1 Basic Representations;158
1.2.11.1.2;13.1.2 Minimization of Reaction Force;162
1.2.11.2;13.2 Uncertainties in Elastic Moduli;169
1.3;Part III Probabilistic and Mixed Probabilistic – GuaranteedApproaches;172
1.3.1;14 Some Basic Notions of Probability Theory;173
1.3.1.1;14.1 Random Variables;173
1.3.1.2;14.2 Some Continuous Distributions;176
1.3.1.3;14.3 Functions of Random Variables;179
1.3.2;15 Probabilistic Approaches for Incomplete Information;185
1.3.2.1;15.1 Probabilistic Problems with Fracture Mechanics Constraints;186
1.3.2.2;15.2 Beams with Random Crack Length;188
1.3.2.3;15.3 Beams with Randomly Placed Cracks;190
1.3.2.4;15.4 The Probabilistic Approach with Constrainton the Stress Intensity Factor;193
1.3.2.5;15.5 Conclusions;195
1.3.3;16 Optimization Under Longevity Constraint;196
1.3.3.1;16.1 Basic Assumptions and Relations;196
1.3.3.2;16.2 Probabilistic Optimization;198
1.3.3.3;16.3 Examples of Probabilistic Problems;201
1.3.3.3.1;16.3.1 Simply Supported Beam;201
1.3.3.3.2;16.3.2 Cantilever Beam;203
1.3.3.3.3;16.3.3 Optimal Design of a Frame;204
1.3.3.3.4;16.3.4 Clamped-Simply Supported Beam;204
1.3.3.4;16.4 Moment Constraints;206
1.3.4;17 Mixed Probabilistic-Guaranteed Optimal Design;211
1.3.4.1;17.1 Probabilistic-Guaranteed Optimization;211
1.3.4.2;17.2 Analytic Solution;213
1.3.4.3;17.3 A Toroidal Shell;215
1.3.4.4;17.4 A Shell Loaded by Forces at the Free Ends;217
1.3.5;References;219
1.3.6;Index;226