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Format: 490 p. , online resource.

Edition: 1st ed. 1989.

ISBN: 9789400911611

Series Statement: Mechanics of Elastic and Inelastic Solids, 8

Note: I.1 Why Optimality Criteria? -- I.2 Classes of Problems in Structural Optimization -- I.3 Case Studies Involving Simple Structures -- I.4 Case Studies Involving More Complex Structures -- I.5 Broader Implications of Optimality Criteria Methods -- 1. Static-Kinematic Optimality Criteria -- 1.1 Aims -- 1.2 An Introductory Example: What This Book Is All About -- 1.3 Plastic Design on the Basis of the Lower Bound Theorem -- 1.4 Basic Variables in Structural Mechanics -- 1.5 Fundamental Relations of Structural Mechanics -- 1.6 The Role of Static-Kinematic Optimality Criteria -- 1.7 The Prager-Shield Theory of Optimal Plastic Design -- 1.8 The G-Gradient Operator -- 1.9 Extensions of the Prager-Shield Theory in Plastic Design -- 1.10 Optimal Elastic Design - Static Problems -- 1.11 Optimal Elastic Design - Buckling and Natural Frequency Constraints -- 1.12 Superposition Principles -- 1.13 Duality Principles in Elastic Design -- 1.14 Concluding Remarks -- 2. Optimal Plastic Design of Beams with Freely Variable Cross-Sectional Dimensions -- 2.1 General Concepts -- 2.2 Optimal Plastic Design of Beams Having a Moment-Dependent Specific Cost Function - Continuously Variable Cross-Section -- 2.3 Optimal Plastic Design of Beams Having a Moment and Shear Dependent Specific Cost Function - Continuously Variable Cross-Section -- 2.4 Dual Formulation for Plastically Designed Beams - Continuously Varying Cross-Section -- 2.5 Concluding Remarks -- 3. Optimal Plastic Design of Beams with Unspecified Actions or Reactions -- 3.1 Preliminary Remarks -- 3.2 External Actions (Reactions) at Prescribed Locations -- 3.3 External Actions or Reactions of Unspecified Location -- 3.4 Concluding Remarks -- 4. Optimal Plastic Design of Beams with Segmentation -- 4.1 Segmentation in Beam Design -- 4.2 Optimality Conditions for Segmented Beams with Prescribed Segment Boundaries -- 4.3 Optimization of Segmentation -- 4.4 Segmented Beams with Multiple Load Conditions -- 4.5 Concluding Remarks -- 5. Optimal Plastic Design of Beams: Allowance for Selfweight, Bounded Spatial Gradients (Niordson-Constraints) and Linear Segments -- 5.1 Introductory Remarks -- 5.2 Allowance for the Effect of Selfweight - Continuously Variable Cross-Section -- 5.3 Bounded Spatial Gradients of the Specific Cost (Niordson-Constraints) -- 5.4 Beams with Segmentation and Selfweight -- 5.5 Beams with Linear Segmentation -- 5.6 Concluding Remarks -- 6. Optimal Elastic Design of Beams - Stress and Deflection Constraints -- 6.1 Optimal Elastic versus Optimal Plastic Design -- 6.2 Linearly Elastic Beams with Stress and Displacement Constraints - Freely Variable Cross-Sectional Dimensions -- 6.3 Prescribed Distribution of the Cross-Sectional Parameters over Given Beam Segments -- 6.4 Concluding Remarks -- 7. Optimal Elastic Design of Beams - Optimization of Segmentation, Constraints on Spatial Gradients (Niordson-Constraints) and Multicriteria Design -- 7.1 Introductory Remarks -- 7.2 Optimization of Beam Segmentation and Location of Hinges and Supports -- 7.3 Optimization of Elastic Beams with Stress, Deflection and Niordson-Constraints -- 7.4 Multicriteria Optimization of Elastic Beams -- 7.5 Concluding Remarks -- 8. The Theory of Optimal Layouts and a Brief Review of Its Applications -- 8.1 Introductory Remarks -- 8.2 The Concept of Structural Universe -- 8.3 Introductory Examples -- 8.4 Classical and Advanced Layout Theories -- 8.5 Applications of the Classical Layout Theory -- 8.6 Applications of the Advanced Layout Theory -- 9. A Short History of Optimality Criteria Methods -- 9.1 The Origins of Optimality Criteria in Structural Mechanics -- 9.2 Later Developments -- 9.3 Historical Notes on Optimal Layout Theory -- Closing Remarks -- Appendix. A Brief Review of Variational Methods -- A.1 Aims -- A.2 Necessary Conditions (Euler Equations) for the Minimum of a Functional - Given Boundary Conditions and No Constraints -- Problems and Solutions -- A.3 Variational Problems with Equality Constraints -- Problems and Solutions -- A.4 Transversality Conditions (Variational Problems with Variable Boundary Conditions) -- Problems and Solutions -- A.5 Inequality Constraints -- Problems and Solutions -- A.6 Mixed Variational Problems -- Problems and Solutions -- A.7 Discontinuous Extremals -- Problems and Solutions -- A.8 The Rocket Problem (Variational Solution) -- Selected Bibliography -- R.1 Books -- R.2 Review Papers -- R.3 Research Papers -- Name Index.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9789401070164

Additional Edition: Printed edition: ISBN 9789024736133

Additional Edition: Printed edition: ISBN 9789400911628

Language: English

DOI: 10.1007/978-94-009-1161-1

URL: https://doi.org/10.1007/978-94-009-1161-1