Structural Design Via Optimality Criteria: The Prager Approach to Structural Optimization

ISBN-13: 9789401070164 / Angielski / Miękka / 2011 / 490 str.

George I. N. Rozvany

Opis

"During the last two decades, research on structural optimization became increasingly concerned with two aspects: the application of general numeri cal methods of optimization to structural design of complex real structures, and the analytical derivation of necessary and sufficient conditions for the optimality of broad classes of comparatively simple and more or less ideal ized structures. Both kinds of research are important: the first for obvious reasons; the second, because it furnishes information that is useful in testing the validity, accuracy and convergence of numerical methods and in assess ing the efficiency of practical designs. - (Prager and Rozvany, 1977a) The unexpected death of William Prager in March 1980 marked, in a sense, the end of an era in structural mechanics, but his legacy of ideas will re main a source of inspiration for generations of researchers to come. Since his nominal retirement in the early seventies, Professor and Mrs. Prager lived in Savognin, an isolated alpine village and ski resort surrounded by some of Switzerland's highest mountains. It was there that the author's close as sociation with Prager developed through annual pilgrimages from Australia and lengthy discussions which pivoted on Prager's favourite topic of struc tural optimization. These exchanges took place in the picturesque setting of Graubunden, on the terrace of an alpine restaurant overlooking snow-capped peaks, on ski-lifts or mountain walks, or during evening meals in the cosy hotels of Savognin, Parsonz and Riom."

Recenzje

`This book can definitely be recommended to all those who are willing to immerse themselves in one of the most important areas of structural optimization,`
H. Eschenauer, ZFW Köln, 1990
`Das Buch kann in jedem Fall all denen empfohlen werden, die bereit sind, sich eines der wichtigen Gebiete der Strukturoptimierung einzuarbeiten.'
Zeitschrift für Flug und Weltraumforschung, 14:1/2, 1990

Spis treści

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.- 1.2.1 Solution via Static-Kinematic Optimality Criteria.- 1.2.2 Check by Differentiation.- 1.2.3 The Use of Optimality Criteria in Optimal Layout Problems.- 1.2.4 Check by Dual Formulation.- 1.2.5 Check through Numerical Examples.- 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.- 1.7.1 Proofs of the Prager-Shield Condition.- 1.8 The G-Gradient Operator.- 1.9 Extensions of the Prager-Shield Theory in Plastic Design.- 1.9.1 Reactions or Unspecified Forces of Non-Zero Cost.- 1.9.2 Optimal Plastic Design for External Load and Body Forces.- 1.9.3 Optimal Plastic Design for Alternate Loads.- 1.9.4 Optimal Plastic Design: Prescribed Cost Distribution.- 1.9.5 Allowance for the Cost of Connections.- 1.9.6 Optimization of Segmentation.- 1.9.7 Optimal Location of Supports.- 1.9.8 Special Features of Homogeneous Specific Cost Functions.- 1.9.9 Optimal Plastic Design with Bounded Spatial Gradients or “Taper” (Niordson-Constraints).- 1.9.10 Extended Duality Principles for Optimal Plastic Design.- 1.9.11 Generalized Specific Cost Functions in Optimal Plastic Design.- 1.9.12 Continuous and Segment-Wise Linear Cost Distribution.- 1.10 Optimal Elastic Design — Static Problems.- 1.10.1 Stress and Displacement Constraints — Continuously Varying Cross-Section.- Applications.- 1.10.2 Optimal Elastic Design with Prescribed Minimum and Maximum Values of the Cross-Sectional Parameters.- 1.10.3 Outline of Proof of Optimality Criteria for Elastic Structures.- 1.10.4 Prescribed Distribution of the Cross-Sectional Parameters over Given Segments.- 1.10.5 Allowance for Selfweight.- 1.10.6 Allowance for Cost of Reactions and Unspecified Actions.- 1.10.7 Elastic Design with Niordson-Constraints.- 1.10.8 Multicriterion Optimal Design and Pareto Optimality.- 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.- Problems and Solutions.- 2.3 Optimal Plastic Design of Beams Having a Moment and Shear Dependent Specific Cost Function — Continuously Variable Cross-Section.- Problems and Solutions.- 2.4 Dual Formulation for Plastically Designed Beams — Continuously Varying Cross-Section.- Problems and Solutions.- 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.- Problems and Solutions.- 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.- Problems and Solutions.- 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.- Problems and Solutions.- 5.3 Bounded Spatial Gradients of the Specific Cost (Niordson-Constraints).- 5.3.1 Beams without Selfweight.- Problems and Solutions.- 5.3.2 Allowance for Selfweight.- Problems and Solutions.- 5.3.3 Dual Formulation for Beams with Niordson-Constraints.- Problems and Solutions.- 5.4 Beams with Segmentation and Selfweight.- Problems and Solutions.- 5.5 Beams with Linear Segmentation.- Problems and Solutions.- 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.- 6.2.1 Bernoulli-Beams with Flexural Stress Constraints and a Single Displacement Constraint.- Problems and Solutions.- 6.2.2 Timoshenko Beams with Normal and Shear Stress Constraints and a Single Displacement Constraint.- 6.3 Prescribed Distribution of the Cross-Sectional Parameters over Given Beam Segments.- Problems and Solutions.- 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.- Problems and Solutions.- 7.3 Optimization of Elastic Beams with Stress, Deflection and Niordson-Constraints.- Problems and Solutions.- 7.4 Multicriteria Optimization of Elastic Beams.- Problems and Solutions.- 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.- (a) Micheli-Frames or Least-Weight Trusses.- (b) Least-Weight Grillages or Beam Layouts of Given Depth.- (c) Archgrids and Cable Nets of Optimal Layout (Prager Structures).- 8.6 Applications of the Advanced Layout Theory.- (a) Optimal Plastic Design of Solid Plates.- (b) Optimal Plastic Design of Perforated Plates.- (c) Optimal Elastic Design of Perforated Plates with a Compliance Constraint.- 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.