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E-raamat: Structural Design via Optimality Criteria: The Prager Approach to Structural Optimization

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Structural Design via Optimality Criteria: The Prager Approach to Structural OptimizationSuurem pilt
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"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.

Arvustused

`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

Muu info

Springer Book Archives
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 forSegmented 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.
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