Structural design via optimality criteria : the prager approach to structural optimization

摘要: I.1 Why Optimality Criteria?.- I.2 Classes of Problems in Structural Optimization.- I.3 Case Studies Involving Simple Structures.- I.4 More Complex I.5 Broader Implications Criteria Methods.- 1. Static-Kinematic Criteria.- 1.1 Aims.- 1.2 An Introductory Example: What This Book Is All About.- 1.2.1 Solution via 1.2.2 Check by Differentiation.- 1.2.3 The Use Optimal Layout Problems.- 1.2.4 Dual Formulation.- 1.2.5 through Numerical Examples.- 1.3 Plastic Design on the Basis Lower Bound Theorem.- 1.4 Basic Variables Mechanics.- 1.5 Fundamental Relations 1.6 Role 1.7 Prager-Shield Theory Design.- 1.7.1 Proofs Condition.- 1.8 G-Gradient Operator.- 1.9 Extensions 1.9.1 Reactions or Unspecified Forces Non-Zero Cost.- 1.9.2 for External Load and Body Forces.- 1.9.3 Alternate Loads.- 1.9.4 Design: Prescribed Cost Distribution.- 1.9.5 Allowance Connections.- 1.9.6 Optimization Segmentation.- 1.9.7 Location Supports.- 1.9.8 Special Features Homogeneous Specific Functions.- 1.9.9 with Bounded Spatial Gradients "Taper" (Niordson-Constraints).- 1.9.10 Extended Duality Principles 1.9.11 Generalized Functions 1.9.12 Continuous Segment-Wise Linear 1.10 Elastic - Static 1.10.1 Stress Displacement Constraints Continuously Varying Cross-Section.- Applications.- 1.10.2 Minimum Maximum Values Cross-Sectional Parameters.- 1.10.3 Outline Proof 1.10.4 Distribution Parameters over Given Segments.- 1.10.5 Selfweight.- 1.10.6 Actions.- 1.10.7 Niordson-Constraints.- 1.10.8 Multicriterion Pareto Optimality.- 1.11 Buckling Natural Frequency Constraints.- 1.12 Superposition Principles.- 1.13 1.14 Concluding Remarks.- 2. Beams Freely Variable Dimensions.- 2.1 General Concepts.- 2.2 Having a Moment-Dependent Function Solutions.- 2.3 Moment Shear Dependent 2.4 Formulation Plastically Designed 2.5 3. Actions Reactions.- 3.1 Preliminary 3.2 (Reactions) at Locations.- 3.3 Location.- 3.4 4. 4.1 Segmentation Beam 4.2 Conditions Segmented Segment Boundaries.- 4.3 4.4 Multiple Conditions.- 4.5 5. Beams: Selfweight, (Niordson-Constraints) 5.1 5.2 Effect Selfweight 5.3 5.3.1 without 5.3.2 5.3.3 5.4 5.5 5.6 6. Deflection 6.1 versus 6.2 Linearly 6.2.1 Bernoulli-Beams Flexural Single Constraint.- 6.2.2 Timoshenko Normal 6.3 6.4 7. Segmentation, Multicriteria 7.1 7.2 Hinges 7.3 Stress, 7.4 Beams.- 7.5 8. Layouts Brief Review Its 8.1 8.2 Concept Universe.- 8.3 8.4 Classical Advanced Theories.- 8.5 Applications Theory.- (a) Micheli-Frames Least-Weight Trusses.- (b) Grillages Depth.- (c) Archgrids Cable Nets (Prager Structures).- 8.6 Solid Plates.- Perforated Plates Compliance 9. A Short History 9.1 Origins 9.2 Later Developments.- 9.3 Historical Notes Closing Appendix. Variational A.1 A.2 Necessary (Euler Equations) Functional Boundary No A.3 Equality A.4 Transversality (Variational Conditions).- A.5 Inequality A.6 Mixed A.7 Discontinuous Extremals.- A.8 Rocket Problem Solution).- Selected Bibliography.- R.1 Books.- R.2 Papers.- R.3 Research Name Index.