Optimal Design of Flexural Systems

PrefaceIntroductionSign ConventionsList of Symbols1. Review of Some Fundamental Concepts 1.1 Basic Variables in Structural Theories. 1.2 Fundamental Relations in Solid Mechanics. 1.3 Special Classes of Strain-Stress Relations. 1.4 Lower and Upper Bound Theorems of Plastic Limit Analysis. 1.5 Euler Equations. 1.6 Variational Problems with Equality Constraints. 1.7 Example - Equality Constraints (Kaliszky's problem). 1.8 Variational Problems with Movable Boundaries and Variable Boundary Values. 1.9 Example - Unspecified Boundary Values. 1.10 Variational Problems with Inequality Constraints. 1.11 Convexity, Local and Global Minima. 1.12 Uniqueness and Sufficiency; Minimum of Convex Function(al)s. 1.13 Example - Inequality Constraints, Convexity and Dual Formulation (Heyman's Problem). 1.14 Mixed Variational Problems. 1.15 Example - Mixed Variational Problem. 1.16 General Concepts in Optimal Design: Cost Functional, Structural Domain, Specific Cost, Behavioral and Geometric Constraints, Prescribed Cost Distribution. 1.17 Concluding Remarks.2. Optimal Plastic Design - Single Load System and Unspecified Cost Distribution. 2.1 Introduction - Static-Kinematic Approach. 2.2 Historical Review. 2.3 Specific Cost Function, Stress Space, Stress Regimes, Constituent Cost Functions, Cost Gradient Vector and Cost Gradient Surface. 2.4 The Prager-Shield Optimality Condition. 2.5 Example - Optimal Plastic Design of a Circular Clamped Sandwich Plate. 2.6 Further Applications of the Prager-Shield Theory. 2.7 Proof of the Prager-Shield Optimality Criterion. 2.8 Upper and Lower Bounds on the Minimum Cost. 2.9 Dual Relation between Plastic Limit Analysis and Optimal Plastic Design. 2.10 Extension of the Prager-Shield Condition to Non-Convex Specific Cost Functions. 2.11 Optimal Plastic Design of Anisotropic Cylindrical Shells having a Variable Rib Depth. 2.12 Upper and Lower Limits on the Specific Cost. 2.13 Example - Optimal Design of Fiber-Reinforced Plate with Prescribed Minimum Specific Fiber Volume. 2.14 Discontinuous Specific Cost Functions.3. Optimal Plastic Design - Alternate and Moving Loads, Multicomponent Systems, Partially Preassigned Cost Distribution and Generalized Cost Functions. 3.1 Introduction. 3.2 Optimal Plastic Design for Alternate Loads. 3.3 Optimal Plastic Design of Multi-Component Systems. 3.4 Example - Optimal Plastic Design of Fiber-Reinforced Plate for Alternate Loads. 3.5 Optimal Plastic Design for Moving Loads. 3.6 Optimal Plastic Design for Partially Prescribed Cost Distribution. 3.7 Example. Beam of Partially Prescribed Cost Distribution. 3.8 Proof of Optimality Conditions for Partially Prescribed Cost Distribution. 3.9 Derivation of Earlier Theories from the Optimality Criterion in Section 3.6. 3.10 Generalized Specific Cost Functions. 3.11 The Hemp-Prager-Nagtegaal Superposition Principle. 3.12 Optimal Multi-Criterion Design.4. Plastic Design - Optimization of Segmentation, Reactions, Generalized Load, Joints, Discretization and Specified Topography. 4.1 Introduction. 4.2 Optimal Segmentation. 4.3 Examples. Optimal Segmentation. 4.4 Optimization of Unspecified Reactions or Loads. 4.5 Various Subclasses of Optimization Problems Involving Beams and Unspecified Reactions or Generalized Loads. 4.6 Optimal Design Taking the Cost of Joints Into Account. 4.7 Optimization of Preassigned Topography. 4.8 Optimal Design of Discrete Systems.5. Optimal Elastic Design. 5.1 Introduction. 5.2 Literature Survey - Optimal Elastic Design by Analytical Methods. 5.3 Optimality Criteria for Elastic Beams - Strength Design. 5.4 Optimality Criteria for Elastic Beams - Deflection Design. 5.5 Proof of Optimality Conditions. 5.6 Generalizations of Optimality Conditions in Sections 5.3 and 5.4. 5.