Structural Optimization: Volume 1: Optimality Criteria

1. Review of Some Basic Concepts and Theorems of Structural Analysis.- 1.1. Static and Kinematic Variables.- 1.2. Linearly Elastic Structures.- 1.3. Rigid, Perfectly Plastic Structures.- 1.4. Elastic, Perfectly Plastic Structures.- 2. Problem Formulation and Optimality Criteria.- 2.1. Terminology.- 2.2. Problem Types.- 2.3. Elementary Problems of Structural Optimization.- 2.4. Empirical Optimality Criteria.- 2.5. Ill-Posed Problems.- 3. Optimal Design of Beams and Frames.- 3.1. Optimality Condition for Prescribed Load Factor at Plastic Collapse.- 3.2. Optimal Plastic Design for Given Collapse Load.- 3.3. Optimality Condition for Prescribed Elastic Compliance.- 3.4. Optimal Elastic Design for Given Compliance.- 3.5. Various Behavioral Constraints: Common Features and Optimality Conditions.- 3.6. Examples of Optimal Single-Purpose Structures for Various Behavioral Constraints.- 3.7. General Formulation of Optimality Conditions for Multipurpose Beams and Frames.- 3.8. Examples of Optimal Design of Multipurpose Structures.- 3.9. Optimization of the Layout.- 4. Optimal Design of Trusses.- 4.1. Optimal Plastic Design of a Truss of Given Layout for a Single Loading.- 4.2. Optimal Layout of a Truss in Plastic Design for a Single Loading.- 4.3. Michell's Problem.- 4.4. Michell Fields.- 4.5. Use of Michell Fields.- 4.6. Optimal Design of an Elastic Truss for Given Compliance.- 4.7. Nearly Optimal Layout of Trusses with a Finite Number of Joints.- 4.8. Some Remarks on Optimal Trusses.- 4.9. Appendix.- 5. Optimal Design of Grillages.- 5.1. Optimal Plastic Design of Rectangular Grillages of Orthogonal Prismatic Beams.- 5.2. Optimal Layout of a Grillage in Plastic Design for a Single Loading.- 5.3. Morley Fields.- 5.4. Matching of Morley Fields.- 5.5. Optimal Polygonal Grillages.- 5.6. Partially Discretized Grillages.- 6. Optimal Design of Plates, Shells, and Disks.- 6.1. Introduction.- 6.2. Circular Plates with Axisymmetric Loading.- 6.3. Other Plate Problems.- 6.4. Cylindrical Shell under Axisymmetric Loads.- 6.5. Other Shell Problems.- 6.6. Circular Disks in Plane Stress.- 6.7. Other Optimal Disk Problems.- 7. Lagrange Multiplier Methods for Optimization with Constraints.- 7.1. Introduction.- 7.2. Beams in Bending.- 7.3. Plates in Bending.- 7.4. Optimal Segmentation and Optimal Location of Supports.- 7.5. General Discussion.- 8. Review of Some Extensions of Design Procedures.- 8.1. Introduction.- 8.2. Extensions to Other Structures.- 8.3. Extensions to Other Behavioral Constraints.- 8.4. Extensions to Other Cost Functions.- 9. Solutions to Exercises.- References.