Optimum Design of Structures

1. Introduction.- 1.1 Structural Optimization.- 1.2 Previous Work.- 1.3 Proposed Improvement in Optimal Design Process.- 1.4 Purpose and Scope.- 1.5 Contents of this Study.- 1.6 Notation.- 2. Geometric Programming with Equality Constraints.- 2.1 Overview.- 2.2 Geometric Programming.- 2.3 Solution of the Primal Problem by Condensation.- 2.4 Generalized Geometric Programming.- 2.5 Geometric Programming with Equality Constraints.- 3. Decomposition and Reduction Techniques for Large Scale Structural Optimization.- 3.1 Overview.- 3.2 Multilevel Systems and Decompositions in Nonlinear Programming.- 3.3 The Model Coordination Method.- 3.4 The Goal Coordination Method.- 3.5 Basis Reduction Techniques.- 3.6 Variable Linking.- 3.7 Relaxation and Linearization.- 4. Parallel Decomposition for Alternative Loads in Structural Optimization.- 4.1 Overview.- 4.2 The Move Coordination Formulation for Alternative Loading Conditions.- 4.3 Solution Algorithm.- 4.4 Relationship between the Move Coordination Method and Global Solution without Decomposition.- 4.5 Example -- the Three Bar Truss.- 4.6 Effect of the Initial Relaxation.- 5. Application to Truss Type Structures.- 5.1 Formulation and Generation of Data.- 5.2 The Ten Bar Truss.- 5.3 The 25-Member Space Truss.- 6. Summary, Conclusions and Plans for Future Work.- 6.1 Summary.- 6.2 Conclusions.- 6.3 Plans for Future Work.- References.