Optimum Design of Structures

With Special Reference to Alternative Loads Using Geometric Programming

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.