Optimum Design of Structures: With Special Reference to Alternative Loads Using Geometric Programming

ISBN-13: 9783540515395 / Angielski / Miękka / 1989 / 154 str.

Lahbib Chibani

Opis

This volume constitutes an important addition in our Lecture Notes in Engineering Series. The search for optimal structural shapes is at the fourtdation of all engineering analysis. Furthermore el)gineering as a whole can be seen as a process of looking for optimum solutions. The importance of Dr Chibani's work is that it deals with the integrated process of analysing and designing the optimum structure in a single operation. The design shape as well as the usual structural constraints are incQr.porated into the mathematical problem. This approach which is more suitable to computer applications has the difficulty of introducing a large number of variables and constraints equations. To overcome this problcm Dr Chibani proposes to apply a multilevel optimization technique which rcduces the dimensionaiity of a large scalc structural problem. The hook exp.I.111ns how a large optimization problem can be divided into Hcvcral partH of .1 smaller dimension which can then be solved eithcr scquentially or in parallel to obtain the solution of the original problem. Applicationsto these type structures provide a demonstration of the effectiveness of the procedure.

Spis treści

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.- 2.5.1 Generalized Geometric Programming with Equality Constraints Algorithm.- 2.5.2 Interactive Generalized Geometric Programming Solver (IGGP).- 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.- 3.3.1 Illustrative Example.- 3.4 The Goal Coordination Method.- 3.4.1 Illustrative Example.- 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.- 4.3.1 Algorithm (a).- 4.3.2 Algorithm (b).- 4.4 Relationship between the Move Coordination Method and Global Solution without Decomposition.- 4.5 Example — the Three Bar Truss.- 4.5.1 Formulation and Direct Solution.- 4.5.2 Solution by the Move Coordination Method.- 4.6 Effect of the Initial Relaxation.- 5. Application to Truss Type Structures.- 5.1 Formulation and Generation of Data.- 5.1.1 Formulation.- 5.1.2 Generation of Data.- 5.2 The Ten Bar Truss.- 5.2.1 Problem Statement.- 5.2.2 Solution by the Move Coordination and the Global Solution.- 5.2.3 Behavior of Bars in the Cyclic Iteration History.- 5.3 The 25-Member Space Truss.- 5.3.1 Problem Statement.- 5.3.2 Solution by the Move Coordination and Global Solution.- 5.3.3 Behavior of the Members in the Cyclic Iteration History.- 6. Summary, Conclusions and Plans for Future Work.- 6.1 Summary.- 6.2 Conclusions.- 6.3 Plans for Future Work.- 6.3.1 The Solution Algorithms.- 6.3.2 Application of the Decomposition Method.- References.