Introduction to optimum design
Optimization is a mathematical tool developed in the early 1960's used to find the most efficient and feasible solutions to an engineering problem.It can be used to find ideal shapes and physical configurations, ideal structural designs, maximum energy efficiency, and many other desired goals o...
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| Hlavní autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
San Diego ; Tokyo
Elsevier Academic Press
2004
Elsevier Science & Technology Academic Press |
| Vydání: | 2 |
| Témata: | |
| ISBN: | 0120641550, 9780120641550 |
| On-line přístup: | Získat plný text |
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- Exercises for Chapter 5 -- 6. Linear Programming Methods for Optimum Design -- 6.1 Definition of a Standard Linear Programming Problem -- 6.2 Basic Concepts Related to Linear Programming Problems -- 6.3 Basic Ideas and Steps of the Simplex Method -- 6.4 Two-Phase Simplex Method-Artificial Variables -- 6.5 Postoptimality Analysis -- 6.6 Solution of LP Problems Using Excel Solver -- Exercises for Chapter 6 -- 7. More on Linear Programming Methods for Optimum Design -- 7.1 Derivation of the Simplex Method -- 7.2 Alternate Simplex Method -- 7.3 Duality in Linear Programming -- Exercises for Chapter 7 -- 8. Numerical Methods for Unconstrained Optimum Design -- 8.1 General Concepts Related to Numerical Algorithms -- 8.2 Basic Ideas and Algorithms for Step Size Determination -- 8.3 Search Direction Determination: Steepest Descent Method -- 8.4 Search Direction Determination: Conjugate Gradient Method -- Exercises for Chapter 8 -- 9. More on Numerical Methods for Unconstrained Optimum Design -- 9.1 More on Step Size Determination -- 9.2 More on Steepest Descent Method -- 9.3 Scaling of Design Variables -- 9.4 Search Direction Determination: Newton's Method -- 9.5 Search Direction Determination: Quasi-Newton Methods -- 9.6 Engineering Applications of Unconstrained Methods -- 9.7 Solution of Constrained Problems Using Unconstrained Optimization Methods -- Exercises for Chapter 9 -- 10. Numerical Methods for Constrained Optimum Design -- 10.1 Basic Concepts and Ideas -- 10.2 Linearization of Constrained Problem -- 10.3 Sequential Linear Programming Algorithm -- 10.4 Quadratic Programming Subproblem -- 10.5 Constrained Steepest Descent Method -- 10.6 Engineering Design Optimization Using Excel Solver -- Exercises for Chapter 10 -- 11. More on Numerical Methods for Constrained Optimum Design -- 11.1 Potential Constraint Strategy
- Cover -- Frontmatter -- Half Title Page -- Title Page -- Copyright -- Author Detail -- Dedication Page -- Preface -- Contents -- 1. Introduction to Design -- 1.1 The Design Process -- 1.2 Engineering Design versus Engineering Analysis -- 1.3 Conventional versus Optimum Design Process -- 1.4 Optimum Design versus Optimal Control -- 1.5 Basic Terminology and Notation -- 2. Optimum Design Problem Formulation -- 2.1 The Problem Formulation Process -- 2.2 Design of a Can -- 2.3 Insulated Spherical Tank Design -- 2.4 Saw Mill Operation -- 2.5 Design of a Two-Bar Bracket -- 2.6 Design of a Cabinet -- 2.7 Minimum Weight Tubular Column Design -- 2.8 Minimum Cost Cylindrical Tank Design -- 2.9 Design of Coil Springs -- 2.10 Minimum Weight Design of a Symmetric Three-Bar Truss -- 2.11 A General Mathematical Model for Optimum Design -- Exercises for Chapter 2 -- 3. Graphical Optimization -- 3.1 Graphical Solution Process -- 3.2 Use of Mathematica for Graphical Optimization -- 3.3 Use of MATLAB for Graphical Optimization -- 3.4 Design Problem with Multiple Solutions -- 3.5 Problem with Unbounded Solution -- 3.6 Infeasible Problem -- 3.7 Graphical Solution for Minimum Weight Tubular Column -- 3.8 Graphical Solution for a Beam Design Problem -- Exercises for Chapter 3 -- 4. Optimum Design Concepts -- 4.1 Definitions of Global and Local Minima -- 4.2 Review of Some Basic Calculus Concepts -- 4.3 Unconstrained Optimum Design Problems -- 4.4 Constrained Optimum Design Problems -- 4.5 Postoptimality Analysis: Physical Meaning of Lagrange Multipliers -- 4.6 Global Optimality -- 4.7 Engineering Design Examples -- Exercises for Chapter 4 -- 5. More on Optimum Design Concepts -- 5.1 Alternate Form of KKT Necessary Conditions -- 5.2 Irregular Points -- 5.3 Second-Order Conditions for Constrained Optimization -- 5.4 Sufficiency Check for Rectangular Beam Design Problem
- 11.2 Quadratic Programming Problem -- 11.3 Approximate Step Size Determination -- 11.4 Constrained Quasi-Newton Methods -- 11.5 Other Numerical Optimization Methods -- Exercises for Chapter 11 -- 12. Introduction to Optimum Design with MATLAB -- 12.1 Introduction to Optimization Toolbox -- 12.2 Unconstrained Optimum Design Problems -- 12.3 Constrained Optimum Design Problems -- 12.4 Optimum Design Examples with MATLAB -- Exercises for Chapter 12 -- 13. Interactive Design Optimization -- 13.1 Role of Interaction in Design Optimization -- 13.2 Interactive Design Optimization Algorithms -- 13.3 Desired Interactive Capabilities -- 13.4 Interactive Design Optimization Software -- 13.5 Examples of Interactive Design Optimization -- Exercises for Chapter 13 -- 14. Design Optimization Applications with Implicit Functions -- 14.1 Formulation of Practical Design Optimization Problems -- 14.2 Gradient Evaluation for Implicit Functions -- 14.3 Issues in Practical Design Optimization -- 14.4 Use of General-Purpose Software -- 14.5 Optimum Design of a Two-Member Frame with Out-of-Plane Loads -- 14.6 Optimum Design of a Three-Bar Structure for Multiple Performance Requirements -- 14.7 Discrete Variable Optimum Design -- 14.8 Optimal Control of Systems by Nonlinear Programming -- Exercises for Chapter 14 -- 15. Discrete Variable Optimum Design Concepts and Methods -- 15.1 Basic Concepts and Definitions -- 15.2 Branch and Bound Methods (BBM) -- 15.3 Integer Programming -- 15.4 Sequential Linearization Methods -- 15.5 Simulated Annealing -- 15.6 Dynamic Rounding-off Method -- 15.7 Neighborhood Search Method -- 15.8 Methods for Linked Discrete Variables -- 15.9 Selection of a Method -- Exercises for Chapter 15 -- 16. Genetic Algorithms for Optimum Design -- 16.1 Basic Concepts and Definitions -- 16.2 Fundamentals of Genetic Algorithms
- 16.3 Genetic Algorithm for Sequencing-Type Problems -- 16.4 Applications -- Exercises for Chapter 16 -- 17. Multiobjective Optimum Design Concepts and Methods -- 17.1 Problem Definition -- 17.2 Terminology and Basic Concepts -- 17.3 Multiobjective Genetic Algorithms -- 17.4 Weighted Sum Method -- 17.5 Weighted Min-Max Method -- 17.6 Weighted Global Criterion Method -- 17.7 Lexicographic Method -- 17.8 Bounded Objective Function Method -- 17.9 Goal Programming -- 17.10 Selection of Methods -- Exercises for Chapter 17 -- 18. Global Optimization Concepts and Methods for Optimum Design -- 18.1 Basic Concepts of Solution Methods -- 18.2 Overview of Deterministic Methods -- 18.3 Overview of Stochastic Methods -- 18.4 Two Local-Global Stochastic Methods -- 18.5 Numerical Performance of Methods -- Exercises for Chapter 18 -- Appendix A: Economic Analysis -- A.1 Time Value of Money -- A.2 Economic Bases for Comparison -- Exercises for Appendix A -- Appendix B: Vector and Matrix Algebra -- B.1 Definition of Matrices -- B.2 Type of Matrices and Their Operations -- B.3 Solution of n Linear Equations in n Unknowns -- B.4 Solution of m Linear Equations in n Unknowns -- B.5 Concepts Related to a Set of Vectors -- B.6 Eigenvalues and Eigenvectors -- B.7 Norm and Condition Number of a Matrix -- Exercises for Appendix B -- Appendix C: A Numerical Method for Solution of Nonlinear Equations -- C.1 Single Nonlinear Equation -- C.2 Multiple Nonlinear Equations -- Exercises for Appendix C -- Appendix D: Sample Computer Programs -- D.1 Equal Interval Search -- D.2 Golden Section Search -- D.3 Steepest Descent Method -- D.4 Modified Newton's Method -- References -- Bibliography -- Answers to Selected Problems -- Index