كتاب Introduction to Optimum Design With Notices
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 كتاب Introduction to Optimum Design With Notices

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عدد المساهمات : 14261
التقييم : 22948
تاريخ التسجيل : 01/07/2009
العمر : 28
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية

مُساهمةموضوع: كتاب Introduction to Optimum Design With Notices   الثلاثاء 16 أبريل 2013, 9:41 am

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Introduction to Optimum Design With Notices
Second Edition
Jasbir S. Arora
The University of Iowa

ويتناول الموضوعات الأتية :

Chapter Introduction to Design
The Design Process
Engineering Design versus Engineering Analysis
Conventional versus Optimum Design Process
Optimum Design versus Optimal Control
Basic Terminology and Notation
Sets and Points
Notation for Constraints
Superscripts/Subscripts and Summation Notation
Norm/Length of a Vector
Functions
US-British versus SI Units
Chapter Optimum Design Problem Formulation
The Problem Formulation Process
Step : Project/Problem Statement
Step : Data and Information Collection
Step : Identification/Definition of Design
Variables
Step : Identification of a Criterion to
Be Optimized
Step : Identification of Constraints
Design of a Can
Insulated Spherical Tank Design
Saw Mill Operation
Design of a Two-Bar Bracket
Design of a Cabinet
Formulation for Cabinet Design
Formulation for Cabinet Design
Formulation for Cabinet Design
Minimum Weight Tubular Column Design
Formulation for Column Design
Formulation for Column Design
Minimum Cost Cylindrical Tank Design
Design of Coil Springs
Minimum Weight Design of a Symmetric
Three-Bar Truss
A General Mathematical Model for Optimum Design
Standard Design Optimization Model
Maximization Problem Treatment
Treatment of “Greater Than Type” Constraints
Discrete and Integer Design Variables
Feasible Set
Active/Inactive/Violated Constraints
Exercises for Chapter
Chapter Graphical Optimization
Graphical Solution Process
Profit Maximization Problem
Step-by-Step Graphical Solution Procedure
Use of Mathematica for Graphical Optimization
Plotting Functions
Identification and Hatching of Infeasible
Region for an Inequality
Identification of Feasible Region
Plotting of Objective Function Contours
Identification of Optimum Solution
Use of MATLAB for Graphical Optimization
Plotting of Function Contours
Editing of Graph
Design Problem with Multiple Solutions
Problem with Unbounded Solution
Infeasible Problem
Graphical Solution for Minimum Weight
Tubular Column
Graphical Solution for a Beam Design Problem
Exercises for Chapter
Chapter Optimum Design Concepts
Definitions of Global and Local Minima
Minimum
Existence of Minimum
Review of Some Basic Calculus Concepts
Gradient Vector
Hessian Matrix
Taylor’s Expansion
Quadratic Forms and Definite Matrices
Concept of Necessary and
Sufficient Conditions
Unconstrained Optimum Design Problems
Concepts Related to Optimality Conditions
Optimality Conditions for Functions of
Single Variable
Optimality Conditions for Functions of
Several Variables
Roots of Nonlinear Equations Using Excel
Constrained Optimum Design Problems
Role of Constraints
Necessary Conditions: Equality Constraints
Necessary Conditions: Inequality Constraints—
Karush-Kuhn-Tucker (KKT) Conditions
Solution of KKT Conditions Using Excel
Solution of KKT Conditions Using MATLAB
Postoptimality Analysis: Physical Meaning of
Lagrange Multipliers
Effect of Changing Constraint Limits
Effect of Cost Function Scaling on
Lagrange Multipliers
Effect of Scaling a Constraint on Its
Lagrange Multiplier
Generalization of Constraint Variation
Sensitivity Result
Global Optimality
Convex Sets
Convex Functions
Convex Programming Problem
Transformation of a Constraint
Sufficient Conditions for Convex
Programming Problems
Engineering Design Examples
Design of a Wall Bracket
Design of a Rectangular Beam
Exercises for Chapter
Chapter More on Optimum Design Concepts
Alternate Form of KKT Necessary Conditions
Irregular Points
Second-Order Conditions for
Constrained Optimization
Sufficiency Check for Rectangular Beam
Design Problem
Exercises for Chapter
Chapter Linear Programming Methods for Optimum Design
Definition of a Standard Linear Programming
Problem
Linear Constraints
Unrestricted Variables
Standard LP Definition
Basic Concepts Related to Linear Programming
Problems
Basic Concepts
LP Terminology
Optimum Solution for LP Problems
Basic Ideas and Steps of the Simplex Method
The Simplex
Canonical Form/General Solution of Ax = b
Tableau
The Pivot Step
Basic Steps of the Simplex Method
Simplex Algorithm
Two-Phase Simplex Method—Artificial Variables
Artificial Variables
Artificial Cost Function
Definition of Phase I Problem
Phase I Algorithm
Phase II Algorithm
Degenerate Basic Feasible Solution
Postoptimality Analysis
Changes in Resource Limits
Ranging Right Side Parameters
Ranging Cost Coefficients
Changes in the Coefficient Matrix
Solution of LP Problems Using Excel Solver
Exercises for Chapter
Chapter More on Linear Programming Methods for
Optimum Design
Derivation of the Simplex Method
Selection of a Basic Variable That Should
Become Nonbasic
Selection of a Nonbasic Variable That Should
Become Basic
Alternate Simplex Method
Duality in Linear Programming
Standard Primal LP
Dual LP Problem
Treatment of Equality Constraints
Alternate Treatment of Equality Constraints
Determination of Primal Solution from
Dual Solution
Use of Dual Tableau to Recover Primal Solution
Dual Variables as Lagrange Multipliers
Exercises for Chapter
Chapter Numerical Methods for Unconstrained Optimum Design
General Concepts Related to Numerical Algorithms
A General Algorithm
Descent Direction and Descent Step
Convergence of Algorithms
Rate of Convergence
Basic Ideas and Algorithms for Step Size Determination
Definition of One-Dimensional
Minimization Subproblem
Analytical Method to Compute Step Size
Concepts Related to Numerical Methods to
Compute Step Size
Equal Interval Search
Alternate Equal Interval Search
Golden Section Search
Search Direction Determination: Steepest
Descent Method
Search Direction Determination: Conjugate
Gradient Method
Exercises for Chapter
Chapter More on Numerical Methods for Unconstrained
Optimum Design
More on Step Size Determination
Polynomial Interpolation
Inaccurate Line Search
More on Steepest Descent Method
Properties of the Gradient Vector
Orthogonality of Steepest Descent Directions
Scaling of Design Variables
Search Direction Determination: Newton’s Method
Classical Newton’s Method
Modified Newton’s Method
Marquardt Modification
Search Direction Determination:
Quasi-Newton Methods
Inverse Hessian Updating: DFP Method
Direct Hessian Updating: BFGS Method
Engineering Applications of Unconstrained Methods
Minimization of Total Potential Energy
Solution of Nonlinear Equations
Solution of Constrained Problems Using Unconstrained
Optimization Methods
Sequential Unconstrained Minimization
Techniques
Multiplier (Augmented Lagrangian) Methods
Exercises for Chapter
Chapter Numerical Methods for Constrained Optimum Design
Basic Concepts and Ideas
Basic Concepts Related to Algorithms for
Constrained Problems
Constraint Status at a Design Point
Constraint Normalization
Descent Function
Convergence of an Algorithm
Linearization of Constrained Problem
Sequential Linear Programming Algorithm
The Basic Idea—Move Limits
An SLP Algorithm
SLP Algorithm: Some Observations
Quadratic Programming Subproblem
Definition of QP Subproblem
Solution of QP Subproblem
Constrained Steepest Descent Method
Descent Function
Step Size Determination
CSD Algorithm
CSD Algorithm: Some Observations
Engineering Design Optimization Using Excel Solver
Exercises for Chapter
Chapter More on Numerical Methods for Constrained
Optimum Design
Potential Constraint Strategy
Quadratic Programming Problem
Definition of QP Problem
KKT Necessary Conditions for
the QP Problem
Transformation of KKT Conditions
Simplex Method for Solving QP Problem
Approximate Step Size Determination
The Basic Idea
Descent Condition
CSD Algorithm with Approximate Step Size
Constrained Quasi-Newton Methods
Derivation of Quadratic Programming
Subproblem
Quasi-Newton Hessian Approximation
Modified Constrained Steepest
Descent Algorithm
Observations on the Constrained
Quasi-Newton Methods
Descent Functions
Other Numerical Optimization Methods
Method of Feasible Directions
Gradient Projection Method
Generalized Reduced Gradient Method
Exercises for Chapter
Chapter Introduction to Optimum Design with MATLAB
Introduction to Optimization Toolbox
Variables and Expressions
Scalar, Array, and Matrix Operations
Optimization Toolbox
Unconstrained Optimum Design Problems
Constrained Optimum Design Problems
Optimum Design Examples with MATLAB
Location of Maximum Shear Stress for Two
Spherical Bodies in Contact
Column Design for Minimum Mass
Flywheel Design for Minimum Mass
Exercises for Chapter
Chapter Interactive Design Optimization
Role of Interaction in Design Optimization
What Is Interactive Design Optimization?
Role of Computers in Interactive
Design Optimization
Why Interactive Design Optimization?
Interactive Design Optimization Algorithms
Cost Reduction Algorithm
Constraint Correction Algorithm
Algorithm for Constraint Correction
at Constant Cost
Algorithm for Constraint Correction
at Specified Increase in Cost
Constraint Correction with Minimum Increase
in Cost
Observations on Interactive Algorithms
Desired Interactive Capabilities
Interactive Data Preparation
Interactive Capabilities
Interactive Decision Making
Interactive Graphics
Interactive Design Optimization Software
User Interface for IDESIGN
Capabilities of IDESIGN
Examples of Interactive Design Optimization
Formulation of Spring Design Problem
Optimum Solution for the Spring
Design Problem
Interactive Solution for Spring Design Problem
Use of Interactive Graphics
Exercises for Chapter
Chapter Design Optimization Applications with
Implicit Functions
Formulation of Practical Design
Optimization Problems
General Guidelines
Example of a Practical Design
Optimization Problem
Gradient Evaluation for Implicit Functions
Issues in Practical Design Optimization
Selection of an Algorithm
Attributes of a Good Optimization Algorithm
Use of General-Purpose Software
Software Selection
Integration of an Application into General-
Purpose Software
Optimum Design of Two-Member Frame with
Out-of-Plane Loads
Optimum Design of a Three-Bar Structure for Multiple
Performance Requirements
Symmetric Three-Bar Structure
Asymmetric Three-Bar Structure
Comparison of Solutions
Discrete Variable Optimum Design
Continuous Variable Optimization
Discrete Variable Optimization
Optimal Control of Systems by Nonlinear Programming
A Prototype Optimal Control Problem
Minimization of Error in State Variable
Minimum Control Effort Problem
Minimum Time Control Problem
Comparison of Three Formulations for
Optimal Control of System Motion
Exercises for Chapter
Chapter Discrete Variable Optimum Design Concepts
and Methods
Basic Concepts and Definitions
Definition of Mixed Variable Optimum
Design Problem: MV-OPT
Classification of Mixed Variable Optimum
Design Problems
Overview of Solution Concepts
Branch and Bound Methods (BBM)
Basic BBM
BBM with Local Minimization
BBM for General MV-OPT
Integer Programming
Sequential Linearization Methods
Simulated Annealing
Dynamic Rounding-off Method
Neighborhood Search Method
Methods for Linked Discrete Variables
Selection of a Method
Exercises for Chapter
Chapter Genetic Algorithms for Optimum Design
Basic Concepts and Definitions
Fundamentals of Genetic Algorithms
Genetic Algorithm for Sequencing-Type Problems
Applications
Exercises for Chapter
Chapter Multiobjective Optimum Design Concepts and Methods
Problem Definition
Terminology and Basic Concepts
Criterion Space and Design Space
Solution Concepts
Preferences and Utility Functions
Vector Methods and Scalarization Methods
Generation of Pareto Optimal Set
Normalization of Objective Functions
Optimization Engine
Multiobjective Genetic Algorithms
Weighted Sum Method
Weighted Min-Max Method
Weighted Global Criterion Method
Lexicographic Method
Bounded Objective Function Method
Goal Programming
Selection of Methods
Exercises for Chapter
Chapter Global Optimization Concepts and Methods for
Optimum Design
Basic Concepts of Solution Methods
Basic Concepts
Overview of Methods
Overview of Deterministic Methods
Covering Methods
Zooming Method
Methods of Generalized Descent
Tunneling Method
Overview of Stochastic Methods
Pure Random Search
Multistart Method
Clustering Methods
Controlled Random Search
Acceptance-Rejection Methods
Stochastic Integration
Two Local-Global Stochastic Methods
A Conceptual Local-Global Algorithm
Domain Elimination Method
Stochastic Zooming Method
Operations Analysis of the Methods
Numerical Performance of Methods
Summary of Features of Methods
Performance of Some Methods Using
Unconstrained Problems
Performance of Stochastic Zooming and
Domain Elimination Methods
Global Optimization of Structural
Design Problems
Exercises for Chapter
Appendix A Economic Analysis
A Time Value of Money
A Cash Flow Diagrams
A Basic Economic Formulas
A Economic Bases for Comparison
A Annual Base Comparisons
A Present Worth Comparisons
Exercises for Appendix A
Appendix B Vector and Matrix Algebra
B Definition of Matrices
B Type of Matrices and Their Operations
B Null Matrix
B Vector
B Addition of Matrices
B Multiplication of Matrices
B Transpose of a Matrix
B Elementary Row–Column Operations
B Equivalence of Matrices
B Scalar Product–Dot Product of Vectors
B Square Matrices
B Partitioning of Matrices
B Solution of n Linear Equations in n Unknowns
B Linear Systems
B Determinants
B Gaussian Elimination Procedure
B Inverse of a Matrix: Gauss-Jordan Elimination
B Solution of m Linear Equations in n Unknowns
B Rank of a Matrix
B General Solution of m ¥ n Linear Equations
B Concepts Related to a Set of Vectors
B Linear Independence of a Set of Vectors
B Vector Spaces
B Eigenvalues and Eigenvectors
B Norm and Condition Number of a Matrix
B Norm of Vectors and Matrices
B Condition Number of a Matrix
Exercises for Appendix B
Appendix C A Numerical Method for Solution of
Nonlinear Equations
C Single Nonlinear Equation
C Multiple Nonlinear Equations
Exercises for Appendix C
Sample Computer Programs
D Equal Interval Search
D Golden Section Search
D Steepest Descent Method
D Modified Newton’s Method
References
Bibliography
Answers to Selected Problems
Index

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كتاب Introduction to Optimum Design With Notices

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