作者：姚寿文，杨阳编著
页数：179页
出版社：北京理工大学出版社
出版日期：2021
ISBN：9787576303667
电子书格式：pdf/epub/txt
内容简介
本教材以机械结构为研究对象，围绕结构优化设计方法在机械结构设计中的应用，开展相关理论和方法的介绍，主要包含结构优化的建模方法、凸规划方法、非凸函数的近似方法、KKT条件、拉格朗日对偶法、优化准则法和设计参数的敏度分析方法等。 本书可供大学高年级机械设计本科生或研究生使用，也可用于机械工程、结构工程、建筑等领域的技术人员参考。
目录
Chapter 1 Introduction
1.1 Brief History of Structural Optimization
1.2 The Basic Idea
1.3 The Design Process
1.4 Definition of Terms in Structural Optimization
1.5 General Structural Optimization Problem and Its Formulations
1.6 Three Types of Structural Optimization Problems
1.7 Discrete and Distributed Parameter Systems
1.8 Exercise
Chapter 2 Basic Mathematical Concepts
2.1 Introduction
2.2 Sets
2.3 n – dimensional Space
2.4 Functions in n – dimensional Space
2.5 Open and Closed Sets
2.6 Sequence
2.7 Convexity
2.8 Conditions for Minima
2.9 Conditions for Constrained Minima
2.10 Duality
Chapter 3 Elementary Concepts in Structural Optimization
3.1 Introduction
3.2 Statistically Determinate Structures
3.2.1 Analysis
3.2.2 Optimum Design of Strength – critical Problem
3.2.3 Optimum Design of Stiffness – critical Problem
3.2.4 Displacement – stress – constrained problem
3.2.5 Multiple displacement – constrained problem
3.3 Statically Indeterminate Structure
3.3.1 Analysis
3.3.2 Optimum Design of Strength – critical Problem
3.3.3 Displacement – constrained Statistically Indeterminate Structure
3.4 Analysis of General Structure
3.5 Exercise
Chapter 4 Basics of Convex Programming
4.1 Local and Global Optima
4.2 Convexity
4.3 KKT Conditions
4.4 Lagrangian Duality Method
4.5 Exercise
Chapter 5 Sequential Explicit, Convex Approximation
5.1 General Solution
5.2 Sequential Linear Programming
5.3 Sequential Quadratic Programming
5.4 Convex Linearization
5.5 Exercise
Chapter 6 Stiffness Optimization of a Truss And Its Properties
6.1 The Simultaneous Formulation of the Problem
6.2 Nested Formulation and Some of Its Properties
6.2.1 Convexity of the Nested Problem
6.2.2 Fully Stressed Design
6.3 Minimization of the Volume Under a Compliance Constraint
Chapter 7 Optimality Criterion Methods in Structural Optimization
7.1 Introduction
7.2 Basic Equations of Analysis
7.2.1 Displacement Method
7.2.2 Scaling of the Design
7.3 Displacement Constraints
7.3.1 Single Displacement Constraint
7.3.2 Multiple Displacement Constraints
7.4 Stress Constraints
7.5 Algorithm with the Reciprocal Design Variable
7.5.1 Optimality Criterion
7.5.2 Recurrence Relations
7.5.3 Evaluation of the Lagrange Multipliers
7.6 The Variable Thickness Sheet Problem
7.6.1 Problem Statement and FE – discretization
7.6.2 The Optimality Criteria Method
7.7 Exercise
Chapter 8 Sensitivity Analysis of Structural Optimization
8.1 Numerical methods
8.2 Analytical Methods
8.2.1 Direct Analytical Method
8.2.2 Adjoint Analytical method
8.3 Sensitivity Calculation of Load and Stiffness Matrix
8.3.1 Bars
8.3.2 Plane Sheets
8.4 Exercise
References
1.1 Brief History of Structural Optimization
1.2 The Basic Idea
1.3 The Design Process
1.4 Definition of Terms in Structural Optimization
1.5 General Structural Optimization Problem and Its Formulations
1.6 Three Types of Structural Optimization Problems
1.7 Discrete and Distributed Parameter Systems
1.8 Exercise
Chapter 2 Basic Mathematical Concepts
2.1 Introduction
2.2 Sets
2.3 n – dimensional Space
2.4 Functions in n – dimensional Space
2.5 Open and Closed Sets
2.6 Sequence
2.7 Convexity
2.8 Conditions for Minima
2.9 Conditions for Constrained Minima
2.10 Duality
Chapter 3 Elementary Concepts in Structural Optimization
3.1 Introduction
3.2 Statistically Determinate Structures
3.2.1 Analysis
3.2.2 Optimum Design of Strength – critical Problem
3.2.3 Optimum Design of Stiffness – critical Problem
3.2.4 Displacement – stress – constrained problem
3.2.5 Multiple displacement – constrained problem
3.3 Statically Indeterminate Structure
3.3.1 Analysis
3.3.2 Optimum Design of Strength – critical Problem
3.3.3 Displacement – constrained Statistically Indeterminate Structure
3.4 Analysis of General Structure
3.5 Exercise
Chapter 4 Basics of Convex Programming
4.1 Local and Global Optima
4.2 Convexity
4.3 KKT Conditions
4.4 Lagrangian Duality Method
4.5 Exercise
Chapter 5 Sequential Explicit, Convex Approximation
5.1 General Solution
5.2 Sequential Linear Programming
5.3 Sequential Quadratic Programming
5.4 Convex Linearization
5.5 Exercise
Chapter 6 Stiffness Optimization of a Truss And Its Properties
6.1 The Simultaneous Formulation of the Problem
6.2 Nested Formulation and Some of Its Properties
6.2.1 Convexity of the Nested Problem
6.2.2 Fully Stressed Design
6.3 Minimization of the Volume Under a Compliance Constraint
Chapter 7 Optimality Criterion Methods in Structural Optimization
7.1 Introduction
7.2 Basic Equations of Analysis
7.2.1 Displacement Method
7.2.2 Scaling of the Design
7.3 Displacement Constraints
7.3.1 Single Displacement Constraint
7.3.2 Multiple Displacement Constraints
7.4 Stress Constraints
7.5 Algorithm with the Reciprocal Design Variable
7.5.1 Optimality Criterion
7.5.2 Recurrence Relations
7.5.3 Evaluation of the Lagrange Multipliers
7.6 The Variable Thickness Sheet Problem
7.6.1 Problem Statement and FE – discretization
7.6.2 The Optimality Criteria Method
7.7 Exercise
Chapter 8 Sensitivity Analysis of Structural Optimization
8.1 Numerical methods
8.2 Analytical Methods
8.2.1 Direct Analytical Method
8.2.2 Adjoint Analytical method
8.3 Sensitivity Calculation of Load and Stiffness Matrix
8.3.1 Bars
8.3.2 Plane Sheets
8.4 Exercise
References
