모모The book \"An introduction to Structural Optimization\" has been used in the past five years.It gives an introductory treatment of problems and methods of structural optimization.However밃some contents are not suitable for mechanical engineering students.In this book밃we focus on concrete numerical solution methods for discrete and 믿 finite element밀 discretized linear elastic structures.The style is explicit and practical밐 mathematical proofs are provided when arguments can be kept elementary but are otherwise only cited밃while implementation details are frequently provided.Moreover밃since the text has an emphasis on geometrical design problems밃where the design is represented by continuously varying-frequently very many-variables밃so - called first order methods are central to the treatment.These methods are based on sensitivity analysis밃i.e.밃on establishing first order derivatives for objectives and constraints.The classical first order method that we emphasize is CONLIN밃which is based on explicit밃convex and separable approximations.It should be remarked that the classical and frequently used so-called optimality criteria method is also of this kind.It may also be noted in this context that zero order methods such as response surface methods밃surrogate models밃neural networks밃genetic algorithms밃etc.밃essentially apply to different types of problems than the ones treated here and should be presented elsewhere. 모모The text is written for students with a background in solid and structural mechanics with a basic knowledge of the finite element method밃although in our experience such knowledge could be replaced by a certain mathematical maturity.Previous exposure to basic optimization theory and convex programming is helpful but not strictly necessary. 모모In Chapter 1 we introduce the basic idea of mathematical design optimization and indicate its place in the broader frame of product realization밃as well as define basic concepts and terminology.Chapter 2 is devoted to basic mathematical concepts밃which is the basis for the following contents.Chapter 3 gives elementary concepts in structural optimization밃such as statistically determinate structure and statistically indeterminate structure.Chapter 4 reviews basic concepts of convex analysis밃and exemplifies these by means of concepts from structural mechanics.Chapter5 is밃from an algorithmic point of view밃the core chapter of the book.It introduces the basic idea of sequential explicit convex approximations밃and CONLIN is presented.Chapter 6 is applied to stiffness optimization of a truss.This is a classical model problem of structural optimization which we investigate thoroughly.In Chapter 7밃we derive the optimality criteria method as a special case of the general explicit convex approximation method.Chapter 8 concerns sensitivity analysis for finite element discretized structures.
【目录】
Chapter 1 Introduction 1밅1 Brief History of Structural Optimization 1밅2 The Basic Idea 1밅3 The Design Process 1밅4 Definition of Terms in Structural Optimization 1밅5 General Structural Optimization Problem and Its Formulations 1밅6 Three Types of Structural Optimization Problems 1밅7 Discrete and Distributed Parameter Systems 1밅8 Exercise
Chapter 2 Basic Mathematical Concepts 2밅1 Introduction 2밅2 Sets 2밅3 n-dimensional Space 2밅4 Functions in n-dimensional Space 2밅5 Open and Closed Sets 2밅6 Sequence 2밅7 Convexity 2밅8 Conditions for Minima 2밅9 Conditions for Constrained Minima 2밅10 Duality
Chapter 3 Elementary Concepts in Structural Optimization 3밅1 Introduction 3밅2 Statistically Determinate Structures 3밅2밅1 Analysis 3밅2밅2 Optimum Design of Strength-critical Problem 3밅2밅3 Optimum Design of Stiffness-critical Problem 3밅2밅4 Displacement-stress-constrained problem 3밅2밅5 Multiple displacement-constrained problem 3밅3 Statically Indeterminate Structure 3밅3밅1 Analysis 3밅3밅2 Optimum Design of Strength-critical Problem 3밅3밅3 Displacement-constrained Statistically Indeterminate Structure 3밅4 Analysis of General Structure 3밅5 Exercise
Chapter 6 Stiffness Optimization of a Truss And Its Properties 6밅1 The Simultaneous Formulation of the Problem 6밅2 Nested Formulation and Some of Its Properties 6밅2밅1 Convexity of the Nested Problem 6밅2밅2 Fully Stressed Design 6밅3 Minimization of the Volume Under a Compliance Constraint
Chapter 7 Optimality Criterion Methods in Structural Optimiztion 7밅1 Introduction 7밅2 Basic Equations of Analysis 7밅2밅1 Displacement Method 7밅2밅2 Scaling of the Design 7밅3 Displacement Constraints 7밅3밅1 Single Displacement Constraint 7밅3밅2 Multiple Displacement Constraints 7밅4 Stress Constraints 몴몴 Chapter 8 Sensitivity Analysis of Structural Optimization References
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