Numerical optimization techniques for engineering design: with applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
McGraw-Hill
1984
|
| Series: | McGraw-Hill series in mechanical engineering.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XVII, 333 S. graph. Darst. |
| ISBN: | 0070669643 |
Staff View
MARC
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| 245 | 1 | 0 | |a Numerical optimization techniques for engineering design |b with applications |c Garret N. Vanderplaats |
| 264 | 1 | |a New York, NY [u.a.] |b McGraw-Hill |c 1984 | |
| 300 | |a XVII, 333 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a McGraw-Hill series in mechanical engineering. | |
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| 650 | 4 | |a Conception technique | |
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| 650 | 4 | |a Optimisation mathématique | |
| 650 | 7 | |a Optimisation mathématique |2 ram | |
| 650 | 4 | |a Engineering design | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Numerical calculations | |
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Record in the Search Index
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| adam_text | CONTENTS
Preface xiii
Chapter 1 Basic Concepts 1
1 1 Introduction 1
1 2 Optimization Concepts 4
1 3 General Problem Statement 9
1 4 The Iterative Optimization Procedure 10
1 5 Existence and Uniqueness of an Optimum Solution 12
1 5.1 Unconstrained Problems 12
1 5.2 Constrained Problems 14
1 5.3 The Kuhn Tucker Conditions 17
1 6 Concluding Remarks 19
1 6.1 Advantages of Using Numerical Optimization 20
1 6.2 Limitations of Numerical Optimization 20
1 6.3 Summary 20
References 21
Problems 21
Chapter 2 Functions of One Variable 24
2 1 Introduction 24
2 2 Polynomial Approximations 26
2 2.1 Polynomial Coefficients 30
2 2.2 The Zero of a Polynomial 32
2 2.3 The Minimum or Maximum of a Polynomial 36
2 3 Golden Section Method 41
2 3.1 The Golden Section Algorithm 43
2 3.2 The Maximum or Zero of a Function 45
2 4 Finding Bounds on the Solution 49
2 4.1 Bounds on F = 0 50
2 4.2 Bounds on the Minimum of F 52
vii
Viii CONTENTS
2 5 Constrained Functions of One Variable 54
2 5.1 The Direct Approach 55
2 5.2 The Indirect Approach 56
2 6 A General Strategy for Minimizing Functions of One Variable 58
2 6.1 Unconstrained Functions 59
2 6.2 Constrained Functions—Initially Feasible 62
2 6.3 Constrained Functions—Initially Infeasible 62
2 7 Summary 64
References 68
Problems 68
Chapter 3 Unconstrained Functions of N Variables 71
3 1 Introduction 71
3 1.1 Search Methods 73
3 1.2 General Optimization Strategy 75
3 1.3 The Optimization Algorithm 78
3 2 Zero Order Methods 79
3 2.1 Random Search 80
3 2.2 Powell s Method 84
3 2.3 Other Zero Order Methods 87
3 3 First Order Methods 88
3 3.1 Steepest Descent 88
3 3.2 The Conjugate Direction Method 89
3 3.3 Variable Metric Methods 92
3 4 Second Order Methods: Newton s Method 93
3 5 Scaling of the Variables 97
3 6 Convergence Criteria 100
3 6.1 Maximum Number of Iterations 100
3 6.2 Absolute or Relative Change in the Objective Function 100
3 6.3 The Kuhn Tucker Conditions 101
3 6.4 The Convergence Algorithm 101
References 102
Problems 103
Chapter 4 Constrained Functions of N Variables:
Linear Programming 104
4 1 Introduction 104
4 2 Standard Linear Programming Form 105
4 2.1 Matrix Form of the Linear Programming Problem 106
4 3 Possible Solutions to the Linear Programming Problem 108
4 4 The Simplex Method 110
4 4.1 The Simplex Algorithm 115
4 5 Some Applications of Linear Programming 116
References 119
Problems 119
CONTENTS IX
Chapter 5 Constrained Functions of N Variables:
Sequential Unconstrained Minimization
Techniques 121
5 1 Introduction 121
5 2 The Exterior Penalty Function 123
5 3 The Interior Penalty Function 128
5 4 The Extended Interior Penalty Function , 132
5 4.1 The Linear Extended Penalty Function 132
5 4.2 The Quadratic Extended Penalty Function 132
5 4.3 The Variable Penalty Function 134
5 5 Scaling of the Constraints 136
5 6 Picking the Initial Penalty Parameter 137
5 7 A Note on the One Dimensional Search 138
5 8 The Augmented Lagrange Multiplier Method 140
5 8.1 Equality Constrained Problems 140
5 8.2 Inequality Constrained Problems 145
5 8.3 The General Constrained Optimization Problem 146
References 150
Problems 151
Chapter 6 Constrained Functions of N Variables:
Direct Methods 153
6 1 Introduction 153
6 2 Random Search 153
6 3 Sequential Linear Programming 155
6 4 The Method of Centers 157
6 5 The Method of Feasible Directions 163
6 5.1 Dealing with Initially Infeasible Designs 171
6 5.2 Search Direction Modification 172
6 5.3 Equality Constraints 175
6 6 The Generalized Reduced Gradient Method 177
6.6.1 Dealing with Initially Infeasible Designs 184
6.6.2 Discussion 185
6 7 A Robust Feasible Directions Method 186
6 7.1 The Search Direction 187
6 7.2 Equality Constraints 189
6 7.3 The One Dimensional Search 191
6 7.4 Initially Infeasible Designs 192
6 7.5 Infrequent Gradient Calculations 193
6 7.6 Discussion 195
6 8 Sequential Quadratic Programming 195
References 201
Problems 202
Chapter 7 Approximation Techniques 204
7 1 Introduction 204
7 2 Design Variable Linking 205
X CONTENTS
7 3 The Reduced Basis Concept 208
7 4 Formal Approximations 211
7 5 Constraint Deletion 215
7 6 Sensitivity of the Optimum Design to Problem Parameters 217
7 6.1 Sensitivity Analysis Using the Kuhn Tucker Conditions 217
7 6.2 Sensitivity Analysis Using the Concept
of a Feasible Direction 220
References 225
Problems 225
Chapter 8 Duality 227
8 1 Introduction 227
8 2 Basic Concepts 227
8 2.1 Convex Sets 228
8 2.2 Convex and Concave Functions 230
8 2.3 The Lagrangian and the Kuhn Tucker Conditions 233
8 2.4 Saddle Points 233
8 2.5 The Max Min Problem 235
8 3 The Primal and Dual Problems 236
8 4 Computational Considerations 237
8 5 Applications of Duality 238
8 5.1 Duality in Linear Programming 238
8 5.2 Duality Applied to Structural Optimization 241
8 5.3 General Use of Duality in Nonlinear Optimization 246
References 248
Problems 249
Chapter 9 Structural Optimization 250
9 1 Introduction 250
9 2 The Finite Element Method 251
9 3 Gradient Computations 255
9 4 Structural Design 258
9 4.1 Fully Stressed Design 258
9 4.2 Approximation Techniques 260
9 5 Truss Structures 263
9 5.1 Design of Trusses of Specified Geometry 264
9 5.2 Design of Trusses, Including Configuration Variables 267
9 6 Design of General Structures of Fixed Configuration 271
9 6.1 Membrane and Shear Structures 272
9 6.2 Continuum Structures 274
9 6.3 Composite Structures 277
9 7 Summary 279
References 279
Chapter 10 General Design Applications 283
10 1 Introduction 283
10 2 Aerodynamic Shape Optimization 283
10 2.1 Wing Aerodynamic Optimization 291
CONTENTS xi
10 3 Machine Components 293
10 3.1 Design of Isotropic and Composite Driveshafts 293
10 3.2 Design of Internal Expanding Brakes 296
10 3.3 Design of Helical Gears 298
10 4 Probabilistic Design 300
10 5 Optimization Using Experimental Data 304
10 6 Design of Heat Exchangers and Steam Condensors 306
10 7 Aircraft and Ship Synthesis 309
10 7.1 Aircraft Synthesis 310
10 7.2 Ship Synthesis 316
10 8 Summary 317
References 317
Indexes 321
Name Index
Subject Index
|
| any_adam_object | 1 |
| author | Vanderplaats, Garret N. |
| author_facet | Vanderplaats, Garret N. |
| author_role | aut |
| author_sort | Vanderplaats, Garret N. |
| author_variant | g n v gn gnv |
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| bvnumber | BV002035518 |
| callnumber-first | T - Technology |
| callnumber-label | TA174 |
| callnumber-raw | TA174 |
| callnumber-search | TA174 |
| callnumber-sort | TA 3174 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | SK 870 |
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| ctrlnum | (OCoLC)9785595 (DE-599)BVBBV002035518 |
| dewey-full | 620/.00425 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620/.00425 |
| dewey-search | 620/.00425 |
| dewey-sort | 3620 3425 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Technik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T15:39:16Z |
| institution | BVB |
| isbn | 0070669643 |
| language | English |
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| spelling | Vanderplaats, Garret N. Verfasser aut Numerical optimization techniques for engineering design with applications Garret N. Vanderplaats New York, NY [u.a.] McGraw-Hill 1984 XVII, 333 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in mechanical engineering. Literaturangaben Calculs numériques Calculs numériques ram Conception technique Conception technique ram Optimisation mathématique Optimisation mathématique ram Engineering design Mathematical optimization Numerical calculations Optimierung (DE-588)4043664-0 gnd rswk-swf Konstruieren (DE-588)4139312-0 gnd rswk-swf Konstruieren (DE-588)4139312-0 s Optimierung (DE-588)4043664-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001330883&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vanderplaats, Garret N. Numerical optimization techniques for engineering design with applications Calculs numériques Calculs numériques ram Conception technique Conception technique ram Optimisation mathématique Optimisation mathématique ram Engineering design Mathematical optimization Numerical calculations Optimierung (DE-588)4043664-0 gnd Konstruieren (DE-588)4139312-0 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4139312-0 |
| title | Numerical optimization techniques for engineering design with applications |
| title_auth | Numerical optimization techniques for engineering design with applications |
| title_exact_search | Numerical optimization techniques for engineering design with applications |
| title_full | Numerical optimization techniques for engineering design with applications Garret N. Vanderplaats |
| title_fullStr | Numerical optimization techniques for engineering design with applications Garret N. Vanderplaats |
| title_full_unstemmed | Numerical optimization techniques for engineering design with applications Garret N. Vanderplaats |
| title_short | Numerical optimization techniques for engineering design |
| title_sort | numerical optimization techniques for engineering design with applications |
| title_sub | with applications |
| topic | Calculs numériques Calculs numériques ram Conception technique Conception technique ram Optimisation mathématique Optimisation mathématique ram Engineering design Mathematical optimization Numerical calculations Optimierung (DE-588)4043664-0 gnd Konstruieren (DE-588)4139312-0 gnd |
| topic_facet | Calculs numériques Conception technique Optimisation mathématique Engineering design Mathematical optimization Numerical calculations Optimierung Konstruieren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001330883&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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