Structural optimization

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Hauptverfasser: Spillers, William R. (VerfasserIn), MacBain, Keith M. (VerfasserIn)
Format: Medienkombination Buch
Sprache:English
Veröffentlicht: Dordrecht [u.a.] Springer 2009
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Datensatz im Suchindex

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0040/TEC 630f 2009 A 5591
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adam_text Contents 1. Introduction .......................................................................................................1 1.1 Problem Statement.......................................................................................1 1.2 An Optimization Problem............................................................................2 1.3 Elementary Calculus.................................................................................... 5 1.4 Optimal Slope for Truss Bars...................................................................... 6 1.5 An Arch Problem .........................................................................................7 1.6 The Gradient of a Function ..........................................................................8 1.7 The Lagrange Multiplier Rule ...................................................................11 1.8 Newton s Method ......................................................................................12 1.9 Solving Linear Equations ...........................................................................14 1.10 Linear Systems Versus Optimization .......................................................14 1.11 Equations of Structures ............................................................................15 1.12 Plastic Analysis ........................................................................................18 1.13 A Beam Problem ......................................................................................19 1.14 Quadratic Programming ...........................................................................20 1.15 Embedding ...............................................................................................21 1.16 Geometric Programming ..........................................................................21 1.17 Plastic Design of Plane Frames ...............................................................22 1.18 Problems ..................................................................................................24 2. Some Tools of Optimization ...........................................................................29 2.1 TheLagrange Multiplier Rule ...................................................................29 2.2 The Kuhn-Tucker Conditions ....................................................................31 2.3 Calculus of Variations ...............................................................................34 2.4 Newton s Method ......................................................................................36 2.4.1 An Example of Newton s Method ......................................................37 2.5 Linear Programming ..................................................................................40 2.5.1 An Example of the Simplex Method ..................................................41 2.5.2 Interior Point Methods .......................................................................43 2.6 Sequential Linear Programming ................................................................44 2.7 Other Methods of Mathematical Programming .........................................46 2.8 Genetic Algorithms ....................................................................................47 2.9 Problems ....................................................................................................48 3. Sequential Linear Programming and the Incremental Equations of Structures .........................................................................................................49 3.1 Introduction ...............................................................................................49 3.2 The Incremental Equations of Structures ...................................................49 3.3 Application to Structural Optimization ......................................................51 3.4 An Example with a Displacement Constraint ............................................52 3.5 Adding Stress Constraints ..........................................................................56 3.6 The 25-Bar Truss .......................................................................................57 χ Contents 3.7 A Frame Example ......................................................................................60 3.8 A Buckling Example .................................................................................63 3.9 The Incremental Equations when Shape Change is Allowed .....................67 3.10 A Beam Example .....................................................................................72 3.11 A Plate Bending Problem .........................................................................74 3.12 Problems ..................................................................................................76 4. Optimality Criteria Methods ..........................................................................77 4.1 Introduction ................................................................................................77 4.2 The Most Simple Optimality Criteria Problem ..........................................78 4.3 Monotone Behavior ...................................................................................79 4.4 An Application ...........................................................................................80 4.5 Sandwich Beams ........................................................................................84 4.6 A Generalization of the Truss problem ......................................................84 4.7 Plastic Design of Frames ...........................................................................86 4.8 Sandwich Plate Design ..............................................................................88 4.9 Truss Design ..............................................................................................89 4.10 A Plane Stress Problem ............................................................................91 4.11 Prager and His Co-workers ......................................................................95 4.11.1 The Axisymmetric Circular Plate .....................................................95 4.12 A Plate Problem .......................................................................................97 4.13 Problems ................................................................................................100 5. Some Basic Optimization Problems .............................................................103 5.1 Multiple Loading Conditions ...................................................................103 5.1.1 An Example ......................................................................................105 5.1.2 Readability .....................................................................................106 5.1.3 Three Loading Conditions ................................................................108 5.2 Deflection Constraints .............................................................................109 5.2.1 Funaro s Example .............................................................................112 5.2.2 Optimality Criteria Approach ...........................................................117 5.2.3 An Example ......................................................................................121 5.3 Optimal Shape ..........................................................................................122 5.3.1 Frame Problems ................................................................................124 5.3.2 Code Design for a Truss Problem .....................................................126 5.4 Generating New Designs Automatically ..................................................128 5.4.1 Algebraic Methods ...........................................................................130 5.4.2 Linguistic Methods ...........................................................................135 5.5 Problems ..................................................................................................137 6. Beams and Plates: The Work of Rozvány ...................................................139 6.1 Introduction ..............................................................................................139 6.1.1 Examples ..........................................................................................140 6.1.2 Reaction Costs ..................................................................................143 6.1.3 Optimal Segmentation ......................................................................144 Contents xi 6.1.4 A More Realistic Beam Model .........................................................145 6.2 Design of Plates .......................................................................................146 6.3 Problems ..................................................................................................149 7. Some Problems of Dynamic Structural Optimization ................................151 7.1 Introduction .............................................................................................151 7.2 Optimization for Transient Vibrations .....................................................152 7.2.1 The Static Case .................................................................................154 7.2.2 The Dynamic Case ...........................................................................154 7.2.3 The Work of Connor ........................................................................160 7.2.3.1 Tuned Mass Dampers ........................................................................161 7.3 Steady-State Problems .............................................................................162 7.3.1 A Truss Problem ...............................................................................165 7.3.2 An Algorithm for the Truss Problem ................................................166 7.3.3 An Incremental Solution of the Truss Problem ................................171 8. Multicriteria Optimization ...........................................................................175 8.1 Introduction .............................................................................................175 8.2 Solving Multicriteria Optimization Problems ..........................................177 9. Practical Matters: The Work of Farkas and Jármai ..................................179 9.1 Introduction .............................................................................................179 9.2 Sizing Member Cross Sections ................................................................179 9.2.1 Effect of Fabrication Costs ...............................................................181 9.3 Tubular Trusses .......................................................................................182 9.3.1 The Effect of Shape ..........................................................................184 9.4 Problems ..................................................................................................186 10. On Going Work ...........................................................................................187 10.1 Design of Tall Buildings ........................................................................187 10.1.1 Wind Loads on Tall Buildings ............................................................187 10.1.2 Tuned Mass Dampers .........................................................................188 10.1.3 Stochastic Processes .......................................................................189 10.2 Heuristic Algorithms .............................................................................192 10.3 Extending the Design Process ................................................................193 10.4 Design Theory .......................................................................................193 10.4.1 Robust Design ................................................................................194 10.4.2 Creativity in Design .......................................................................194 10.4.3 Design Ontologies ..........................................................................195 10.4.4 Architectural Design ......................................................................195 10.5 Available Computational Algorithms ................................................195 A. Using the Computer .....................................................................................197 A.I Using Computer Languages and Programs .............................................197 Al. 1 Fortran ..............................................................................................197 xii Contents А1.2Рег1 ...................................................................................................199 A1.3 Makefiles ..........................................................................................199 A.2 Matlab .....................................................................................................199 A3 Microsoft Excel .......................................................................................200 A.3.1 The Solver Routine ..........................................................................200 A.3.2 Visual Basic .....................................................................................203 A.5 Freeware ..................................................................................................205 A.6 Graphical Interface Applications ............................................................205 B. The Node Method for Trusses .....................................................................207 B.I Introduction .............................................................................................207 B.2 A Formal Description of the Truss Problem ...........................................208 B.3 A Decomposition ....................................................................................212 C. Convex Sets and Functions: Homogeneous Functions ..............................219 C.I Convex Sets and Functions .....................................................................219 C.2 Homogeneous Functions .........................................................................220 D. Structural Optimization Classics ................................................................223 D.I Micheli Trusses .......................................................................................223 D.2 Keller s Optimal Column ........................................................................233 D.3 The Paper of Venkayya, Khot, and Berke ...............................................245 References ..........................................................................................................289 Index ...................................................................................................................299 William R. Spillers Keith M. MacBain Structural Optimization Structural Optimization is intended to supplement the engineers box of analysis and design tools making optimization as commonplace as the finite element method in the workplace. This book brings the methods of structural optimization into common usage like those of the finite element method. Providing the structural engineer with the right analysis tools and optimization tools. Drawing upon years of practical experience and using numerous examples and illustrative applications, Keith MacBain and William Spillers discuss: • Structural optimization and the methods of nonlinear programming such as Lagrange multipliers, Kuhn- Tucker conditions, and calculus of variations • Solution methods for optimization problems emphasizing the classic method ot linear programming and the method of sequential linear programming • Using sequential linear programming together with the incremental equations of structures as a general approach tor structural optimization. ) springer.com Included is a CD-ROM packed with Microsoft Excel, MATLAB , and FORTRAN (IMSL) routines, and а DLL with linear programming capabilities that will be invaluable to readers. Structural Optimization will be of interest to structural engineers, mechanical engineers, aerospace engineers and architects, particularly those who use the finite element method and want to include optimization in their designs. EXTR* extras.springer.com
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spellingShingle Spillers, William R.
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Structural optimization
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title Structural optimization
title_auth Structural optimization
title_exact_search Structural optimization
title_full Structural optimization William R. Spillers ; Keith M. MacBain
title_fullStr Structural optimization William R. Spillers ; Keith M. MacBain
title_full_unstemmed Structural optimization William R. Spillers ; Keith M. MacBain
title_short Structural optimization
title_sort structural optimization
topic Strukturoptimierung (DE-588)4183811-7 gnd
FORTRAN (DE-588)4017984-9 gnd
Konstruktionselement (DE-588)4165100-5 gnd
topic_facet Strukturoptimierung
FORTRAN
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