Chapter1-Introduction

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1、Chapter1Introduction1.WhatisOptimization?Whatitcando?2.Terminologyandbasicconcepts3.Mathematicalstatementoftheoptimum-structural-designproblem4.OptimizationmethodsWhatisOptimization?Whatitcando?Peopleoptimize.Investorsseektocreateportfoliosthatavoidexcessiveriskwhileac

2、hievingahighrateofreturn.Manufacturersaimformaximumefficiencyinthedesignandoperationoftheirproductionprocesses.Engineersadjustparameterstooptimizetheperformanceoftheirdesigns.Natureoptimizes.Physicalsystemstendtoastateofminimumenergy.Themoleculesinanisolatedchemicalsys

3、temreactwitheachotheruntilthetotalpotentialenergyoftheirelectronsisminimized.Raysoflightfollowpathsthatminimizetheirtraveltime.Optimizationisanimportanttoolindecisionscienceandintheanalysisofphysicalsystems.Optimizationisthemathematicaldisciplinewhichisconcernedwithfin

4、dingthemaximaandminimaoffunctions,possiblysubjecttoconstraints.Application:Architecture/Nutrition/Electricalcircuits/Economics/Transportation/etc.Terminologyandbasicconcepts1．DeignvariablesThedesignvariablesofanoptimum-structural-designproblemmayconsistofthenumbersizes

5、,parametersthatdescribethestructuralconfigurationandmechanicalorphysicalpropertiesofthematerial,aswellasotherquantifiableaspectsofthedesign.Thesimplestdesignvariableisthe“size”ofamemberrepresentingthecross-sectionalareaofatrussmember,themomentofinertiaofaflexuralmember

6、,orthethicknessofaplate.Manypracticalstructureshavefixedgeometryandmaterialproperties.Configurationvariables,oftenrepresentedbythecoordinatesofelementjoints,arenextinorderofdifficulty,followedbymaterialproperties.Theithdesignvariableisdesignedhereinasxi,andthefullsetof

7、variablesforagivenstructureislistedinthevectorx.Thedesignspaceisdescribedbyaxesrepresentingtherespectivedesignvariables.Figure1.1showsathree-variable,andconsequentlythree-dimensionaldesignspace,forexample,thethree-bartruss.Thenumberofdesignvariablesnisgenerallyverymuch

8、greaterthanthree,andthereforedefinesillustration:then-dimensionalspaceistermedahyperspace.Manyofthedesignalgorithmsto