Chapter 8 Matrix displacement method

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1、Chapter8Matrixdisplacementmethod§8-1OverviewWiththedevelopmentofeconomyandadvancesinscienceandtechnologies,structuralanalysisproblemsraisedfromengineeringpracticetendtobelarge-scaleandgetmorecomplex,whichmakesitdifficultforthetraditionalmethodsandmeansofstructuralanalysistobeapplied.The

2、mainobstacleistheprohibitivehugeamountofcalculation.Thus,useofcomputationaltoolsofhighefficiencybecomesthekeytothesolutionsofsuchproblems.Ontheotherhand,rapiddevelopmenthasbeenachievedincomputertechnologyinrecentdecades,whichlaysthefoundationforfundamentaladvancestobeachievedinmethodsof

3、structuralanalysis.Whenusingtheforcemethodordisplacementmethodforstructuralanalysis,amechanicalproblemeventuallytransformsintoasetoflinearalgebraicequations.Thus,useofcomputerizedstructuralanalysisrequiresaunifiedapproachandstepssothatthecomputerprogramcanautomaticallybuildsuchequations

4、.Thisapproachcanbeachievedinsuchawaythat,thestructureisdiscretizedfirstintoelementswithgoverningequationsoftheirmechanicalbehavior.Subsequently,theelementgoverningequationscanbeassembledfollowingthewaythattheelementsareassembledintothestructure,fromwhichthegoverningequationsofthestructu

5、recanbeestablished.Solvingtheseequationsyieldsthecriticalunknownsandthusthestructuralanalysisofthestructurecanbeaccomplished.Theseanalysisprocedurescanbeexpressedconciselyandinastandardizedmannerbymeansofmatrixform,whichisreferredtoasthematrixanalysismethodofstructures.Withsuchahighlyun

6、iformandstandardizedanalysismethod,wecancodifycomputerprogramsofgeneralapplicabilityforacertainclassofproblemssoastoachievetheobjectiveofcomputerizedstructuralanalysis.Thematrixanalysismethodneedstobeestablishedbasedonthetheoryofmechanics.Thisraisestheproblemofthechoiceoftheoreticalbasi

7、s.Whenusingtheforcemethodtoanalyzestaticallyindeterminatestructures,differentprimarystructurescanbeusedforthesamestructure,thustheanalysisproceduresarecoupledwiththechoiceofprimarystructures;whilewhenusingthedisplacementmethod,theformoftheprimarystructureisconstantforacertainst