含SMA复合材料层合板的弯曲和热后屈曲分析

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1、上海交通大学硕士学位论文含SMA复合材料层合板的弯曲和热后屈曲分析姓名：刘俊申请学位级别：硕士专业：固体力学指导教师：孙国钧20060201上海交通大学硕士学位论文摘要摘要现对板的弯曲变形控制。热后屈曲问题研究了在均匀热场作用下的含SMA复合材料层合板的热后屈曲行为。采用Shen和Lin提出的摄动-Galerkin混合法，得到了其热后屈曲平衡路径。应用热后屈曲平衡路径公式，通过计算分析了SMA铺设方向、SMA铺设方式、层合板叠层顺序对板的热后屈曲行为的影响。分析表明，SMA丝能够有效实现对板的热屈曲临界温度和热后屈曲变形控制。关键词：形状记忆

2、合金，恢复力线性化模型，复合材料板，弯曲，热后屈曲II上海交通大学硕士学位论文摘要ABSTRACTTHEANALYSISOFDEFLECTIONANDTHERMALPOST-BUCKLINGOFCOMPOSITELAMINATEDPLATESEMBEDDEDWITHSMAWIRESABSTRACTEmployingtheoreticalanalysisandincorporatingwithnumericalcomputation,deflectionandthermalpost-bucklingofcompositelaminatedpla

3、tesembeddedwithshapememoryalloy(SMA)wiresareanalyzed.AndhowtouseshaperecoverystressofrestrainedSMAwirestocontrolthebendingdeflection,criticalthermalbucklingtemperatureandpost-bucklingdeformationoftheplatesismainlydiscussed.Firstly,Brinson’sone-dimensionalconstitutivemodelfo

4、rSMAisgiven.Basedonhisconstitutivemodel,arecoveryforcelinearconstitutivemodelisproposedforfullyrestrainedSMAwire.UsingBrinson’snonlinearmodelandtherecoveryforcelinearmodelrespectivelytocalculatetherecoverystressofSMAandplotcorrespondingstress-temperaturerelationgraphs,twoII

5、I上海交通大学硕士学位论文摘要ABSTRACTresultsarecompared.Thelittledifferencebetweenthetworesultsprovesthattherecoveryforcelinearmodelhasnotonlysimplicitybutalsohighprecision.Secondly,basedonmicromechanicallawofcompositematerialsandBrioson’sone-dimensionalconstitutivemodel,aconstitutiverel

6、ationforcompositelaminatedplatesembeddedwithSMAwiresisderived.Finally,deflectionandthermalpost-bucklingofcompositelaminatedplatesembeddedwithSMAwiresareanalyzedrespectively.Small-deflectionbendingofcompositelaminatedplatesembeddedwithSMAwiressubjectedtocombinedmechanicalloa

7、danduniformtemperatureloadingisfirstanalyzed.UsingLevy’smethod，small-deflectionbendingdeflectionexpressionoftheplatesisderived.Thenbyusingtheexpression,theeffectsofvariousfactorsonthebendingdeflectionoftheplatesareanalyzed,whichincludevolumefractionofSMA,initialstrainofSMA,

8、andSMAembeddingtheplatessubjectedtodifferentamountoftransverseload.Thebendingdefle