基于平面梁单元的分阶段成形结构线形控制方程.pdf

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1、桥梁建设２０１７年第４７卷第４期（总第２４５期）４２BridgeConstruction，Vol．４７，No．４，２０１７（TotallyNo．２４５）文章编号：１００３－４７２２（２０１７）０４－００４２－０６基于平面梁单元的分阶段成形结构线形控制方程１１，２１２但启联，秦顺全，魏凯，许磊平（１．西南交通大学桥梁工程系，四川成都６１００３１；２．中铁大桥勘测设计院集团有限公司，湖北武汉４３００５６）摘要：为探讨分阶段成形结构最终目标线形与无应力状态量的关系，选择目标线形以大地坐标为参照，将外力势定义为外力相对于坐标轴的力势，以单元无应力状态作为起点计

2、算结构总应变能。由势能驻值原理建立结构线形控制方程，该方程根据目标线形可以惟一确定结构中各个单元的无应力状态量，只要保证各个单元按照无应力状态量对应的单元构形进行安装，成形后的线形必将自动逼近目标线形，与具体的成形过程无关。通过数值分析表明，所建立的线形控制方程是准确可靠的，可用于分阶段成形结构的线形控制计算。关键词：平面梁单元；分阶段成形结构；线形控制方程；无应力状态量；无应力构形中图分类号：U４４５；U４４１．５文献标志码：AEquationforGeometricShapeControlofStructureFormedinStagesBased

3、onPlaneBeamElements１１，２１２DANQilian，QINShunquan，W‐EIKai，XULei‐ping（１．DepartmentofBridgeEngineering，SouthwestJiaotongUniversity，Chengdu６１００３１，China；２．ChinaRailwayMajorBridgeReconnaissance&DesignInstituteCo．，Ltd．，Wuhan４３００５６，China）Abstract：Toprobeintotherelationshipbetweenthefinalt

4、argetgeometricshapeandtheun‐stressedstateamountsofthestructureformedinstages，thegeodeticcoordinatesarechosenasthereferenceforthetargetgeometricshape，theexternalforcepotentialisdefinedastheforcepoten‐tialrelativetothecoordinateaxesandbytakingtheunstressedstateoftheelementsasthest

5、artingpoint，thetotalstrainenergyofthestructureiscalculated．Ontheprincipleofthestationarypo‐tentialenergy，theequationforthegeometricshapecontrolofthestructureisestablished．Thee‐quationcandetermineexclusivelytheunstressedstateamountsofthevariouselementsinthestructureaccordingtothe

6、targetgeometricshape．Aslongastheelementscanbeinstalledaccord‐ingtotheelementconfigurationcorrespondingtotheunstressedstateamounts，thegeometricshapeoftheformedstructurewillbeboundtoautomaticallyapproximatethetargetgeometricshapeandwillbeirrelevanttothespecificformationprocessofth

7、estructure．Theanalysisofanu‐mericalexampleshowsthattheequationforthegeometricshapecontrolasestablishedinthispa‐perisaccurateandreliableandcanbeappliedtothecalculationofthegeometricshapecontrolofthestructureformedinstages．Keywords：planebeamelement；structureformedinstages；equation

8、forgeometricshapecon‐trol；unstressedstateamount