BEM试题

1272006级硕士研究生考试试题BoundaryElementMethods—TheoryandProgramming边界单元法理论及程序设计1.WhydiscontinuouselementsareusedinBEM?Illustratewhattypesofboundaryconditionsrequiretheuseofthediscontinuouselements.边界单元法中为何要用非连续单元？用图示说明哪些类型的边界条件需要用非连续单元。2.Usingthefollowinginformationtoderivetheboundaryintegralequationforthree-dimensionalpotentialproblems.利用下列信息推导三维位势问题的边界积分方程。Governingequation(控制方程)：02222222iixuxzuyuxuuFundamentalsolution(基本解)：ru413.Usingtheradialintegrationmethod(RIM)totransformthefollowingvolumeintegralintosurfaceintegral.用径向积分法将下列体积分转换成面积分。bduijwhereristhedistancefromsourcepointpixtothefieldpointix(其中r为源点pix到场点ix之间的距离)。)3(41,,2jiijijrrrujjxb1284.Basedonthefollowingprovidedinformation,provethattheintegraltransformationJacobiansJfromatriangularelementtothequadrilateralelementiszeroatthemergednodep.基于下列所提供的信息，证明从三角形单元到四边形单元的积分转换雅可比sJ在合并点p为零。4312PP4371,2,58P6431，p2ddJdds),(),(),(),(),(),(),(),(sJ4141),(),(),(),(NN)1)(1(41),()1)(1(41),()1)(1(41),()1)(1(41),(4321NNNN5.DescribethedistinctfeaturesofBEM.阐述边界单元法的特点。