二维弹性薄体问题的虚边界元法  

Virtual boundary element method for 2D thin body in elastic problems

作　　者：屈文镇[1] 袁飞[1] 张耀明[1] 

机构地区：[1]山东理工大学理学院,山东淄博255091

出　　处：《山东理工大学学报（自然科学版）》2012年第3期64-67,共4页Journal of Shandong University of Technology:Natural Science Edition

基　　金：山东省自然科学基金资助项目(ZR2010AZ003)

摘　　要：拓展了虚边界元方法的应用范围,将其应用于二维弹性薄体问题,避免了奇异边界积分和几乎奇异边界积分的计算.通过数值算例验证了虚、实边界的距离公式,公式的特点是距离与边界离散单元数有关,表明公式对于二维薄体结构同样适用.按照张耀明等虚边界元法的理论分析公式选择虚、实边界间的距离,即使结构狭窄到纳米级(10-9 m),依然可获得高精度的数值解.In this paper, virtual boundary element method （VBEM） is used for dealing with 2D thin body problems in elastic theory, which extends the application field of VBEM. It should be noted that the evaluation of singular and nearly singular integrals is also avoided successfully. For VBEM, the choice of distance between virtual boundary and real boundary is a key problem and may greatly affect the accuracy of the results. Some of the existing formulas, which are related with the number of discrete elements on the boundary, are further verified by numerical exam- ples. Numerical experiments show that fairly high accuracy of numerical results can be achieved by utilizing the formula of distance between virtual and real boundary, even when the structure is narrowed down to the nano （10-9m） scales, which sufficiently indicates that VBEM is suitable for solving 2D thin body problems.

关 键 词：虚边界元法 弹性问题 薄体 

分 类 号：O342[理学—固体力学]