Symmetric Galerkin BEM and FE~BE Coupling for 3D Elastostatic Problems

• Main Authors: Yung-Yen Ko, 柯永彥
• Other Authors: Cheng-Hsing Chen
• Format: Others
• Language: zh-TW
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/93275373758470606983

博士 === 國立臺灣大學 === 土木工程學研究所 === 94 === As compared to the conventional collocation boundary element method (CBEM), the primary advantage of the symmetric Galerkin boundary element method (SGBEM) is the ability to produce a symmetric system matrix. Besides, through the application of the weighted residual method in SGBEM, it becomes easier to regularize the singular integrals and shows better numerical behaviors than the conventional CBEM. In this study, a SGBEM procedure to form linear quadrilateral elements for 3-D elastostatic problems is established. The formulation adopts the form of dual boundary integral equations (DBIEs) based on the Kevin’s fundamental solutions. In order to evaluate the singular double integrals in the SGBEM, including the types of weak, strong or hyper-singularity, techniques of coordinate transformation and mappings of integral domains are utilized in company with the basic properties of kernel functions. Through some numerical examples, the validity of this SGBEM procedure in application to well-supported 3-D elastostatic problems is verified. The coupling of FEM and BEM is a profitable result that exploits the advantages of each. When SGBEM is combined with FEM through appropriate techniques, a symmetric global system matrix can be obtained without ruining the symmetric virtue of the FE part. The FE~BE coupling strategy adopted in this study is to use the free-term components in the SGBEM, so that the equilibrium conditions between the nodal forces on the FE part and the nodal tractions on the BE part are reserved. Nevertheless, when SGBEM is applied to interior or exterior Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid body motion term involved. In this study, discussions on this phenomenon and methods that had been used to remove the rigid-body-motion terms are investigated for the problems modeled with the SGBEM and the FE~BE coupling formulations. For general equilibrated Neumann problems, the rigid body motions can be effectively removed by using these approaches. However, for half-space problems in which the free surface are modeled by limited number of elements, the solutions obtained are still not satisfactory because of the errors introduced from the truncation of the free surface. Among the methods investigated, the one using the modified boundary integral equations based on the Fredholm theory is relatively preferable.