tailieunhanh - The boundary element method with programming for engineers and scientists - phần 7

khu vực giao diện. Có hai cách tiếp cận có thể được thực hiện trong việc thực hiện của phương pháp. Trong lần đầu tiên, chúng ta sửa đổi các thủ tục lắp ráp, vì vậy một hệ thống lớn hơn của phương trình là thu được bao gồm cả các ẩn số bổ sung tại các giao diện. | 294 The Boundary Element Method with Programming region interfaces. There are two approaches which can be taken in the implementation of the method. In the first we modify the assembly procedure so that a larger system of equations is now obtained including the additional unknowns at the interfaces. The second method is similar to the approach taken by the finite element method. Here we construct a stiffness matrix K of each region the coefficients of which are the fluxes or tractions due to unit temperatures displacements. The matrices K for all regions are then assembled in the same way as with the FEM. The second method is more efficient and more amenable to implementation on parallel computers. The method may also be used for coupling boundary with finite elements as outlined in Chapter 12. We will therefore only discuss the second method here. For the explanation of the first approach the reader is referred for appropriate text books2 3. STIFFNESS MATRIX ASSEMBLY The multi-region assembly is not very efficient in cases where sequential excavation construction for example in tunnelling is to be modelled since the coefficient matrices of all regions have to be computed and assembled every time a region is added or removed. Also the method is not suitable for parallel processing since there the region matrices must be assembled and computed completely separately. Finally significant efficiency gains can be made with the proposed method where only some nodes of the region are connected to other regions. The stiffness matrix assembly utilises a philosophy similar to that used by the finite element method. The idea is to compute a stiffness matrix KN for each region N. Coefficients of KN are values of t due to unit values of u at all region nodes. In potential flow problems these would correspond to fluxes due to unit temperatures while in elasticity they would be tractions due to unit displacements. To obtain the stiffness matrix KN of a region we simply solve