The Multi-Domain Spline Fictitious Boundary Element Method And Its Application In Analysis Of High Rise Building Structures

In this thesis, the multi-domain spline fictitious boundary element method is proposed and applied in analysis of high rise building structures. Numerical examples are given to show the accuracy and efficiency of the proposed method. The research work in this thesis can be summarized as follows :1. The method of singular points exterior to domain is reviewed systematically. The classification and comparison of the method as well as its developments and research achievements are introduced in details. The boundary element method, the application of spline functions as well as the new progress in analysis of high rise building structures are also reviewed.2. The multi-domain spline fictitious boundary element method is presented for analysis of elastic plane problems (including isotropic and or-thotropic cases). In the proposed method, the method of singular points exterior to domain and the multi-domain techniques are first used to deduce the non-singular fictitious boundary integral equations. Then the unknown fictitious load functions are expressed in terms of the basic spline functions which are of favourable properties, and the least square segments method is proposed to eliminate the boundary residues. Using the above methods, the numerical solutions to the integral equations can be achieved. The numerical stability and the error estimate of the proposed method are also discussed in this thesis.3. The multi-domain spline fictitious boundary element method is adopted to deduce the lateral stiffness matrices of the plane lateral-force-resistant structures in high rise buildings. The proposed method can be used for static and dynamic analysis of high rise building structures.4. The multi-domain spline fictitious boundary element method is presented for analysis of Reissner plates with non-even elastic supports. The proposed method can be used to analyze the bending problems of thin as well as thick plates under the action of arbitrary loads, and the plates under study can be of different boundary conditions and with arbitrary supports (or without supports) within domain.5. According to the theory deduced in the thesis, the corresponding computer programms are coded in FORTRAN. The programs can deal with elastic plane problems, plate bending problems as well as static and dynamic analysis of plane lateral-force-resistant structures in high rise buildings.