A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering, School of Engineering and Technology

Thesis (M.Eng.) - Asian Institute of Technology, 2003

The superposition of eigenvectors from subspace and Lanczos eigensolvers was implemented, investigated and yielded accurate response with computational efficiency. A static correction technique accounting for all higher modes as static effects were applied to increase accuracy and stability of the method. A load dependent Ritz vector algorithm was programmed and examined for various types of frames. Those Ritz vectors are proved to account for spatial distribution of loads, only a small number of vectors can approximate the response of the structure. More approachable to practical structures, a nonproportional damping solution by the combination of vector superposition and pseudo force methods was worked out and tested for structures with externally nonproportional damping modeled by discrete dampers. By vector superposition analysis, the real behaviors of the structure under loading are well visualized. The accuracy and operational time of the calculation process can be controlled showing that the vector superposition method is a good choice for dynamic analysis of large structures. Furthermore, originating from the advantages of vector superposition method and from LD Ritz vectors, a nonlinear dynamic analysis algorithm based on Newmark's integration scheme using updated LD Ritz vector basis was proposed and has preliminarily been implemented.