A Lanczos Algorithm For Eigenvalue Analysis Of Multi-level Substructure

With the rapid development of modern engineering and technology, the system of structures has become more and more complex and huge, such as airplanes, marine ships, high buildings, large machines and spaceships etc.. The systems modeled by conventional finite element method usually include millions of degree of freedom (DOF). For such huge and complex systems, it is very difficult or even impossible to compute the eigenvalues by using classic eigensolution algorithms. To solve the problem, the dynamic substructure method was proposed to deal with the computation of dynamic characteristics for large-scale structures. However, due to some approximating assumption, the numerical precision of conventional dynamic substructure method, such as the modal synthesis techniques, is unsatisfactory. A multi-level substructuring technique based on the tree travelling strategy was proposed for solving the dynamic problems of super large-scale structures lately, and had good accuracy and efficiency. In this thesis, a combined method of multi-level substructuring technique and Lanczos algorithm is developed to solve eigenvalue problems of the super large-scale and complicate structures.Differing from the traditional dynamic substructure method, the proposed method in this thesis is to apply the tree traveling strategy to the Lanczos iteration process, which contains the inverse iteration, the orthogonalization and the model standardization. Since the contribution of all internal DOF of each substruture to the dynamic characteristics of overall structure is considered, the accuracy of the proposed method is the same as the result that would be achieved by solving the overall structure. The proposed method is able to solve the eigenvalues of super large-scale structures with high efficiency, less computational cost and robust stability. With the technique of scaling of stiffness and mass, it is more convenience to analyze the characteristics of each substructure. The results are independent of the substructure partitioning scheme, and the finite element modeling has great flexibility.The primary work of this thesis is implemented on JIGFEX Software System, which was developed by Institue of Mechanics Engineering of Dalian University of Technology. Some examples are given to show that the solutions obtained by the proposed multi-level substructuring method are in reasonable agreement with the overall structure solution.