Modify The Dynamics Of Structural Topology Re-analysis Methods

Topological optimization of structure can greatly improves structural design. Furthermore, it can save much material than that for certain optimization of structure. Therefore, recent study about topological optimization is a hotspot in the field of optimization of structures. For structural optimization, the procedures are generally iterative and require repeated analysis as the structures are progressively modified. If the whole reanalysis is carried out after every modification, the process of structure optimization will be greatly slowed as a result of huge computational cost of reanalysis especially for large and complex structures. Therefore, it is necessary to put forward fast and easy reanalysis methods of structure optimization so as to enhance the efficiency of structure optimization and speed up the optimization process, which is also one the main content of this dissertation.In this thesis, the methods for solving eigenvalue problems and conventional reanalysis methods are studied firstly. Then, a new reanalysis method for real modal reanalysis of structures subjected to topological modification with added degrees of freedom is presented. This method is composed of the single step perturbation method and the Rayleigh-quotient iteration. The numerical examples show that this reanalysis method is very effective and high-quality.In the following, complex modal reanalysis methods for topological optimization of structures are studied. Aiming at difference between real modal reanalysis and complex modal reanalysis, a new complex modal reanalysis method which is composed of the complex eigenvalue subspace condensation technique and the Rayleigh-quotient iteration for topological optimization of structures is proposed. The numerical examples also show that this complex modal reanalysis method is also effective for topological optimization with added degrees of freedom of structures.