Research Of Structural Topology Modification Reanlysis Algorithm And Optimization Algorithm

With the rapid development of space, shipbuilding, automotive industry and civil engineering in China, the structural design is becoming more and more complex. The analysis and optimization of complex structures can not be solved by the traditional design method any more. The generation of CAE technology has made up this contribution. CAE is becoming a necessary process and step in structural design, and it is becoming more and more useful and common. With the structural model growing, the cost of the CAE computations is increasing. As the most familiar process in the structural design, the structural topology modification and optimization are becoming more important.This thesis is supported by National Natural Science Foundation of China"Fast Optimization of Cross-Sectional Parameters for Simplified Car Body Multi-Elements Frame Structure Based on Reanalysis Theory"(No.50975121), Specialized Research Fund for the Doctoral Program of Higher Education"The Research of Adaptive Reanalysis Algorithm of the Defective Vibration System"(No.20090061110022) and FAW Group Science and Technology Innovation Project"The Multi-Optimization Platform for Car-Body Performance"(No.0837and093715). The structural dynamic reanalysis algorithm is generated, and the applications of the reanalysis method in structural dynamic modifications and structural optimizations have been discussed in this thesis.Based on even lines Epsilon accelerated method, structural topological modifications reanalysis are used in the thesis. The newly added degrees of freedom are assumed to be linked to the original DOFs of the modified structure by means of the Guyan reduction so as to obtain the condensed equation. The displacements of the original DOFs of the modified structure are solved using the even lines Epsilon accelerated method. And the displacements of the newly added DOFs resulting from topological modification can be recovered. In order to illustrate the application of the present method, the present method is applied to a numerical example. The numerical results show the exactitude and effectiveness of the presented reanalysis algorithm.The influence of numbers of basis vectors in the CA (Combined Approximations ) method is discussed in this thesis. The advantage of hybrid programming of C++ and MATLAB is both the powerful function of character operating in C++ language and the convenience of matrix treatment in MATLAB. As the result, the mix-language programming is applied in structure reanalysis using combined approximations method. It is efficient and convenient to reanalyze the structure by running the application in ANSYS, thus the secondary development of ANSYS is achieved. At the same time, it provides a powerful approach to reanalyze large-scale structures.This thesis introduces the concept of homotopy in topology theory to the theory of matrix perturbation, and thus attempts to solve the eigenvalue problems of defective systems with the application of homotopy perturbation theory, which provides a new access of research to the problems of structural dynamic modification of defective systems.We change the size of the amount of structural modifications via adjusting the perturbation parameter, then calculate the eigenpairs of the modified structure by the second-order perturbation of matrix method and the homotopy perturbation method, respectively. The results show that the homotopy perturbation algorithm has higher accuracy than the second-order perturbation algorithm, and with the increase in the amount of structural modifications, the advantages of homotopy perturbation is more significant.We solve the eigenvalue problems of defective systems successfully with the application of the method dealing with bifurcation problems . In the subsequent numerical examples of a defective system , the effectiveness of the algorithm is checked,which accesses to a high precision. In this thesis,a method of generating the initial population of genetic algorithms (GAs) for continuous global optimization by using Orthogonal Experiment Design instead of a pseudo-random sequence is presented. The generated initial population is much more evenly distributed, which can avoid causing rapid clustering around an arbitrary local optimal. We design a GA based on this initial population for global numerical optimization with continuous variables. So, the obtained population is more evenly distributed and the GA process is more robust. We executed the proposed algorithm to solve a multimodal function. The results showed that the proposed algorithm can find globally optimal solutions.