Research On Complex Structures Optimum Reanalysis Algorithm And Structure Optimization In Autobody

The purpose of structure optimization is to obtaining the best results under given conditions. Structure optimization usually includes size optimization, shape optimization and topology optimization. Topology optimization aims at finding the optimal distribution of materials in a prescribed design domain and the optimal way of component connection in a discrete structure. The field of the application of structural topology optimization is steadily growing, for the efficient use of structures and mechanical components is more important than that of sizing or shape optimization. An improved structure topology could enhance the structure performance or decrease weight of it, and this lead to more benefit.In structural optimization, we have to modify the structure and resolve the displacement or generalized eigenproblem repeatedly in order to achieve an optimal design. Two difficulties in optimization are reanalysis and sensitivity analysis. In this paper, the methods of both static and dynamic for structural topological modifications are discused, and efficient reanalysis and sensitivity analysis methods are presented.In chapter 2, the methods for structural static reanalysis of topological modifications based on preconditioning Lanczos algorithm is presented. According to the analysis result of original system, three suitable preconditioners are selected and the response of modified structure is gained by Lanczos algorithm. The proposed procedure is easy to implement and suit for three cases of modifications: (a) the number of Degree of Freedom (DOFs) is unchanged; (b) the number of DOFs is decreased; (c) the number of DOFs is increased. And then the modified preconditioning Lanczos algorithm for structural static reanalysis of topological modifications is presented, which based on the preconditioning Lanczos algorithm. In order to get better preconditioner, three suitable preconditioners are selected and modified. After preconditioning and modifying the preconditioner, the condition number of the system matrix is decreased remarkably. The response of modified structure is gained by modified preconditioning Lanczos algorithm. Both the present method and the Lanczos algorithm are applied to numerical examples, respectively. The Convergence of the two methods are compared. The time complexity of present method and CA are compared also. The computational cost is significantly reduced by the proposed method.In chapter 3, the BFGS algorithm for structural static reanalysis of topological modifications is presented. This presented method using the quadratic termination property of the BFGS quasi-Newton algorithm. The proposed procedure is easy to implement and suit for three cases of modifications. According to the analysis result of original system, three suitable approximations of inverse Hesse and starting point are selected. The response of modified structure is gained by the presented method.In chapter 4, a new approach of structural modal reanalysis for topological modifications based on iterative combined approximation method is presented. According to the analysis result of original system, three suitable original matrix are selected and accurate results of modified structure is gained by subspace iteration (SI) algorithm. In the present method, ICA algorithm instead of direct resolve is used to solve the modified systems which reduced the computational cost significantly. In chapter 5, a new method to transform non-classical damped system into classical system with respect to the multi-degree-of-freedom equations and single-degree-of-freedom system is presented. The main idea of the method proposed here lies in introducing a transformation. The transformed problem does get rid of the damping term. Then it analysis the vibration behaviors based on the matrix transfer function in the non-classical system. As it can be seen that the transformed problem has changed the time-varying system into the quasi time-invariant system, it provides a analytical result about characteristic vector shows a better accuracy than before. A matrix function transformation is introduced to reduce a non-viscous damping system which have a complete eigenvector, so that the original non-proportional damped in non-proportionally damped linear vibration complete systems is transformed into a easier set of 2nd-order differential equations which does not possess the damping term. The new set of equations leads to a computational advantage and get rid of the effect of the damping part in solution of eigenproblem. And the generalized modes method of defective systems for eigenvector sensitivity analysis is presented. It is proposed to establish a feature space about generalized modes by using the theory of generalized modes for sensitivity analysis in linear vibration defective systems which does not possess a complete set of eigenvectors in N-space. Simultaneously a brief and rapid algorithm is introduced to calculate the coefficients of the power series expression of generalized modes by gradual and recursive solution.In chapter 6, stiffness criterion are applied to calculate the sensitivity of the whole autobody. Based on the result of sensitivity analyse, Uniform Design is used to arrange tests. The size optimization of parts of body-in-white are implemented. The stiffness sensitivity of the whole structure tends to reasonable after the optimization. The experiment indicated that after appropriate optimization the weight of the vehicle automobile body obviously reduced when the anti-curving and anti-torsional rigidity of the autobody maintained invariable.