【作者】 杨志军；

【导师】 陈塑寰；

【作者基本信息】 吉林大学 ， 固体力学， 2006， 博士

【摘要】 拓扑优化设计解决结构设计中最优构造问题,它是结构优化设计中最有潜力、发展最快的领域之一。结构优化过程的两个难点就是灵敏度分析和重分析方法。由于拓扑优化过程中,自由度的变化,使得重分析问题变得非常复杂。此外,在优化中,尺寸优化、形状优化和各种类型的拓扑优化同时发生,使得单纯为某种优化而研究的重分析理论无法满足实际优化计算的需要。本文研究了各类优化过程中重分析问题的统一解法和计算机实施。并结合工程优化设计需要,研究了客车静态拓扑优化问题和大吨位沥青混凝土搅拌设备中振动筛的动态设计问题,提出了相关的优化算法。主要内容有:1)研究了结构参数修改的静态重分析方法,提出了迭代组合近似方法。2)提出了静态拓扑重分析的统一算法,并给出了可扩展的统一算法流程。3)研究了解决重频/密频结构的特征问题重分析方法,提出了构造Neumann级数时的预处理方法,使得重频/密频重分析问题和孤立模态重分析方法实现统一。4)改进了模态拓扑重分析统一算法,也给出了结构修改特征问题重分析方法的统一算法流程。5)结合客车车身结构轻量化课题,研究了多工况下车身顶棚的拓扑优化方法,提出了一种复合单元灵敏度准则和优化方法,避免了“载荷病态”。6)结合国家高技术产业化项目——大吨位系列化间歇式沥青混凝土搅拌设备产业化,研究了振动筛的动态设计技术,提出了一种新的有频率约束的优化方法。并研究了弹簧刚度参数优化方法,提高振动筛的筛分效率。7)结合吉林省科技厅重点项目——汽车结构拓扑优化软件开发,在大型有限元分析软件I-DEAS平台上,给出了结构拓扑修改重分析算法的软件实施。更多还原

【Abstract】 In the optimization process of an engineering structure, we have to modify thestructure and resolve the displacement or generalized eigenproblem repeatedly inorder to achieve an optimal design. The iterative displacement or vibrationanalysis may be expensive for large and complex structures. Thus, it is necessaryto seek a faster computational method for reanalysis. Reanalysis methods areintended to analyze efficiently structures that are modified due to changes in thedesign. The object is to compute the structural solution for such changes withoutperforming the full analysis. The reanalysis methods usually use the originalsolutions of the original structure.There are various reanalysis methods for static and eigenproblems of modifiedstructures. When changes in design parameters are small, the 1st order and 2ndorder perturbation method can give good approximate solutions. For largechanges in the design, the accuracy of the 1st and 2nd perturbation solutionsoften deteriorates, and they may become meaningless. Thus, it is highly desirableto improve the perturbation method in its accuracy for case of large modificationof the structural parameters. To this end, the perturbation combined with theRayleigh quotient is used to improve the accuracy of eigenvalue reanalysis.Recently, the Pade’ approximate and the extended Kirsch combined methodswere used in approximate eigenvalue reanalysis of the modified structures.Topological optimization concerning the topological variations of a structure(number and orientation of elements) is difficult because of changes in thestructural model. The solutions of topological optimization problems are moredifficult because of changes in the structural model. Members and joints aredeleted or added during the solution process and the reanalysis model becomescomplicated. Developing reanalysis procedures for general topologicalmodifications is particularly important when the number of degrees of freedom(DOFs) is modified and the structural response is significantly changed. It seemsthat more efforts are still required in order to implement topologicalmodifications in practical structural design.In this paper, the unified methods of both static and modal reanalysis forstructural topological modifications are disused, and efficient methods arepresented and implement on computers based on general I-DEAS software. Thepaper still forcus on the static and dynamic topological optimization and someeffective methods for topological optimization are developed.In chapter 2, an iterative combined approximate method for static reanalysis ispresented. When the number of iterations is equal to one, the present iterative CAmethod is reduced to the basic CA.In chapter 3, a universal method of structural reanalysis for topologicalmodification is proposed. The presented method is suitable for all three cases oftopological modifications including deletions and additions of members andjoints. In cases when the number of DOFs is increased, it is necessary toestablish the condenced equation by the Guyan reduction such that the newdegrees of freedom are included in the analysis model. The procedure isbasically an approximate two-step method. First, the newly added degrees offreedom (DOFs) are assumed to be linked to the original DOFs of the modifiedstructure by means of the Guyan reduction so as to obtain the condensedequation. Second, the displacements of the original DOFs of the modifiedstructure are solved by using the static reanalysis method discussed in chapter 2.And the displacements of the newly added DOFs resulting from topologicalmodification can be recovered.In chapter 4, the eigensolution reanalysis is discussed. The forcus mainly onextended Kirsch combined method, and selection of the basis vector for thecombined method is proposed. In case of the repeated (or closed) eigenvalue, theeigenvectors of the orinal structure have been recalculated according to theincreasment of the stiffness matrix and mass matrix. As a result, theeigensolution reanalysis method of both repeated and distinct eigenvalue systemcan be deal with in the same way.In chapter 5, a unified method for structural modal reanalysis for three cases oftopological modifications is presented. In this method, the newly added degreesof freedom (DOFs) are linked to the original DOFs of the modified structure bymeans of the dynamic reduction so as to obtain the condensed equation.Furthermore, the extended Kirsch method is used to improve the accuracy of thestarting solutions of the initial structure. And then, the eigenvectors of newlyadded DOFs resulting from topological modification can be recovered. At last,the Rayleigh-Ritz analysis is used to evaluate the eigenvalues and eigenvectorsfor the modified structure. In the present method, the expanded basis vectors areformed by direct decomposition of the matrix ( ΔK mm ?λ 0 iΔMmm) and forwardand backward substitution of the manupulation matrix, just avoid the conditionalconvergence when using iterative perturbation method based on the results of theinitial structure and the accuracy is improved with the extended Kirsch method,where the inverse, , was calculated by the Neumannconvergent series.1( ΔK mm ?λ0 iΔMmm)?In chapter 6, the mass of bus structure was minimized using static topologicaloptimization under multiple loading cases. In order to avoid the tedium solutionof mapping and ill loading cases, the sensitivity of stain energy density waspresented. The non-dimensional measure used for identification of the element tobe removed is given. The optimal procedure is described. In the optimal process,the elements of the structure were divided into two groups: optimizable groupand non-optimizable one. And available stiffeners were added to the structure asto form the base structure. The exact solution of base structure is considered theoriginal solution of the reanalysis method. The structure is modified according tothe non-dimensional measurement of each element, and the reanalysis methodpresented by chapter 3 is used to solve the modified structure. The presentprocedure was implemented for the bus structure, and effective results wereobtained.In chapter 7, the dynamic design of mixer is discussed. An ESO like method isdeveloped. In this method, small section elements are added to the mixerstructure to form the base structure, and the element is recovered according to theelement sensitivity. Using the critiral methods, the torsion strength of thevibrational griddle is improved, and the abnormal diagnal vibration is avoided.Also, the efficiency of griddle is improved using spring parameteral optimization.The fact must be noted that the modified structure is sovled using the modalreanalysis method presented in chater 5.In chapter 8, the impletement of topological reanalysis methods are presented.Base on the open architecture of the CAD/CAE/CAM software, the structure ofthe reanalysis methods is developed, and the core commands and modules of theI-DEAS open solution are discussed.更多还原