改进的参数化水平集拓扑优化方法与应用研究

发布时间：2018-03-17 05:32

  本文选题：拓扑优化　切入点：参数化水平集　出处：《华中科技大学》2016年博士论文　论文类型：学位论文

【摘要】：结构拓扑优化是指在给定的设计空间内,寻找满足约束条件并使结构某项或多项性能达到最优的优化设计方法。结构拓扑优化应用领域涵盖了航空航天、汽车工业、生物工程、材料工程、土木水利以及能源工业等,其不仅可以提高结构性能,减轻结构重量,缩短研发周期,还可以应用于传统设计方式无法解决的复杂结构的创新性设计问题。随着计算机技术、有限元方法和力学理论的迅速发展,结构拓扑优化方法得到了一定的发展。基于水平集的拓扑优化方法与传统拓扑优化方法相比,能够实现拓扑和形状的同时优化,且设计结果具有光滑的结构边界和清晰的几何信息,因此得到了广泛的关注和研究。然而传统水平集方法存在的一些缺陷,影响其进一步应用与发展。本文针对传统水平集方法存在的数值计算困难,提出相应的解决措施,并将所提出的方法推广并应用到多工况结构拓扑优化、结构频率响应拓扑优化、挤压成型结构拓扑优化以及多孔材料/结构一体化拓扑优化中。首先,研究了基于参数化水平集的结构拓扑优化方法。为克服传统水平集方法的数值计算困难,提出了基于紧支径向基函数(CSRBF)和离散小波分解(DWT)的参数化水平集方法,构建了基于参数化水平集的结构刚度拓扑优化模型,开展了基于形状导数的敏度分析,设计了基于优化准则法的优化算法,实现了基于参数化水平集的结构拓扑优化设计。在所提出的方法中,紧支径向基函数用于对水平集函数进行插值,保留了传统水平集方法的优点,有效避免了直接求解复杂的Hamilton-Jacobi偏微分方程所导致的数值计算困难,离散小波分解用于压缩紧支径向基函数的插值矩阵,进一步提高了求解效率。其次,研究了参数化水平集方法在多工况结构拓扑优化中的应用。针对该问题的研究现状,结合参数化水平集方法,提出了基于归一化指数加权准则(NEWC)的多目标优化建模方法,消除了载荷病态问题,保证了在Pareto前端非凸时也能找到Pareto最优解。针对子目标权重的确定,提出了基于模糊多属性群体决策(FMAGDM)的权重计算方法,减少了主观因素的影响。首次提出了考虑扩展最优性的多工况结构拓扑优化设计,实现了各子工况下结构柔度和结构体积分数的同时优化,得到了重量更轻的结构。第三,研究了参数化水平集方法在结构频率响应拓扑优化中的应用。针对不同类型的结构频率响应,分别提出了基于参数化水平集的结构全局和局部频率响应拓扑优化方法,保证了光滑的结构边界,并有效地提升了结构的动态性能。针对频带激励下结构频率响应的有限元分析过程,引入了多频拟静力Ritz向量(MQSRV)进行有限元模型降阶,减少了反复调用有限元分析所产生的计算成本。第四,研究了参数化水平集方法在挤压成型结构拓扑优化中的应用。以结构边界和截面两个方面为切入点,研究挤压成型结构拓扑优化技术。针对结构边界问题,采用所提出的参数化水平集方法构建了面向挤压成型工艺的结构拓扑优化模型,保证了最优拓扑结构具有完整的边界几何信息。针对相同截面的设计要求,引入了挤压成型约束,并提出了截面投影法处理挤压成型约束,确保了优化设计结果的可制造性,提高了方法的优化效率。第五,研究了参数化水平集方法在多孔材料/结构一体化拓扑优化中的应用。针对当前材料/结构一体化拓扑优化在计算效率和加工成本方面的问题,提出了一种两阶段的设计方法。在宏观结构布局优化阶段,采用SIMP材料密度插值模型,获得了结构域内的分层材料密度分布;在材料微结构拓扑优化阶段,采用参数化水平集方法描述微结构边界,获得了边界光滑且宏观等效性能各异的材料微结构构型。通过组合两阶段的优化结果,得到了具有多种功能特性的最优材料/结构。第六,将所提出的方法应用于两个实际工程案例。结果表明,所提出方法极大地简化了结构设计流程,提升了结构性能,实现了工程产品的轻量化设计,有效地支持了工程产品的结构优化设计。最后,总结了本文的研究成果及主要创新点,展望了未来的研究工作。
[Abstract]:Topology optimization refers to the design of a given space, for which satisfy the constraint condition and optimization design method of the structure of one or more to achieve optimal performance. The topology optimization application fields include aerospace, automotive industry, biological engineering, materials engineering, civil water and energy industry, it can not only improve the structure performance and to reduce the structural weight, shorten the development cycle, the innovative design of complex structures can also be used in the traditional design method can not be solved. With the development of computer technology, finite element method and the mechanical theory of the rapid development, structural topology optimization method has been developed. Compared with the traditional topology optimization method for topology optimization of level set method based on the topology and shape optimization can be achieved at the same time, and the design results with smooth boundary structure and clear geometric information, so it is widely Attention and study. However, the traditional level set method has some defects, affecting its further development and application. Based on the traditional level set method in numerical calculation, put forward the corresponding measures, and the proposed method is generalized to multi condition topology optimization, topology optimization of structure response frequency, topology integration optimization of extrusion molding and structure topology optimization of porous materials / structures. Firstly, research the topology optimization method of parameter based on the level set. In order to overcome the traditional level set method for numerical calculation of difficulties, proposed based on compactly supported radial basis function (CSRBF) and discrete wavelet decomposition (DWT) parametric level set method based on the parametric structure level set stiffness topology optimization model, the shape derivative sensitivity analysis based on optimization algorithm is designed based on the method of realizing the optimization criterion. The topology optimization design based on parametric level set. In the proposed method, compactly supported radial basis functions for level set function interpolation, retains the advantages of traditional level set method, effectively avoiding the difficulties caused by the direct numerical calculation for solving complex partial differential equations Hamilton-Jacobi, discrete wavelet decomposition for compression compactly supported radial basis function interpolation matrix, further improve the efficiency of the algorithm. Secondly, the application of the parametric level set method in topology optimization under multiple working conditions in the structure. According to the research status of the problem, combined with the parametric level set method, proposed the normalized weighted index (NEWC) criterion based on multi-objective optimization modeling method that eliminates the problem of load sickness, which can find the optimal solution in the Pareto Pareto front-end. Determine the needle on non convex object weight, is proposed based on fuzzy multiple attribute Group decision making (FMAGDM) method to calculate the weight, reduce the influence of subjective factors is put forward for the first time. Considering the extension of the optimality of the topology optimization design of multi working structure, optimize the volume fraction and structure flexibility sub conditions at the same time, lighter structure is obtained. Third, we study the parametric level set response method application of topology optimization in the structure frequency. According to the structure of different types of frequency response are proposed topology optimization method for structural response of global and local parametric level set based on the frequency, to ensure the smooth boundary structure, and effectively improve the dynamic performance of the structure. According to the finite element structure under frequency response band the incentive analysis process, the introduction of multi frequency quasi static Ritz vector (MQSRV) reduced order finite element model, reduces the computation repeatedly calling the finite element analysis generated by the research. Fourth. The application of the parametric level set method in extrusion molding in structural topology optimization. In the two aspects of structural boundary and cross section as the starting point, to study the structure of extrusion molding technology of topology optimization for structure boundary problem, set method to construct the topology optimization model for extrusion molding process using the proposed parametric level, guarantee the optimal topology structure with geometric boundary information complete. According to the requirement of the same design section, introduced the extrusion molding constraint, and put forward the projection section extrusion molding processing constraints, to ensure that the optimization design results of manufacturability, improves the optimization efficiency of the method. Fifth, the application of the parametric level set method in topology optimization of structure integration in porous materials / materials / structures. In view of the current integration of topology optimization in the computation efficiency and the processing cost of the problem, put forward a The design method of two stages. In the macro structure layout optimization stage, using SIMP material density interpolation model, layered material density distribution domain is obtained; in the material micro structure topology optimization stage, using parametric level set method to describe the micro structure of the boundary, the boundary is smooth and the equivalent performance of different material microstructure configuration the optimization results obtained. Combination of the two stage, the optimal material / has a variety of functional properties of structure are obtained. Sixth, the proposed method is applied to two practical engineering case. The results show that the proposed method greatly simplifies the structure design process, improve the structure performance, realize the lightweight design of engineering products the structure optimization design, and effectively support the engineering products. Finally, this paper summarizes the research achievements and main innovation points, the prospect of future research work.

【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TB21
，

本文编号：1623400