基于动态特性的箱型梁拓扑优化设计

发布时间：2019-02-13 07:40

【摘要】：箱型梁结构是机械设备中较为常见的承载结构,传统方法设计所得的结构往往比较笨重,市场竞争力低下。本文针对箱型梁结构,基于变密度法理论,在完成静力学拓扑优化问题的分析后,进一步研究了动力学优化问题,在考虑静力性能的同时兼顾其动态特性,编写程序计算优化模型后获得了新的拓扑结构。本文的主要研究内容如下:1、选用了变密度法拓扑理论,通过密度-刚度插值数学模型构建了设计变量与材料属性的关系,建立了描述箱型梁结构拓扑优化的数学模型。2、对于优化过程中常出现的数值问题,采用了不同的过滤函数进行解决,对于动态优化问题中的局部模态问题,通过修改SIMP模型予以解决,优化过程中变量的迭代计算通过OC准则实现。3、基于有限单元法进行箱型梁结构的力学分析,分别选用了四节点矩形单元和八节点长方体单元对二维以及三维连续体结构进行离散处理,推导获得了总体刚度和质量矩阵后,分析了边界条件和载荷的处理方法,完成了静力学参数求解,同时采用MATLAB功能函数、矢量逆迭代法以及子空间法计算了结构的低阶固有频率。4、对于静力学优化问题,建立了最小柔顺度优化模型,通过算例求解了二维结构和三维结构的优化问题并对惩罚因子和过滤半径等参数进行了分析,对特殊的带有规则几何约束结构的拓扑问题和大规模网格划分下的拓扑优化问题也进行了研究。5、关于动力学优化问题,在静力学的研究上建立了位移-基频约束数学模型,并以算例分析了在拓扑寻优过程中位移、基频和结构质量的变化情况,同时对种类繁多的拓扑问题进行了总结,设计了一个简易的界面便于程序的直观便捷使用。本文的研究内容对连续体结构的静力学和动力学拓扑优化具有一定的参考价值,优化获得的拓扑结构可以指导与箱型梁结构相关的工程机械的设计,从而可以提高此类产品的市场竞争力。
[Abstract]:Box girder structure is a common bearing structure in mechanical equipment. In this paper, based on the theory of variable density method and the theory of variable density method, the dynamic optimization problem of box girder structure is further studied after the static topology optimization problem is analyzed, and its dynamic characteristics are taken into account while the static performance is considered. A new topology is obtained after programming the optimization model. The main contents of this paper are as follows: 1. The topological theory of variable density method is used to construct the relationship between design variables and material properties through the density stiffness interpolation mathematical model, and the mathematical model to describe the topology optimization of box girder structure is established. Different filtering functions are used to solve the numerical problems that often occur in the optimization process. The local modal problems in the dynamic optimization problems are solved by modifying the SIMP model. The iterative calculation of the variables in the optimization process is realized by OC criterion. 3. Based on the finite element method, the mechanical analysis of box girder structure is carried out. The four-node rectangular element and the eight-node cuboid element are used to discretize the two-dimensional and three-dimensional continuum structures respectively. After the overall stiffness and mass matrix are derived, the boundary conditions and load processing methods are analyzed. At the same time, the MATLAB function, vector inverse iteration method and subspace method are used to calculate the low order natural frequency of the structure. 4. For the static optimization problem, the minimum compliance optimization model is established. The optimization problems of two-dimensional and three-dimensional structures are solved by an example, and the penalty factor and filter radius are analyzed. The special topology problems with regular geometric constraints and the topology optimization problems under large-scale meshing are also studied. 5. For dynamic optimization problems, the displacement-fundamental frequency constrained mathematical model is established in static mechanics. An example is given to analyze the variation of displacement, fundamental frequency and structure mass in the process of topology optimization. At the same time, various topology problems are summarized, and a simple interface is designed to facilitate the intuitive and convenient use of the program. The research content of this paper has certain reference value for the static and dynamic topology optimization of the continuum structure. The optimized topology structure can guide the design of the construction machinery related to the box beam structure. Thus, the market competitiveness of this kind of products can be improved.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH122

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