自适应无网格伽辽金拓扑优化方法研究

发布时间：2018-05-06 21:19

本文选题：无网格Galerkin法 + 自适应　；参考：《三峡大学》2013年硕士论文

【摘要】：随着结构拓扑优化方法和无网格法的不断成熟，将无网格方法应用于结构拓扑优化中是一个研究热点。不断深入研究发现，在无网格法拓扑优化离散和求解的过程中依然会存在诸多的问题，如离散点云现象、棋盘格式、计算不稳定、计算效率低等问题。本文针对无网格法求解效率低的问题，提出基于无网格伽辽金法的自适应方法，并将该方法引入二维结构的拓扑优化中，主要研究内容如下： 1）基于节点应变能梯度的自适应无网格伽辽金法。以节点应变能梯度的大小作为节点加密准则选出需要加密的节点，然后按照一定的节点加密方法完成对需要加密节点的局部细化，再次根据新的节点分布情况进行下一轮的无网格求解，如此循环计算，有效的提高计算的精度。通过多个典型的算例验证了该自适应无网格伽辽金法的有效性。 2）基于上述研究成果，提出以节点相对密度值作为设计变量的自适应无网格伽辽金拓扑优化方法。对于使用无网格方法求解结构拓扑优化时计算效率低，结果存在离散点云及求解困难等问题，在结构拓扑优化无网格离散的过程中，以节点相对密度作为设计变量，以优化后的节点相对密度值作为拓扑优化的节点加密准则，，选出需要加密的节点，然后采用自适应节点加密方法完成对该节点的加密，再次根据新的节点分布进行下一轮无网格拓扑优化计算，直到能得到清晰的拓扑结果为止。算例结果表明，采用本文提出的自适应EFG拓扑优化方法可以减少结构分析和优化的设计变量数目，提高优化效率。 3）将前述研究成果拓展到柔性机构拓扑优化设计领域，进行柔性机构自适应无网格拓扑优化设计。柔性机构是利用自身柔性构件的弹性变形来实现设计功能的一类机械，具有自身运动大变形的特征，因此使用本文前述提出的自适应EFG法进行柔性机构拓扑优化，能满足其几何非线性及求解效率的要求，该方法发挥了无网格无需依赖网格和重构网格的优点，又有效的提高了无网格拓扑优化的求解效率，拓展了本文研究方法的应用领域。本文利用无网格法易于对节点进行加密的特点，提出适用于无网格伽辽金法力学分析和基于节点密度的自适应结构拓扑优化方法。深入研究了自适应节点加密准则、节点加密方法和新增节点设计变量更新方法，通过对多个典型算例的编程计算，验证了该自适应EFG法的正确性和优越性，提高了求解精度和拓扑优化的优化效率，并有效的应用于柔性机构拓扑优化中。
[Abstract]:With the development of structural topology optimization method and meshless method, it is a hot topic to apply meshless method to structural topology optimization. It is found that there are still many problems in the discretization and solution of meshless topology optimization, such as discrete point cloud phenomenon, chessboard format, unstable computation, low efficiency and so on. In this paper, an adaptive method based on meshless Galerkin method is proposed to solve the problem of low efficiency, and the method is introduced into the topology optimization of two-dimensional structure. The main research contents are as follows: 1) Adaptive meshless Galerkin method based on nodal strain energy gradient. The size of the strain energy gradient of the node is used as the encryption criterion to select the nodes that need to be encrypted, and then the local refinement of the nodes needed to be encrypted is completed according to a certain node encryption method. Based on the new node distribution, the next round of meshless solution is carried out, so the calculation accuracy can be improved effectively. The effectiveness of the adaptive meshless Galerkin method is verified by several typical examples. 2) based on the above research results, an adaptive meshless Galerkin topology optimization method with the relative density of nodes as the design variable is proposed. For the problems of low computational efficiency, discrete point cloud and difficulty in solving structural topology optimization using meshless method, the relative density of nodes is taken as the design variable in the process of structural topology optimization without meshless discretization. Using the optimized relative density value of the node as the topology optimized node encryption criteria, select the node to be encrypted, and then use adaptive node encryption method to complete the encryption of the node. The next round of meshless topology optimization is carried out again according to the new node distribution until clear topological results can be obtained. The numerical results show that the proposed adaptive EFG topology optimization method can reduce the number of design variables for structural analysis and optimization and improve the optimization efficiency. 3) the research results are extended to the field of topology optimization design of flexible mechanism, and adaptive meshless topology optimization design of flexible mechanism is carried out. The flexible mechanism is a kind of machinery which realizes the design function by using the elastic deformation of its own flexible members. It has the characteristics of large deformation of its own motion. Therefore, the adaptive EFG method proposed in this paper is used to optimize the topology of the flexible mechanism. This method can satisfy the requirements of geometric nonlinearity and solving efficiency. This method takes advantage of meshless and meshless without relying on meshes and reconstructing meshes, and improves the efficiency of solving meshless topology optimization effectively, which expands the application field of this method. In this paper, the meshless method is used to encrypt nodes easily, and a new adaptive topology optimization method based on node density is proposed for the meshless Galerkin method. The adaptive node encryption criterion, node encryption method and new node design variable updating method are deeply studied. The correctness and superiority of the adaptive EFG method are verified by programming calculation of several typical examples. It improves the accuracy and efficiency of topology optimization, and is applied to the topology optimization of flexible mechanism effectively.
【学位授予单位】：三峡大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TH122

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