一种高精度四面体单元及在汽车设计中的应用

项目名称： 一种高精度四面体单元及在汽车设计中的应用

项目编号： No.11202074

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 何智成

作者单位： 湖南大学

项目金额： 25万元

中文摘要： 在现在的汽车发动机及底盘等复杂三维结构的前期设计中，有限元分析发挥了非常重要的作用，然而在其前处理中，网格剖分工作量巨大。随着四面体单元自动化网格生成技术的出现，四面体单元受到广大工程人员和研究者的关注。但是受到单元精度的影响，四面体的应用还不是很广泛。为了解决以上问题，本项目将基于光滑弱-弱形式，结合有限元，无网格等技术，提出一种高效高精度的新型四面体单元，并应用于汽车零部件的静态分析和振动噪声分析中。本方法采用广义的光滑Galerkin弱形式来离散系统，通过构造新型的积分域，并且通过插值域和积分域相分离，即位移通过关注的节点插值形成，而应变场通过梯度光滑操作在积分域内形成光滑的应变场，从而达到提高单元精度的目的。另外通过刚度矩阵和质量矩阵匹配，进一步提高四面体单元的精度。本项目对于推广四面体单元来降低前处理的工作量，从而达到缩短整车开发周期的目的，为推进汽车行业进步做出积极贡献。

中文关键词： 四面体单元；数值方法；汽车；；

英文摘要： The finite element analysis (FEA) has played a very important role in the early design stage of the complex structure of the vehicle engine and chassis, however, the workload of meshing is very huge in the pre-processing. With the advent of automatic mesh generation for the tetrahedral element, the tetrahedral mesh are of great concern for the engineers and researchers. Due to the over-stiffness of linear elements, the tetrahedron meshes are not widely used in the current. In order to improve the accuracy of the tetrahedron mesh, the project will be construct a new high accuracy and efficiency smoothed tetrahedron element by combining gradient smoothing operation, finite element method and meshfree method. In this method, the generalized smoothed Galerkin weakform is adopted to discretize the domain, the smoothing operaiton is conducted on the new constructed smoothing domain, which serving as an integration unit in assmembing stiffness matrix. The shape functions are constructed using interpolation though a set of nodes located in a local suppot domain, which is different from the intergarion unit. The gradient operaiton can smoothed the discontinuous strain field, and can improve the accuracy of the tetrahedron mesh. In addition, the balance of the stiffness matrix and mass matrix is also studied and optimized

英文关键词： Tetrahedral element；Numerical method；Vehicle；；