【作者】 王悦；

【导师】 兰朋；

【作者基本信息】 哈尔滨工业大学 ， 机械设计及理论， 2018， 硕士

【摘要】 在“工业4.0”与“智能制造”概念的影响下,人们日益关心如何能够将工业生产效率最大化。实现计算机辅助设计(CAD)系统与计算机辅助分析(CAA)系统的“合二为一”便是提高生产效率的解决方法之一。由于传统有限元分析中的单元形函数与CAD系统中的形状基函数不兼容,导致CAA系统中的对几何体的描述只是几何近似而非几何精确,无法完全复现原CAD模型,极大地阻碍了二者的交互,延长产品设计周期。本论文是研究将CAA系统与未来使用T样条作为行业标准的CAD系统的整合方法—基于等几何分析理论,以CAD几何描述为中心,改变CAA系统中的单元形函数,使用以T样条曲面基函数为形函数的等几何有限元—即基于T样条曲面的等几何薄板单元对薄板系统进行离散与分析。建立基于T样条的等几何薄板单元的运动学模型,使用T样条的混合函数作为单元形函数,控制点坐标作为单元节点向量。为表达出柔性体的弯曲变形以及由柯西-拉格朗日应变张量表示的拉伸与剪切变形,需要求解出单元形函数的一阶导数与二阶导数。参考绝对节点坐标法(ANCF),推导出单元广义力向量、质量阵、弹性力以及切线刚度阵,使用该单元对系统进行离散并进行静力学分析与动力学分析,并分别使用Newton-Raphson迭代法和广义-α法对系统方程进行求解。算例表明,等几何薄板单元在求解柔性体变形时有较好的准确性以及单元收敛性,且与绝对节点坐标法相比,该方法同样能够保证较高的准确率。因此可将该单元推广应用于解决大变形柔性多体系统问题。基于上述理论与建模方法,使用基于T样条的等几何薄板单元应用于解决实际工程问题。使用T样条建模带有矩形孔的薄板,并对该薄板进行受平面内拉力时的应力集中问题研究。使用T样条薄板单元对矩形孔周边的危险区域进行局部细化,以较少的单元得到系统最大等效应力,进而求得更为精确的应力集中系数,体现出该单元在整合CAD与CAA方面的优势。更多还原

【Abstract】 Under the influence of the concept of "Industry 4.0" and "Intelligent Manufacturing",people are increasingly concerned about how to maximize industrial production efficiency than before.Combing Computer Aided Analysis(CAA)with Computer Aided Design(CAD)is one of the approaches to improving efficiency.Due to the incompatibility of the traditional FEM’s shape function and the basis function in the CAD system,the description of the geometry in the CAA system is only a geometrical approximation rather than a geometrical accuracy,and the original CAD model cannot be completely reproduced,which greatly hinders the interaction between each other and extends the product design cycle.This dissertation is aimed at the integration of CAA and CAD that,based on the theory of isogeometric analysis,taking the CAD geometric description as the center,changing the element shape function in CAA system to the basis function of CAD geometrical description.Discretization and analysis of thin-plate systems using isogeometric finite elements based on T-spline basis functions as shape functions,ie T-spline based isogeometric thin-plate elements.To establish a kinematic model of thin plate elements based on T-spline surface isogeometry.Use a T-spline blending function to eatablish the element shape function amd use coordinates of control points to be element’s node vector.In order to express the bending deformation,the stretching derfoamation and the shear deformation of the flexible body represented by the Cauchy-Lagrangian strain tensor,the first derivatives and the second derivatives of the element shape function need to be solved.Reference the absolute node coordinate formula(ANCF),element generalized force vector,mass matrix,elastic force,and tangential stiffness matrix are derived.Using this element,the system is discretized,static analysis and dynamics analysis are performed.Newton-Raphson iteration method and generalized-α method are used to solve the system static equations and dynamics equations respectively.The numerical examples show that the accuracy of isogeometric thin plate element in the solution of flexible body deformation and the convergence of the element.Compared with the ANCF,it also can ensure high accuracy.Therefore,this element can be used to solve the problem of large deformation flexible multibody system.With the above all theory and modeling methods,the T-spline based isogeometric thin plate element is applied to solve practical engineering problems.Use T-spline to model a thin plate with a rectangular hole,and to study the stress concentration when the plate is subjected to in-plane tension.Using the T-spline plate element to locally refine the hazardous area around the rectangular hole can obtain the maximum stress of the system with fewer elements,and then obtain a more accurate stress concentration factor,whicn reflects the element’s advantages in integrating CAD and CAA.更多还原