基于刚(粘)塑性流动理论的自然单元法研究  

Natural element method based on flow theory of rigid plastic/viscoplastic mechanics

作　　者：王卫东[1] 赵国群[2] 程钢[3] 马新武[2] 

机构地区：[1]山东大学土建与水利学院工程力学系,济南250061 [2]山东大学模具工程技术研究中心,济南250061 [3]山东建筑大学机电工程学院,济南250101

出　　处：《计算力学学报》2011年第4期596-600,共5页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(50905098);山东省自然科学基金(ZR2010EM032);山东省中青年科学家科研奖励基金(BS2009CL047)资助项目

摘　　要：将自然单元法与刚(粘)塑性流动理论相结合,对自然单元法在金属塑性成形过程数值模拟中的应用进行了研究。采用基于Voronoi图和Delaunay三角化结构的Non-Sibsonian插值方法构造近似速度场向量,实现无网格方法中速度边界条件的直接精确施加,提出了基于刚(粘)塑性流动理论的无网格自然单元法。运用不完全广义变分原理,采用罚函数法实现体积不变条件,推导出基于刚(粘)塑性流动理论的无网格自然单元法的离散控制方程,并给出了基于刚(粘)塑性流动理论的自然单元法及其关键算法,拓展了自然单元法的应用范围。典型算例的数值计算结果表明了该方法的可行性和有效性。The properties of interpolation of nodal data, ease of imposing essential boundary conditions, not needing any user-defined parameters, and the computational efficiency are some of the most important advantages of natural element method. A new method for simulating the metal forming process is given by combining natural element method with the flow theory of rigid plastie/viscoplastic mechanics. Accurate imposition of velocity boundary conditions is accomplished directly by constructing vector of the displacement field by using the non-Sibsonian interpolation method, which are based on the Voronoi diagram and its dual Delaunay tessellation. The discrete governing equations of natural element method are developed by utilizing the generalized variational principle of rigid plastic/viseoplastic materials and accomplishing the incompressibility constraint condition by penalty method. The numerical simulation of a plain strain upset forging reveals the effectiveness and feasibility of the present method.

关 键 词：刚(粘)塑性流动理论 自然法单元法 Non—sibsonian插值 金属塑性成形 数值模拟 

分 类 号：TB24[一般工业技术—工程设计测绘] TG302[金属学及工艺—金属压力加工]