Study on Contact Algorithms for the Polygonal Hybrid Stress Element Method
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摘要: 针对单元较小的情况下,现有的非均匀模型难以得到精确应力场和应力集中现象的问题,采用直接约束法,提出了一种基于多边形应力杂交单元的优化接触算法.多边形应力杂交单元在应力函数的构造以及积分区域划分上的优势,使其能适应复杂的模型边界与材料边界,更易划分网格.根据上述理论研究成果编制了完整的计算程序,算例结果发现该方法能够得到粉末压制过程的宏观非线性力学响应、高精度的应力场以及明显的应力集中现象,为复杂优化问题的求解提供了有效手段.Abstract: In the case of small elements, it is difficult to obtain accurate stress fields and stress concentration with existing nonuniform models. An optimization algorithm for the theory of the PHSEM (polygonal hybrid stress element method) was proposed with the direct restriction method. The advantages of the PHSEM in the construction of stress functions and the division of integral regions make it more suitable for complex model boundaries and material boundaries and easier to realize-element meshing. The complete computing program was made according to the theoretical analysis. The results show that, the PHSEM can obtain macroscopic nonlinear mechanical responses, highly accurate stress fields and obvious stress concentration phenomena in the powder compaction process, which provides an effective means for the solution of the complex optimization problems.
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Key words:
- polygonal hybrid stress element /
- direct restriction /
- contact algorithm
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[1] 王曼灵, 王爱涛, 李阳, 等. 基于FEMLIP的全风化边坡失稳破坏全过程的数值模拟研究[J]. 应用数学和力学, 2019,40(3): 269-281.(WANG Manling, WANG Aitao, LI Yang, et al. Numerical simulation of the whole instability and destruction process for fully weathered slopes based on the FEMLIP[J]. Applied Mathematics and Mechanics,2019,40(3): 269-281.(in Chinese)) [2] 江成, 甯尤军, 武鑫. 地应力条件下的凿岩爆破数值模拟[J]. 工程爆破, 2017,23(1): 16-20.(JIANG Cheng, NING Youjun, WU Xin. Numerical simulation of drilling blasting under earth stress[J]. Engineering Blasting,2017,3(1): 16-20.(in Chinese)) [3] TAN Liming, HE Guoai, LIU Feng, et al. Effects of temperature and pressure of hot isostatic pressing on the grain structure of powder metallurgy superalloy[J]. Materials,2018,11(2): 328-338. [4] MINDLIN R D. Compliance of elastic bodies in contact[J]. Journal of Applied Mechanics,1949,16(9): 259-268. [5] MUSKHELISHVILI N I. Some Basic Problems of the Mathematical Theory of Elasticity: Fundamental Equations Plane Theory of Elasticity Torsion and Bending [M]. Springer, 1977. [6] RAHMAN M U, ROWLANDS R E, COOK R D, et al. An iterative procedure for finite-element stress analysis of frictional contact problems[J]. Computers & Structures,1984,18(6): 947-954. [7] 陈文胜, 郑宏. 岩石块体三维接触判断的侵入边法[J]. 岩石力学与工程学报, 2004,23(4): 565-571.(CHEN Wensheng, ZHENG Hong. Detection of 3D rock block contacts by penetration edges[J]. Chinese Journal of Rock Mechanics and Engineering,2004,23(4): 565-571.(in Chinese)) [8] SHI Genhua. Discontinuous deformation analysis: a new numerical model for the statics and dynamics of block system[J]. Engineering Computations, 1992,9: 157-168. [9] UNDERHILL W R C, DOKAINISH M A, ORAVAS G.A method for contact problems using virtual elements[J]. Computer Methods in Applied Mechanics & Engineering,1997,143(3): 229-247. [10] PIAN T H H. Derivation of element stiffness matrices by assumed stress distributions[J]. AIAA Journal,1964,2(3): 1333-1336. [11] 郭然. 颗粒增强复合材料界面脱层和热机疲劳的数值模拟[D]. 博士学位论文. 北京: 清华大学, 2003.(GUO Ran. Numerical simulation of interfacial delamination and thermal-mechanical fatigue of particulate reinforced composites[D]. PhD Thesis. Beijing: Tsinghua University, 2003.(in Chinese)) [12] 赵建才, 郝旺身, 姚振强. 基于直接约束法的密封条与车门之间的接触特性研究[J]. 弹性体, 2005,15(3): 17-20.(ZHAO Jiancai, HAO Wangshen, YAO Zhenqiang. Study on contact characteristics between seal and door based on direct restriction[J]. Elastomer,2005,15(3): 17-20.(in Chinese)) [13] 杜丽惠, 刘先行, 刘宁. 评价高边坡断层的直接约束方法[J]. 清华大学学报(自然科学版), 2005,45(12): 1613-1616.(DU Lihui, LIU Xianxing, LIU Ning. Direct constraint procedure forevaluating faults on steep slopes[J]. Journal of Tsinghua University(Natural Science Edition ), 2005,45(12): 1613-1616.(in Chinese)) [14] FARAHANI K, MOFID M, VAFAI A. A solution method for general contact-impact problems[J]. Computer Methods in Applied Mechanics & Engineering,2000,187(1): 69-77. [15] 李小凯, 郑宏. 基于线性互补的非连续变形分析[J]. 岩土力学, 2014,35(6): 1777-1794.(LI Xiaokai, ZHENG Hong. Discontinuous deformation analysis based on linear complementarity theory[J]. Rock and Soil Mechanics,2014,35(6): 1777-1794.(in Chinese)) [16] 蒲军平. 二维含缺陷弹性体移动和滚动接触的边界元法[D]. 博士学位论文. 北京: 清华大学, 2000.(PU Junping. Boundary element method for moving and rolling contact of 2D elastic bodies with defects[D]. PhD Thesis. Beijing: Tsinghua University, 2000.(in Chinese)) [17] 周书助, 彭卫珍, 杜亨全. YF06纳米硬质合金粉末压制性能的研究[J]. 硬质合金, 2004,21(3): 138-141.(ZHOU Shuzhu, PENG Weizhen, DU Hengquan. The study of the pressing-pepformance of the peg-added and spraryed nanometer cemented carbide powderm[J]. Cemented Carbide,2004,21(3): 138-141.(in Chinese))
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