数值流形位移法在岩体裂缝扩展中的应用
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摘要
基于三角形网格,对裂缝扩展过程中流形单元变化情况进行了深入研究,从几何网格的角度对数值流形方法的连续与非连续统一处理方式进行解读.采用一阶覆盖函数,推导出数值流形算法的权函数表达式,建立局部位移函数.通过数值流形计算程序,得出裂缝尖端位移,并计算尖端应力强度因子.通过经典的中心裂纹板模型,对数值流形位移法求得的尖端应力强度因子进行验证,算例的数值解和解析解吻合度较高,证明数值流形法计算裂缝扩展的准确性,为裂纹扩展过程中尖端应力强度因子的求解提供了新的数值解法.
Based on the finite element triangle mesh,the changing of manifold elements in crack propagation process was studied in depth,and the continuous and discontinuous unified processing of the numerical manifold method are interpreted from the perspective of geometric mesh. The first-order coverage function was used to derive the weight function expression of numerical manifold algorithm,so that the local displacement function can be established. Through the numerical manifold calculation program,the crack tip displacement was obtained,and the tip stress intensity factor was calculated and verified by the classical cracked plate model. The numerical result is in good agreement with the analytical solution,which proves the numerical manifold method is accuracy and can be used as a new numerical solution for solving the tip stress intensity factor in the crack propagation process.
Based on the finite element triangle mesh,the changing of manifold elements in crack propagation process was studied in depth,and the continuous and discontinuous unified processing of the numerical manifold method are interpreted from the perspective of geometric mesh. The first-order coverage function was used to derive the weight function expression of numerical manifold algorithm,so that the local displacement function can be established. Through the numerical manifold calculation program,the crack tip displacement was obtained,and the tip stress intensity factor was calculated and verified by the classical cracked plate model. The numerical result is in good agreement with the analytical solution,which proves the numerical manifold method is accuracy and can be used as a new numerical solution for solving the tip stress intensity factor in the crack propagation process.
引文
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[7]Zheng H,Xu D D. New strategies for some issues of numerical manifold method in simulation of crack propagation[J]. International Journal for Numerical Methods in Engineering,2014,97(13):986-1010.
[8]Zheng H,Liu F,Du X L. Complementarity problem arising from static grow th of multiple cracks and M LS-based numerical manifold method[J]. Computer Methods in Applied Mechanics and Engineering,2015,295:150-157.
[9]Yang Y T,Zheng H. A three-node triangular element fitted to numerical manifold method w ith continuous nodal stress for crack analysis[J]. Engineering Fracture Mechanics,2016,162:51-75.
[10]任中俊,陈跃欣.有限大平板中心裂纹应力强度因子分析[J].矿业工程研究,2013(28):1-3.(Ren Zhong-jun,Chen Yue-xin. Investigation of stress intensity factor of centre crack in finite plate[J]. Mineral Engineering Research,2013(28):1-3.)
[11]徐慧,伍晓赞,程仕平,等.复合裂纹的应力强度因子有限元分析[J].中南大学学报(自然科学版),2007,38(1):79-83.(Xu Hui,Wu Xiao-zan,Chen Shi-ping,et al. Finite element analysis of stress intensity factor in composite mode crack[J]. Journal of Central South University(Science and Technology),2007,38(1):79-83.)
[2]Shi G H. Manifold method of material analysis[C]//The9th Army Conference on Applied M athematics and Computing. M inneapolis,1991:57-76.
[3]Shi G H. Manifold method[C]//Proceedings of the First International Forum on DDA and Simulations of Discontinuous M edia. Berkeley,1996:52-204.
[4]Shi G H. Numerical manifold method[C]//Proceedings of the Second International Conference on Analysis of Discontinuous Deformation. Kyoto,1997:1-35.
[5]王水林,葛修润.流形元方法在模拟裂纹扩展中的应用[J].岩石力学与工程学报,1997,16(5):405-410.(Wang Shui-lin,Ge Xiu-run. Application of manifold method in simulating crack propagation[J]. Chinese Journal of Rock Mechanics and Engineering,1997,16(5):405-410.)
[6]Liu Z J,Zheng H. Two-dimensional numerical manifold method w ith multilayer covers[J]. Science China Technological Sciences,2016,59(4):515-530.
[7]Zheng H,Xu D D. New strategies for some issues of numerical manifold method in simulation of crack propagation[J]. International Journal for Numerical Methods in Engineering,2014,97(13):986-1010.
[8]Zheng H,Liu F,Du X L. Complementarity problem arising from static grow th of multiple cracks and M LS-based numerical manifold method[J]. Computer Methods in Applied Mechanics and Engineering,2015,295:150-157.
[9]Yang Y T,Zheng H. A three-node triangular element fitted to numerical manifold method w ith continuous nodal stress for crack analysis[J]. Engineering Fracture Mechanics,2016,162:51-75.
[10]任中俊,陈跃欣.有限大平板中心裂纹应力强度因子分析[J].矿业工程研究,2013(28):1-3.(Ren Zhong-jun,Chen Yue-xin. Investigation of stress intensity factor of centre crack in finite plate[J]. Mineral Engineering Research,2013(28):1-3.)
[11]徐慧,伍晓赞,程仕平,等.复合裂纹的应力强度因子有限元分析[J].中南大学学报(自然科学版),2007,38(1):79-83.(Xu Hui,Wu Xiao-zan,Chen Shi-ping,et al. Finite element analysis of stress intensity factor in composite mode crack[J]. Journal of Central South University(Science and Technology),2007,38(1):79-83.)