摘要
针对岩石裂纹开裂扩展问题,将应变光滑技术与连续-非连续细胞自动机方法相结合,构建了非连续裂纹贯穿单元和裂纹尖端单元光滑应变场,提出快速自适应光滑边域连续-非连续细胞自动机方法.构建了裂纹面位移非连续精细表征的非连续增强形函数,建立了裂纹贯穿单元和裂纹尖端单元的光滑应变矩阵求解方法,利用高斯散度定理将单元的区域积分转换为光滑域边界线积分,推导给出了光滑边域连续-非连续细胞自动机应变矩阵计算表达式,并提出了快速自适应更新方法,建立了加速因子随元胞更新而同步更新的自适应加速算法,基于此,最佳加速因子随更新自动获得,收敛速度较传统细胞自动机方法得到极大提高.利用C++编制了分析计算程序,针对多裂纹开裂扩展过程进行了模拟,并与扩展有限元进行了比较.研究发现,光滑边域连续-非连续细胞自动机方法在解的精确性、稳定性和收敛性上较扩展有限元有显著优势.
In order to achieve the optimal convergence and overcome the poor accuracy of the derivatives close to regions of high gradient,the strain smoothing technique is combined with the continuous-discontinuous cellular automaton method to solve the crack propagation in rock.Firstly,the smooth strain fields of the discontinuous crack penetration element and the crack tip element are constructed,then a discontinuous precisely-represented enhanced shape function for crack surface displacements is constructed,the smooth strain matrix is solved using the Gauss divergence theorem,the area integral of the element is converted into a smooth domain boundary line integral,and the calculation expression of the smoothboundary-domain continuous-discontinuous cellular automaton strain matrix is deduced.Secondly,the fast adaptive smooth-edge-domain continuous-discontinuous cellular automaton is proposed,and an adaptive acceleration algorithm is established based on the fast overrelaxation iteration technique,in which the acceleration factor is updated synchronously with the cell updating.Based on mathematical theory,the spectral radius of iteration matrix for the presented method can be approximately obtained by incremental displacements,then the optimal acceleration factor is automatically obtained with the updating,and the convergence speed is greatly improved compared with the traditional cellular automaton method.Finally,the analysis and calculation program are compiled with C++,and the multi-crack propagation process is simulated and compared with the conventional cellular automaton and traditional extended finite element methods,and the accuracy,stability and convergence of the presented method are discussed in different numerical examples;besides,comparisons between the presented method and the conventional cellular automaton and traditional extended finite element methods are given to illustrate the advantages of the presented method.It is found that the smooth-edge-domain continuous-discontinuous cellular automaton method has significant advantages over the conventional finite element method in accuracy,the stability and convergence of the presented method are much higher than the conventional cellular automaton and traditional extended finite element methods,and it can be widely used for larger scale analysis of multiple crack propagation.
作者
唐志丹
晏飞
李云
任玲瑛
汪小宇
罗贞华
马耀
杨皓然
郑虹
Zhidan Tang;Fei Yan;Yun Li;Lingying Ren;Xiaoyu Wang;Zhenhua Luo;Yao Ma;Haoran Yang;Hong Zheng(POWERCHINA Chengdu Engineering Corporation Limited,Chengdu,611130;State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan,430071;The Institute of Hydrogeology and Engineering Geology of Wuhan,Hubei Province Geological Survey,Wuhan,430051;Petroleum Engineering Supervision Center of Southwest Branch Co.,SINOPEC,Deyang,618000;Research Institute of Drilling&Production Engineering Technology,CNPC Chuanqing Drilling Engineering Company Limited,Xi’an,710018;National Engineering Laboratory for Exploration and Development of Low Permeability Oil&Gas Fields,Xi’an,710018)
出处
《固体力学学报》
CAS
CSCD
北大核心
2023年第2期249-263,共15页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金项目(51879261)资助
关键词
应变光滑
光滑应变矩阵
光滑边域连续-非连续细胞自动机
裂纹扩展
增强形函数
strain smoothing
smooth strain matrix
smooth edge domain continuous-discontinuous cellular automaton
crack growth
enhanced shape function
作者简介
通讯作者:晏飞,E-mail:fyan@whrsm.ac.cn.
