温度场及温度应力模拟的高阶非连续变形分析方法  

High-order discontinuous deformation analysis method for simulation of temperature field and thermal stress

作　　者：徐栋栋[1] 邬爱清[1] 卢波[1] 汪斌[1] 蒋昱州[1] 李聪[1] 刘小红[1] XU Dongdong;WU Aiqing;LU Bo;WNAG Bin;JIANG Yuzhou;LI Cong;LIU Xiaohong(Key Laboratory of Geotechnical Mechanics and Engineering of Ministry of Water Resources,Changjiang River Scientific Research Institute,Wuhan,Hubei 430010,China)

机构地区：[1]长江科学院水利部岩土力学与工程重点实验室,湖北武汉430010

出　　处：《岩石力学与工程学报》2019年第S02期3595-3602,共8页Chinese Journal of Rock Mechanics and Engineering

基　　金：国家重点研发计划(2018YFC0407002);国家自然科学基金资助项目(51879014,51579017)。

摘　　要：对于某些岩体工程问题,如核废料地下存储,温度应力是必须考虑的一个重要影响因素,因为它可能会导致岩石发生破裂而带来危害性后果。传统非连续变形分析方法(DDA),作为岩体稳定分析的主流数值方法之一,尚无法模拟岩体内部的温度场和温度应力分布。针对这一情况,通过在DDA块体外覆盖一等边三角形来构造块体上的高阶位移函数和高阶温度场函数,辅之以强制位移连续和温度场连续的接缝单元,建立可用于模拟温度场及温度应力分布的高阶非连续变形分析方法。该方法建立起DDA与基于单位分解的有限元法(FEM)之间的联系,可直接借鉴FEM成熟的温度场及温度应力数值分析理论。最后,将所建立的非连续变形分析方法应用到解析算例的温度场和温度应力数值求解中。结果表明,模拟结果与解析解非常接近,具有较高的精度。证实了所提方法的正确性及有效性。For some rock engineering problems,such as underground storage of nuclear waste,thermal stress is an important factor to be considered,because it may lead to rock fracture and bring harmful consequences.Traditional discontinuous deformation analysis method(DDA),as one of the main numerical methods for stability analysis of rock mass,cannot simulate the distribution of temperature field and thermal stress in rock mass.In order to solve this problem,a high-order discontinuous deformation analysis method for simulating the distribution of temperature field and thermal stress is established by constructing higher-order displacement function and higher-order temperature field function on DDA block covered by an equilateral triangle outside it,supplemented by joint elements used to force the continuities of displacement and temperature between blocks.This method has established the relationship between DDA and partition of unity based finite element method(FEM).The mature theory of FEM in the simulation of temperature field and thermal stress can be directly used for reference.Finally,the established discontinuous deformation analysis method is applied to the numerical solution of temperature field and thermal stress in the analytical examples.The results show that the simulated results are very close to the analytical solutions and have very high accuracy.The correctness and effectiveness of the proposed method have been verified.

关 键 词：数值分析 温度场 温度应力 非连续变形分析 有限元法 接缝单元 

分 类 号：O241[理学—计算数学]