混凝土断裂的连续-非连续方法  

CON-DISCONTINUOUS METHOD FOR CONCRETE FRACTURE

作　　者：杜效鹄[1] 段云岭[1] 王光纶[1] 

机构地区：[1]清华大学水利水电工程系,北京100084

出　　处：《固体力学学报》2005年第4期405-413,共9页Chinese Journal of Solid Mechanics

摘　　要：采用有限元形函数作为单位分解函数,位移间断用富集节点的附加自由度表示,建立了允许在单元内部位移非连续的局部富集公式以表征混凝土的开裂区域.富集基函数由节点形函数和节点形函数与间断函数的乘积的并集构成.非连续位移的扩展路径完全与网格结构无关.不同于以非协调应变为基础的嵌入非连续模型,对单元的类型没有限制而且间断位移可以贯穿单元边界.局部富集思想与扩展有限元类似,但富集点自由度保持节点位移的物理意义不变,使相邻单元无需进行富集运算.在变分公式中引入混凝土粘结本构定律,推导了考虑断裂过程区非线性影响的基本方程.对混凝土粘结裂纹扩展的数值模拟说明了该计算方法的有效性.Using finite element shape functions as the partitions of unity, the discontinuous displacement is represented by extra degrees of freedom at enriched node. Local enrichment formulation based on dual overlapping meshes is developed to characterize fracture zone in concrete. The enriched basis is formed from a union of the set of nodal shape functions with a set of products of nodal shape functions and the enrichment function. The crack evolution is completely independent of the mesh structure. Unlike so-called embedded discontinuity＇ models which are based on incompatible strain modes, there is no restriction on the type of finite element and displacement jumps are continuous across element boundaries. Local enrichment idea is similar to XFEM. The physical meaning of the degrees of freedom associated with enriched nodes is still of nodal displacements. Neighbor element does not need enhancement operation. Cohesive constitutive law is introduced into variational principle for describing the nonlinear effects caused by fracture process zone and for forming iterative equations. The effectiveness of the proposed approach is demonstrated by simulations of cohesive crack growth in concrete.

关 键 词：单位分解 富集节点 非连续近似 嵌入非连续模型 扩展有限元 粘结裂纹 

分 类 号：TU528[建筑科学—建筑技术科学]