非节点连接有限元及其在加筋结构中的应用

Theory of non-nodal connection finite element methods and its applications in reinforced structures

针对现有加筋结构有限元模型的不足,提出了自由度层次的非节点连接方法。加筋单元的各节点可位于一个或多个其它单元内部,内节点的自由度无需全部与母单元的位移场一致;通过在节点坐标系下对内节点设置独立自由度,可模拟加筋构件与基体材料之间的粘结滑移、无粘结和体外布置等位移不连续性。节点为内节点的单元的刚度矩阵和荷载向量利用虚功原理变换到对应于其广义自由度向量的形式,按照广义自由度的位置向结构整体刚度矩阵和荷载向量组装,以此实现单元间非节点位置的连接。利用开发的有限元软件计算了多个算例,验证了非节点连接方法用于加筋结构有限元建模的正确性和便利性。

Against the flaws in the existing finite element models of reinforced structures,a non-nodal connection method at the level of degree of freedom is put forward:the nodes of reinforcement elements can be embedded into the non-nodal locations of one or more other elements,while the inner-node's DOF does not need to match the parent element's displacement field.By means of introducing independent DOFs for the inner-node on a special coordinates,the displacement discontinuity between reinforcements and matrix materials,such as bond-slip,non-bonded,and disposed external,etc.,can be simulated naturally.When any node of an element is embedded into other element,the element's stiffness matrix and force vector are transformed by using the virtual work principle and assembled according to its generalized DOF vector.A number of problems are calculated by the non-nodal FEM software;the numerical results validate and demonstrate the feasibility and correctness of this method to model and analyze reinforced structures.