二点接触单元法及其数值验证

TWO-NODE CONTACT ELEMENT METHOD AND ITS NUMERICAL VALIDATION

提出了二点接触单元法的概念及构造方法,推导了相应的刚度矩阵方程。二点接触单元是由2个节点(即一个接触点对)及其相应的影响域构成。每个接触单元的节点力大小只决定于单元自身接触点对的相对位移,而与其他相邻接触点对的相对位移无关。它在插值方式上摒弃了传统节理单元的插值方法,而是采用影响函数进行插值,这样在有限元处理上不必考虑其他接触点对相对位移的影响,这使得接触单元在构造形式上更为简洁,应用上更具灵活性,能够处理较为复杂的节理问题。最后,通过一个简单的节理模型算例,表明该方法是有效的。

A new type of contact element, two-node contact element (TCE), is proposed. The TCE is composed of two nodes and its impacting domain. Because it doesn't use the interpolation method as the traditional joint element does, but employs the impacting function as its interpolation function; it shows considerable flexibility in dealing with the more complex joint cases. It means that the mechanical behavior of one small joint section, which possesses one contacted node-couple, is only determined by the behavior of its own contacted node-couple, and is not related to the behavior of node-couples of other joint sections. The special constitution of TCE makes its application more extensive. TCE stiffness matrix is deduced. At last, the proposed method is employed to model a simple jointed rock mass, then the numerical results from TCE is compared with that from traditional 4-node joint element. The comparison shows that a well agreement exists between the two methods, which indicates that the proposed method is valid and applicable.