比例边界有限元法求解裂纹面接触问题

CRACK FACE CONTACT PROBLEM ANALYSIS USING THE SCALED BOUNDARY FINITE ELEMENT METHOD

比例边界有限元侧面上有任意荷载时,将侧面载荷分解成关于径向方向局部坐标的多项式函数的和,推导给出了考虑侧面载荷存在的新型形函数,并基于该形函数推导了刚度矩阵和等效节点载荷列阵.首次对比例边界有限元法求解裂纹面接触问题进行了研究,运用Lagrange乘子引入接触界面约束条件,推导给出了比例边界有限元求解裂纹面接触问题的控制方程.将裂纹面单元分为非裂尖单元和含有侧面的裂尖单元.在非裂尖单元中的裂纹面,裂纹面作为多边形单元的边界,边界上的接触力可等效到节点上,通过在节点上构造Lagrange乘子,采用点对点接触约束进行处理.对于含有侧面的裂尖单元,在整个侧面上构造Lagrange乘子的插值场,采用边对边接触约束进行处理.对三个不同的接触约束状态下的算例进行了数值计算,通过与解析解及有限元软件ABAQUS计算结果的对比,验证了本文提出的比例边界有限元点对点和边对边接触求解裂纹面接触问题的精确性与有效性.

In the case of arbitrary tractions on the side faces of the crack,a polynomial function of the radial coordinate can be employed to describe the side face loads in the scaled boundary finite element method(SBFEM).The SBFEM new shape function considering the side face loads is presented.The corresponding stiffness matrix and equivalent node load is derived together based on the SBFEM new shape function.The model of crack face contact using the SBFEM is proposed in this paper for the first time.Lagrange's multiplier method is used to establish the contact constraints of contact model between crack faces.The governing equations for the nonlinear surface contact problems in SBFEM is derived,including adhesion contact problems and sliding friction problems.The elements where the crack faces lie are divided into non crack tip elements and the crack tip element.For the former,the crack faces act as the boundary of the SBFEM element,the contact tractions on the boundary can be assigned to the nodes equivalently and the Lagrange's multiplier is applied for the point constraints.For the latter,the interpolation field of Lagrange's multiplier is constructed on the whole side faces.The Lagrange's multiplier is assumed to be linear along the side faces,the segment constraint approach is proposed to optimize the fulfilment of the contact constraints along the crack faces.By comparing the results of the calculation of analytical solution and software ABAQUS on three different numerical contact problems of crack faces,the accuracy and e_ectiveness of the proposed point-to-point and segment-to-segment contact model for fracture surfaces contact problems is verified in this paper.