有初始间隙摩擦接触问题的有限元混合法

针对三维有初始间隙摩擦接触问题,提出了一种新的迭代求解方法--有限元混合法。根据接触问题局部非线性的特点,将作用在接触体上的力系分解为外力和接触界面上的接触力,以接触体的位移为基本未知量,而以接触区域局部坐标系下的结点接触力为迭代变量,将非线性接触迭代收缩在可能接触面上进行,把复杂的摩擦接触非线性反映在接触力的变化上,使得迭代计算变得简单易行,并且对于存在多个接触界面的多体接触问题,可以保持柔度矩阵的对称性和稀疏性,大大提高了计算效率。文中首先给出了三维有初始间隙摩擦接触问题的力学模型,推导得出了相应的有限元柔度方程,然后详细给出了迭代求解步骤。最后通过两个数值算例来验证本文方法的正确性和有效性。

Mixed finite element method for contact problems with friction and initial gaps

A new iterative method—mixed finite element method,was proposed for contact problems with friction and initial gaps.Based on the characteristic of local nonlinearity for this problem,the system of forces acting on the contactor was divided into two parts: external forces and contact forces.The displacement of contactor was chosen as the basic variable and the nodal contact force in possible contact region was chosen as the iterative variable,so that the nonlinear iteration process was only limited in the possible contact surface.In this way,the sophisticated contact nonlinearity was shown by the variation of the contact forces.Moreover,in the case of multi-body contact problem,the flexibility matrix is symmetric and sparse.Thus the iterative procedure became easily to be carried out and much more economical.Firstly,the mechanical model for three-dimensional contact problems with friction and initial gaps was presented,and its finite element compliance equations were obtained.And then,the iteration process was given in detail.At last,the validity and accuracy of the proposed procedure was demonstrated with two numerical examples.