转换位移自由度法求解滑动接触问题

A new method for solid contact analysis by transfering displacement DOF space

有限元分析中,一般都是以节点沿坐标轴方向的位移组成位移自由度空间,以单个节点上沿坐标轴方向的位移和等效节点荷载作为边界条件。而接触问题的位移边界条件,一般都采用多个节点位移线性组合的形式,其相应的荷载边界条件则为接触面上的法向接触力和切向摩擦力。本文从广义自由度的概念出发,通过对总刚矩阵进行处理,直接用接触点的位移自由度的组合表征相关节点沿法向和切向的位移自由度,其荷载边界条件亦相应转化为切向和法向荷载,从而可以方便地输入接触边界条件,完成接触分析。采用本文提到的方法,不必增加位移自由度,并可以保证总刚矩阵的对称性和各接触条件的独立性。试验证明,本方法是正确有效的。

A method to analyse the solid contact problem with friction is presented in this paper. The original fundamental vectors of the displacement field in which the direction of every displacement freedom in accordance with the global coordinate is replaced by new fundamental vectors in which the direction of every displacement freedom is in accordance with the contact direction at the node in contact with other surface. Using this method ,no degree of freedom is added as the Lagrange method. The rigid matrix keeps its symmetry along so the difficulty to solve the linear system of equations is not increased. Some tests indicate the method is correct and efficient.