中文摘要：

为了解决裂纹面可能发生的接触摩擦问题，精确求解裂纹尖端附近应力，提出了一种逐点Lagrange乘子法．将Lagrange乘子逐点转到局部坐标系下，采用Gauss-Seidel迭代法求解法向乘子和切向乘子，并在求解过程中对切向乘子的约束进行修正，待所有点的乘子求解完成后再将其变换到整体坐标系下迭代求解位移．与传统接触算法相比，该算法无需对总刚度阵求逆，降低了求解规模．利用该算法计算了压剪作用下中心裂纹板以及纯剪作用下中心界面裂纹板的应力强度因子，计算结果与已有文献结果吻合良好．随后考察了Comninou接触模型在远场纯剪作用下不同摩擦系数对位移场、接触区和裂尖附近应力场的影响，结果表明，接触对裂尖正应力影响较大，忽略裂纹面接触摩擦作用，应力强度因子可能被高估．

英文摘要：

In order to solve the stress near the crack tip accurately, a new algorithm--point-by-point Lagrange multiplier method （PLMM） for solving the crack contact problem in an infinite plate is proposed. First, the Lagrange multiplier is transformed to a local coordinate system. Then, the itera- tive solution of normal and tangential multiplier forces is solved by using the Gauss-Seidel iteration method and the constraint modification of the tangential multiplier is made. After the calculation of all point multiplier forces completed, they are transformed to a global coordinate system to solve dis- placements iteratively. Compared with the conditional contact algorithms, the PLMM without finding the inverse global stiffness matrix requires less computer storage. The stress intensity factors （SIFs） for the center cracked plate under compression and shear and the center interface crack under shear traction are calculated by the PLMM method, and the calculation results show good agreement with the results in literature. The influences of the friction coefficients on the displacement field, contact zone, and stress fields near the crack tip of the Comninou contact model are studied. The results show that the effect of contact on the distribution of normal stress is great and the SIF may be overes- timated without considering crack surface contact.