有初始间隙弹性摩擦接触问题的罚有限元法

针对三维有初始间隙带摩擦的弹性接触问题,提出了一种新的迭代求解方法——罚有限元法。根据接触问题局部非线性的特点,将接触区域的法向非嵌入条件及切向连续性条件作为罚因子引入系统的总势能泛函中,由最小势能原理,得出了求解有初始间隙带摩擦弹性接触问题的罚有限元公式系统。最后通过两个数值算例验证方法的正确性和有效性。

On the Penalty Finite Element Method for Elastic Contact Problems with Friction and Initial Gaps

A new iterative method—penalty finite element method,was proposed for contact problems with friction and initial gaps.Based on the characteristic of local nonlinearity for this problem,the no-interpenetration condition on the normal and the continuity condition on tangent being treated as the penalty terms are introduced into the total potential energy.Then,from the theorem of minimum potential energy,the formula system of solving elastic contact problems with friction and initial gaps by means of penalty FEM is obtained.At last,the validity and accuracy of the proposed procedure was demonstrated with two numerical examples.