奇异积分方程方法在接触压力分析中的应用

总结回顾了奇异积分方程的数值解法,对于第二类奇异积分方程使用分段连续函数法进行了求解;对于两个弹性体接触问题,通过接触体之间的滑移函数和间隙函数,建立求解接触压力的奇异积分方程.分别针对圆柱体与弹性半空间体、抛物线型压头与弹性半空间体、榫头与榫槽3类接触问题,确立奇异积分方程的具体表达式,而后使用分段连续函数方法进行求解,获得接触面上的接触压力.最后将计算所得的接触压力分别与理论解和有限元解进行了对比.对于圆柱体与弹性半空间体接触问题,奇异积分方程法的最大接触压力与理论解和有限元解的相对误差分别为0.3%和0.5%;对于榫头与榫槽接触问题,奇异积分方程方法计算所得的最大接触压力与有限元解的相对误差为1.8%,验证了奇异积分方程方法的有效性. 

Contact pressure analysis by using singular integral equation method

The numerical solution of singular integral equation (SIE) was summarized, the 2nd type of SIE was solved by piece-wise continuous linear function procedurefor two elastic bodies contact, the SIE was deduced by correlating the slip function and gap function between the two bodies. The contact bodies include the cylinder contact with half space body, parabola shape indentor contact with half space body and tenon contact with mortise cases. These equations were solved by using the piece-wise continuous function method, then contact pressure on the contact surface was acquired. The results of SIE analysis were compared with those obtained from contact theory and finite element method (FEM) analysis. For cylinder contact with half space body, the maximum contact pressure of SIE method is compared with contact theory and FEM, the relative tolerance is 0.3% and 0.5% respectivelyfor tenon contact with mortise, the relative tolerance of maximum contact pressure between SIE method and FEM is 1.8%, proving the effectiveness and applicability of SIE method.