三维接触动力学中的瞬态位移分布

Transient Displacements Distribution in Three Dimensional Contact Dynamics

目的确定瞬态接触过程中接触区以外位移与应力的关系．方法利用Ｌａｐｌａｃｅ变换和二重Ｆｏｕｒｉｅｒ变换研究问题在变换域中的解．用改进后的Ｌａｐｌａｃｅ反演算法证明不同接触区域和不同材料的数值计算都是稳定的．结果与结论发展了三维瞬态接触动力学问题的分析解法，对于给定的相当普遍的接触应力，可以确定接触区域特别是椭圆形接触区域外位移的封闭解析解．还针对不同接触区域的几何特征和常用的５种固体介质材料进行了数值计算。

Aim To determine the relationship between stress and displacement outside the contact domain. Methods\ The Laplace transform and the double Fourier transform were used to study the solution in the transform domain. Some improved algorithms of the Laplace inversion procedure were used to prove all the calculations for different contact regions and materials to be stable. Results and Conclusion\ An analytic solution to three dimensional problem of transient contact dynamics is developed. Based on the solution, contact displacements outside the elliptic contact domain can be determined analytically when the given contact stress is some quite general functions. The correctness of the theorem is also examined by numerical computations for several typical materials and different geometrical characters of the contact domain.