等厚双层涂层材料受切向集中力作用的三维理论解

THREE DIMENSIONAL THEORETICAL SOLUTION OF A TANGENTIAL FORCE ON THE SURFACE OF TWO COATING MATERIALS WITH THE SAME THICKNESS

基于三维弹性问题Papkovitch一般解和半无限体表面受切向集中力作用的基本解,通过利用镜像点方法和Dirichlet等值性原理,推导了等厚双层涂层材料受切向集中力作用的显式理论解。该理论解是以固定在各镜像点上的局部坐标系下的位移函数的形式给出的。由于载荷点通过涂层自由表面和界面的反复映射,可产生无穷多个镜像点,但最后的数值验算表明,我们只需考虑有限个镜像点,即可获得足够精度的解,这不仅说明推导的正确性,而且也表明只有前面几个镜像点的位移函数才对结果有较大影响。该理论解还可用作格林函数,进一步求解复杂问题的理论解。

Based on the Papkovitch＇s general solution of spatial elasticity and the fundamental solution of a semi-infinite body subject to a tangential concentrated force, the theoretical solution of a tangential force acting at the free surface of two bonded dissimilar coating materials with the same thickness has been derived by utilizing rrfirror point method and the Dirichlet uniqueness principle. The solution is expressed by the displacement fimctions defined under the local coordinate systems whose origins are placed at their mirror points individually. There are infinite mirror points because of repeating imaging of the load point through the free surface and the interfaces, but the last numerical analysis indicates that we can get enough accurate solution by taking the first several mirror points into account, which proves the correctness of the theoretical deduction and shows that only the displacement functions corresponding to the first several mirror points have an effect on the accuracy of the solution. The theoretical solution can also be used as the Green Function to deal with more complicated problems.