摘要
界面应力的正确评价是分析薄膜涂层材料力学特性的难题之一。利用镜像点法和Dirichlet等值性原理,本文推导了等厚双层薄膜涂层材料受表面集中力作用的平面问题理论解。该显式理论解是以固定在各镜像点上的局部坐标系下的Goursat应力函数的形式给出的。对应于高阶镜像点的应力函数,可通过递推的方法,从对应于低阶镜像点的应力函数求得,而且也易于计算机编程。随着镜像点阶数的增大,它与界面的距离也越来越大,因而相对应的应力函数对界面应力的影响越来越小。最后的算例表明,只需考虑前面有限个镜像点,便可获得足够精度的解。该理论解可作为格林函数,以求解复杂问题的理论解,也可用作边界元法的基本解,提高数值计算的精度和效率。
The evaluation of interfacial stress is one of the difficult problems in determining the mechanical properties of coating material. The theoretical solution of a concentrated force acting on the free surface of coating materials with two same thickness layers has been deduced by introducing mirror point method and Dirichlet uniqueness theorem. This fundamental solution was given by the Goursat stress functions defined under the local coordinate systems with their origins placed at each mirror point. Its found that the stress functions corresponding to the mirror point of higher order can be determined from the lower order ones by recurrence, which is easy for computer programing. The numerical analysis indicates that one can get accurate enough solution by considering only the first several mirror points. This theoretical solution can be used as the Green function to deal with the complicated problems. Moreover, it can also be used as the foundamental solution of boundary element method to improve the accuracy and efficiency of numerical analysis.
出处
《力学季刊》
CSCD
北大核心
2004年第4期457-462,共6页
Chinese Quarterly of Mechanics
基金
国家自然科学基金资助项目(10372058)
关键词
薄膜涂层
理论解
应力函数
镜像点
界面
coating material
theoretical solution
stress function
mirror point
interface
