一种显隐式积分方法及其应用

An explicit-implicit integration method and its application

在实际工程结构动力反应分析中,往往由于结构型式十分复杂,常用的两种直接积分方法,即显式积分方法和隐式积分方法,在使用中都存在着一定的局限性,如何将这两种积分方法合理有效地结合起来,是一个十分有意义的研究课题。针对实际工程问题中整体结构计算时间步长的选择往往受局部区域的材料特性、尺寸大小等因素影响的这一现象,提出了一种对结构局部区域进行隐式积分、对其余区域进行显式积分的显隐式积分方法,这种积分格式相对于显式积分格式而言,能显著提高整体结构的计算速度。最后采用两个数值计算实例对这一方法进行验证。

In the dynamic response analysis of practical engineering structures, two direct integration methods commonly used, i.e., explicit integration method and implicit integration method, both have some limitations, especially when structures are complicatedly designed. How to combine them rationally and effectively is a very interesting research field. In this paper, an explicit-implicit integration method is put forward, in which implicit integration is used in local regions of structure, and explicit integration is used in other regions. Because the time step is often influenced by such factors as material characteristics and size of local region, the proposed method can effectively overcome the shortcomings of explicit or implicit integration method and improve calculation speed. Two numerical examples are also given to examine the proposed method.