中心偏心差分法

Centraleccentric Difference Method

摘要:

提出了构造差分显式位移动力算法的通式,并得到了三步显式位移算法.此法对加速度采用中心差分近似,但对速度采用三点偏心差近似,因此也称为中心偏心差分法.此法可以认为是对中心差分法的改进,克服了中心差分法在计算阻尼矩阵为非对角阵时退化为隐式算法的缺点.中心偏心差分法的算法精度为二阶.对此算法的稳定性进行了分析.分析表明,与同类显式算法相比,本方法具有时间和空间两方面的算法优势.

关键词:显式算法; 中心差分法; 偏心差分

Abstract:

A kind of general explicit displacement algorithm is derived and threestep explicit displacement method with secondorder precision is obtained.The acceleration is approximated by central difference and the velocity is approximated by threepoint eccentric difference.Therefore,this method is also called centraleccentric difference method,which can be looked as an improved form of central difference method because it remians as an explicit method when the damp matrix is not diagonal. The stabilization of this method is analyzed and results show that this method is superior in costs of calculation time and storage space over the other similar explicit methods.

Key words:explicit method; central difference method; eccentric