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工程力学  2014 

求解无限域动力刚度矩阵的双渐近算法

DOI: doi:10.6052/j.issn.1000-4750.2012.12.0991

Keywords: 比例边界有限元法,无限域,动力刚度矩阵,双渐近连分式,矢量波

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Abstract:

采用连分式算法可以有效地求解无限域动力刚度表示的比例边界有限元方程,它具有收敛范围广、收敛速度快等优点.该文在高频渐近连分式算法的基础上考虑了低频渐近,发展了一种针对矢量波动方程的双渐近算法.随着展开阶数的增加,双渐近算法可以在全频域范围内快速逼近准确解.引入了系数矩阵?X(i)来增强连分式算法的数值稳定性.通过在高频极限、低频极限时满足动力刚度表示的比例边界有限元方程,建立了递推关系以求得动力刚度矩阵.通过二维半无限楔形体、三维均质弹性半空间数值算例表明,双渐近算法比单渐近算法更稳定、优越.

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