摘要
针对大型工程结构动力响应求解效率较低的问题,提出了一种基于减基法的快速求解方法。该方法对动力学方程进行时间域积分构建减基空间,利用Galerkin映射向减基空间进行投影得到减缩方程,利用减缩方程快速求得原系统的逼近解,从而大大提高了动力学方程的求解效率。该方法还考虑了Galerkin映射下的奇异性计算,文中算例验证了该方法的有效性。
An effective method based on the conception of reduced basis method is developed to improve the efficiency of solving for the dynamic responses of large-scale engineering structures. In this method, the dynamic equations are integrated in time field to construct the reduced basis space, and then the Galerkin mapping is employed to conduct projection from the original problem onto the reduced basis space to obtain the reduced equations. Subsequently, the approximate solutions are derived rapidly from the reduced equations. Also,the singularity conditions under Galerkin mapping are taken into consideration. The numerical example in this paper has demonstrated the validity of the proposed method.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2011年第5期671-675,共5页
Chinese Journal of Computational Mechanics
基金
国家973项目(2010CB832705)
国家杰出青年基金(10725208)资助项目
关键词
减基法
有限元
时间积分
Galerkin映射
求解效率
reduced basis method
finite element
time integration
Galerkin mapping
solution efficiency
