双因子显式二阶积分法  

DOUBLE FACTOR SECOND-ORDER EXPLICIT INTEGRATION METHOD

作　　者：刘慧鹏 刘付钧 周福霖[1] 傅向荣[3] LIU Hui-peng;LIU Fu-jun;ZHOU Fu-lin;FU Xiang-rong(Earthquake Engineering Research&Test Center,Guangzhou University,Guangzhou 510006,China;RBS Partners S&T Co.Ltd,Guangzhou 510180,China;Department of Civil Engineering,China Agricultural University,Beijing 100083,China)

机构地区：[1]广州大学工程抗震中心,广州510006 [2]广州容联建筑科技有限公司,广州510180 [3]中国农业大学土木工程系,北京100083

出　　处：《工程力学》2025年第1期20-31,共12页Engineering Mechanics

基　　金：国家重点研发计划项目(2019YFE0112500);国家自然科学基金重大研究计划项目(51778163);国家自然科学基金项目(11672362,11472014)。

摘　　要：研究了一类超收敛的显式二阶积分方法。该方法从哈密顿体系动力相场出发,利用二阶泰勒展开式,构造了动力时程分析迭代算法的基本格式。采用高斯积分处理在迭代步内荷载项的积分,并引入超收敛因子α和β来提高算法的收敛步长和计算稳定性。该方法避免了整体刚度矩阵的求逆和相乘,因此不需要进行整体刚度矩阵的组集,是一种快速的新型动力显式积分法。引入超收敛因子后,该算法可大幅提高收敛步长,可在理论时间步长下稳定收敛。数值算例表明:双因子超收敛显式二阶积分法比传统精细积分法具有更高算法稳定性和精度;在合适分析步长下可与常用积分算法保持一致的精度和稳定性,且随着分析步长的增大具有更好的精度稳定性。A super convergent explicit second-order precise integration method is presented,which establishes the iterative algorithm for dynamic time history analysis base on the second-order Taylor expansion.The Gauss integral is used to deal with the integration of load term in each iteration step,and the super-convergence factor α and β is introduced to improve the convergence and computational stability of the algorithm.The inverse and multiplication of the global stiffness matrix is avoided,so that it is not necessary to assemble the global stiffness matrix and it is a new explicit method for dynamic analysis.This method can be unconditionally stable and greatly improve the convergence step after introducing super-convergence factor.The numerical results show that super-convergence explicit second-order precise integration method has high computational efficiency and algorithm stability compared to traditional explicit precise integration;its accuracy and stability can be consistent with the common integration algorithms under the appropriate analysis time step,with better accuracy stability with the increase of analysis time step.

关 键 词：精细积分 显式积分 超收敛 动力时程分析 哈密顿体系 

分 类 号：TU311.3[建筑科学—结构工程]