基于预估-校正的Generalized-α法及其在非线性结构动力学中的应用  

The predictor-corrector scheme based Generalized-αmethod and its application in nonlinear structural dynamics

作　　者：李志彬 江鹏[1] 潘嘉诚 张群 赵国忠[1] 关振群[1] LI Zhi-bin;JIANG Peng;PAN Jia-cheng;ZHANG Qun;ZHAO Guo-zhong;GUAN Zhen-qun(State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,China;INTESIM(Dalian)Co.Ltd.,Dalian 116023,China)

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,大连116024 [2]英特工程仿真技术(大连)有限公司,大连116023

出　　处：《计算力学学报》2020年第1期28-33,共6页Chinese Journal of Computational Mechanics

基　　金：国家重点基础研究发展计划(613277);国家自然科学基金(11272074)资助项目.

摘　　要：直接积分法是求解动力学方程的一种有效方法。应用一种预估-校正的Generalized-α法对结构大变形动力学问题进行分析求解,并与Newmark法和Bathe法进行对比研究。首先预估当前计算步的解,然后以预估值作为起始值进行非线性迭代计算,并对解不断校正,直到满足收敛条件,进入下一时间步的计算。在保证Generalized-α法性能的基础上,简化了非线性迭代公式,便于编程实现。通过壳和实体的大变形动力学算例,证明了本文方法具有较高的稳定性和精度。Direct integration methods are effective methods in solving dynamic equation.This paper applied a predictor-corrector scheme based Generalized-αmethod for nonlinear structure dynamic equation,and compared it with Newmark method and Bathe method.In this method,the solution of the current computational step is firstly predicted;then,the nonlinear iteration is performed by initializing the solution with the predicted value;the solution is corrected until convergence condition is met,and than the calculation entered the next time step.The method guarantees the performance of Generalized-αmethod;at the same time it simplifies the nonlinear iterations and is easy to implement.Finally,the examples with large deformation shell and solid elements show the proposed method is stable and accurate.

关 键 词：时间积分法 Generalized-α法 预估-校正 结构动力学 

分 类 号：O327[理学—一般力学与力学基础] O342[理学—力学]