摘要
黏弹性人工边界是解决土-结构动力相互作用问题的有效手段之一,但其在分析过程中通常需要进行大量的非线性动力时程计算,效率较低。建立采用黏弹性人工边界求解土-结构动力相互作用问题控制方程求解的高效计算方法,为此,引入隔离非线性法高效求解思想,构造基于隔离非线性法-黏弹性人工边界的非线性土-结构动力相互作用分析模型,推导的动力控制方程在形式上与固定边界的隔离非线性动力控制方程基本一致,仅需将黏弹性人工边界的弹簧-阻尼器元件的刚度直接集成到近场土-结构模型的初始刚度矩阵与阻尼矩阵上即可。此外,结合Woodbury公式与组合近似法提出了改进Woodbury近似法,该改进方法能同时降低控制方程求解的时间复杂度与空间复杂度,实现了黏弹性人工边界求解土-结构动力相互作用问题动力控制方程的高效求解。研究方法同时保留了黏弹性人工边界与隔离非线性法的优点,数值算例验证了所提方法的正确性与高效性。
Viscous-spring artificial boundary is one of the effective means to solve the problem of dynamic soil-structure interaction,but it usually requires a lot of nonlinear dynamic time-history calculation in the process of analysis,and the efficiency is low.This paper aims to establish an efficient calculation method for solving the governing equations of dynamic soil-structure interaction problem with viscoelastic artificial boundary.Therefore,the efficiently inelasticity-separated solve idea is introduced to construct the nonlinear dynamic soil-structure interaction analysis model based on the inelasticity-separated finite element method and viscous-spring artificial boundary.The derived dynamic governing equation is basically same as the governing equation of the fixed boundary that only need to directly add the spring-damper stiffness of the viscous-spring artificial boundary into the initial stiffness matrix and damping matrix of the near-field soil-structure model.In addition,an improved Woodbury approximation method is proposed by combining Woodbury formula with the combined approximation approach,which can reduce the time and space complexity in solving governing equation,and realize the efficient solution of the dynamic governing equation of dynamic soil-structure interaction problem by using viscous-spring artificial boundary.The proposed method retains the advantages of viscous-spring artificial boundary and inelasticity-separated finite element method,and the correctness and efficiency are verified by a numerical example.
作者
李佳龙
任东兴
李志远
LI Jialong;REN Dongxing;LI Zhiyuan(Chengdu Surveying Geotechnical Research Institute Co.,Ltd.,of MCC,Chengdu 610023,China;Earthquake Engineering Research Center,China Institute of Water Resources and Hydropower Research,Beijing 100038,China)
出处
《地震工程与工程振动》
CSCD
北大核心
2024年第4期208-221,共14页
Earthquake Engineering and Engineering Dynamics
基金
国家自然科学基金项目(52038002,52008075)
国家自然科学青年基金项目(52209168,52209157)
四川省自然科学基金项目(2024NSFSC0156)。
关键词
隔离非线性法
黏弹性人工边界
土-结构动力相互作用
改进Woodbury近似法
inelasticity-separated finite element method
viscous-spring artificial boundary
dynamic soil-structure interaction
improved Woodbury approximation approach
