结构-地基动力相互作用的时域模型

发布时间：2018-05-02 21:34

本文选题：比例边界有限元法 + 结构-地基动力相互作用　；参考：《岩土力学》2014年04期

【摘要】：结构-地基动力相互作用是结构地震响应分析及安全评估的一个非常重要课题。基于比例边界有限元法,提出了一种新颖的结构-地基动力相互作用的时域模型,即采用比例边界有限元子域模拟近场有限域部分,采用高阶透射边界模拟远场无限域部分。通过采用连分式展开和引入辅助变量,有限域的动力方程采用高阶的静力刚度矩阵和质量矩阵表示。高阶透射边界精确满足无限远处的辐射边界条件,具有全局精确、时间局部和收敛速度快等优点。它是基于改进的连分式法求解无限域动力刚度矩阵而建立的,在时域里表示为一阶常微分方程组。通过联立有限域和无限域的运动方程,建立了结构-地基相互作用的标准动力学方程,采用Newmark法可直接求解。3个算例结果表明,该算法在时域里比黏弹性边界更精确、有效。
[Abstract]:Structure-foundation dynamic interaction is a very important subject in structural seismic response analysis and safety assessment. Based on the proportional boundary finite element method, a novel time-domain model of structure-ground dynamic interaction is proposed, in which the near-field finite field part is simulated by the proportional boundary finite element subdomain and the far-field infinite part is simulated by the high-order transmission boundary. By using continuous fraction expansion and introducing auxiliary variables, the dynamic equations in finite field are expressed by high order static stiffness matrix and mass matrix. The high order transmission boundary satisfies the radiation boundary condition at infinite distance accurately, and has the advantages of global accuracy, local time and fast convergence. It is based on the improved continuous fraction method to solve the dynamic stiffness matrix in infinite domain and is expressed as the first order ordinary differential equation in time domain. Through simultaneous finite and infinite motion equations, the standard dynamic equations of structure-soil interaction are established and solved directly by using Newmark method. The results of three examples show that the proposed algorithm is more accurate and effective than the viscoelastic boundary in time domain.
【作者单位】：三峡大学土木与建筑学院;河海大学工程力学系;
【基金】：国家自然科学基金项目(No.51309143) 三峡大学科学基金(No.KJ2013B003)
【分类号】：TU470;TU311.3

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