地震作用下水-结构-土动力相互作用分析

该文基于ABAQUS建立了地震作用下水-结构-土系统数值模型,分析了地震动水平和竖向作用时在不同水深条件下水-结构、水-土相互作用对结构、土体和水体响应的影响.结果表明,水平地震动作用下水-土相互作用对系统响应的影响远小于水-结构相互作用,且对水、土、结构响应的影响较小,可忽略不计.竖向地震动作用下水-结构相互作用对系...     

考虑水-结构-土相互作用下深水圆柱的地震响应分析

以水中圆柱体为模型,考虑水?结构?土的相互作用,研究柱体结构在地震和波浪共同作用下的动力响应.采用有限元法将柔性柱体结构离散为欧拉?伯努利梁单元,水?结构相互作用通过附加质量代替,土?结构相互作用通过线性弹簧代替.基于结构自振频率分析,讨论土?结构和水?结构相互作用对结构自振频率的影响.研究土?结构相互作用、地震动水力...     

一种高精度圆柱形人工边界条件:水-柱体相互作用问题

针对水-柱体动力相互作用问题,提出一种用于模拟无限域水体的圆柱形高精度时域人工边界条件。首先,基于三维可压缩水体的波动方程和边界条件,采用分离变量法建立了时空全局的精确人工边界条件;然后,将其动力刚度表示为外域模型和波导模型人工边界条件动力刚度的嵌套形式;之后,应用时间局部化方法得到时间局部的高精度人工边界条件;最后,离散高精度人工边界条件,并将其与近场有限元方程耦合,形成一种能够采用显式时间积分方法求解的时间二阶常微分方程组。数值算例表明:提出的三维圆柱形高精度人工边界条件精确、高效、稳定。     

基于FEM-SBFEM的坝-库水动力耦合简化分析方法

在坝-库水动力流固耦合分析中,比例边界有限元方法（SBFEM）仅需对流固交界面进行离散,就可以模拟半无限域库水,节省了节点自由度个数,具有较高效率。但采用数值方法处理动水压力时得到的附加质量阵为满阵,进行大规模的面板坝弹塑性动力分析时用于求解方程的时间较多。该文根据动水压力附加质量阵的物理意义与分布特点,提出了一种基于FEM-SBFEM的坝与库水的动力耦合简化计算方法,仅需提供一个保留系数β（0 ≤ β ≤ 1.0）即可实现不同程度的动水压力附加质量阵化简,简单易行;将其应用在面板坝与库水的动力弹塑性耦合计算中,建议了β的取值范围,在保证具有良好精度的前提下大幅提高了计算效率。     

地震作用下深厚土层-结构相互作用的高效分析方法

基于黏弹性边界和将场地反应转化为等效地震荷载的有限元直接法是目前进行地震作用下土-结构相互作用分析的常用时程分析方法之一。当土层厚度较深时,整个深厚土层-结构系统的有限元模型自由度数目较多,尤其对于三维问题,计算效率低。该文提出一种高效分析方法,即一维场地反应分析仍然针对整个深厚土层,在后续的土-结构相互作用分析中将土-结构计算模型的底面人工边界从深厚土层底面（基岩面）向上移动到接近结构的位置,通过缩减土-结构相互作用模型尺寸来提高计算效率。采用理论分析与数值算例,通过与采用整个深厚土层的传统土-结构相互作用分析结果对比,说明提出的高效分析方法能够满足精度要求,并且给出底面人工边界位置以及边界条件和地震动输入方式的建议。     

考虑子结构间相互作用的结构地震反应并行计算方法研究

提出一种用于结构地震反应分析的并行计算方法,此方法将被分析的整体结构划分为多个子结构进行并行计算,计算中考虑子结构间的相互作用。此系统中的核心是协调器,用于保证各子结构边界处的变形协调与力平衡。协调器基于柯西-牛顿迭代算法,通过修正边界处的不平衡力与刚度矩阵得到精确的位移数值解。此方法的特点是各子结构完全独立,相互之间只通过标准数据输入与输出接口传递力与位移。以一个包括四个塔楼的复杂结构为例验证了此方法的有效性。该复杂结构被划分为4个子结构进行并行计算,分析结果表明该并行计算方法对于动力弹性时程分析问题可以得到与整体分析一致的解,对于动力弹塑性时程分析问题,当步长足够小的时候,可得到具有足够精度的解。     

动力荷载作用下水-桩-土相互作用简化分析研究EI北大核心CSCD

针对近海结构单桩基础在动力荷载作用下发生复杂的水-桩-土相互作用问题,建立了三维水-桩-土全耦合动力有限元分析模型。土体、桩和水体分别采用实体单元和声学单元模拟,土体截断边界采用滚轴边界条件、水体截断边界采用无反射吸收边界条件,并确定了合理的截断边界位置;以全耦合分析模型计算结果为参考解,系统研究了四种动荷载作用下水-桩不耦合(两者界面自由)和水-土不耦合(两者界面自由)对桩体和海床表面位移和动水压力响应的影响,揭示了不同水深和桩体半径变化下不考虑两种相互作用的影响规律。     

土-结构相互作用下网架结构动力性能研究

采用整体有限元法分析土-结构动力相互作用(SSDI)下网架的动力性能。以大型有限元软件ABAQUS为平台,结合FORTRAN程序实现粘弹性动力人工边界精确施加、土体自重应力平衡及粘弹性边界条件下地震动输入,并通过算例验证有限元计算过程的有效性与合理性;建立地基土-支承体系-网架屋盖相互作用的三维整体模型,分析SSDI对网架结构动力性能影响。研究表明,SSDI使网架结构自振周期较刚性地基下延长且地基土越软周期越长,网架结构自振频率随地基土变软更密集;SSDI使基础底面峰值加速度较自由场地表峰值加速度增大5%~30%,且地基土越软增大幅度越大;SSDI效应可增大网架结构节点加速度及节点水平相对位移,且使网架结构节点水平相对位移随地基土的变软逐渐增大。     

二维土-结构地震动力相互作用时域有限元分析

土与结构动力相互作用是地震工程研究中的一个十分重要的课题。给出了分析地震作用下二维土-结构动力相互作用的时域有限元方法。重点放在如何模拟瞬态波在无穷介质中的传播以及如何实现地震动的输入方面。在给出的有限元过程中,地震动的输入方法以及用于截断无穷介质以获得有限计算域的局部透射人工边界都是基于柱面波动方程推导建立的,这种方法非常简单有效,结合Newmark时间积分法是无条件稳定的,使得时域计算有效而可靠。数值算例验证了这种方法的精度和有效性。     

考虑动力相互作用的地下平面钢框架地震反应分析

建立了一种考虑结构与围岩动力相互作用的地下离壁式框架结构地震反应有限元分析模型,该方法采 用杆系模型模拟框架构件,围岩采用平面应变单元,在人工边界截取问题上采用了多次透射公式。在此基础上,对某拟 建大型地下多跨多层钢结构建筑的地震反应进行了分析,结果表明离壁式建筑设置水平支撑对改善结构构件的内力特 征具有明显的作用。     

基于有限元与宽频快速多极边界元的二维流固耦合声场分析

采用有限元/快速多极边界元法进行水下弹性结构的辐射和散射声场分析。Burton-Miller法用于解决传统单Helmholtz边界积分方程在求解外边界值问题时出现的非唯一解的问题。该文采用GMRES和快速多极算法加速求解系统方程。针对传统快速算法在高频处效率低和对角式快速算法在低频处不稳定这一问题,该文通过结合这两种快速算法形成宽频快速算法来克服。同时该文通过观察不同参数条件设置下,宽频快速多极法得到的数值结果在计算精度和计算时间上的变化,得到最优的参数组合值。最后通过数值算例验证该文算法的正确性和有效性。     

Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods

We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally convergent polyhedral FEM. We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the virtual element method, irrespective of the topology of the element, as long as the shape functions vary linearly on the boundary. Using this connection, we propose a new stable approach to strain smoothing for polygonal/polyhedral elements where, instead of using sub‐triangulations, we are able to use one single polygonal/polyhedral subcell for each element while maintaining stability. For a similar number of degrees of freedom, the proposed approach is more accurate than the conventional SFEM with triangular subcells. The time to compute the stiffness matrix scales with the in case of the conventional polygonal FEM, while it scales as in the proposed approach. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Copyright © 2015 John Wiley & Sons, Ltd.     

任意轴对称荷载作用下的圆杆分析

锚杆与周围介质相互作用问题涉及圆杆在轴对称荷载作用下的应力应变分析，本文提出一种付里叶方法来分析圆杆在任意轴对称荷载作用下的位移场和应力场，而且考虑了付里叶级数中任意两项的耦合。为了验证这一方法的正确性，本文还导出圆杆在均匀轴对称荷载作用下的理论解。分析成果表明所提方法对于任意轴对称荷载作用下的圆杆问题具有相当好的精度，分析时必须考虑付里叶级数中任意两项的耦合作用。     

A semi‐analytical curved element for linear elasticity based on the scaled boundary finite element method

This work introduces a semi‐analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method (SBFEM). This approach adapts the fundamental idea of the SBFEM concept to scale a boundary to describe a geometry. Until now, scaling in SBFEM has exclusively been performed along a straight coordinate that enlarges, shrinks, or shifts a given boundary. In this novel approach, scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction. The derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures. The resulting elements can be coupled to general SBFEM or FEM domains. For elastodynamic problems, computations are performed in the frequency domain. Results of this work are validated using the global matrix method and standard finite element analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

计算圆筒动态应力强度因子的有限元方法与叠加积分方法

本文计算了厚壁筒的动态应力强度因子，研究了有限单元法计算动态应力强度因子的几个主要问题，提供了合理计算方案，本文还提供了计算厚壁筒动态应力强度因子的叠加积分法，方便于各种动态内压下的动态应力强度因子的计算。     

A modified scaled boundary finite element method for three‐dimensional dynamic soil‐structure interaction in layered soil

This paper is devoted to the analysis of elastodynamic problems in 3D‐layered systems which are unbounded in the horizontal direction. For this purpose, a finite element model of the near field is coupled to a scaled boundary finite element model (SBFEM) of the far field. The SBFEM is originally based on describing the geometry of a half‐space or full‐space domain by scaling the geometry of the near field / far field interface using a radial coordinate. A modified form of the SBFEM for waves in a 2D layer is also available. None of these existing formulations can be used to describe a 3D‐layered medium. In this paper, a modified SBFEM for the analysis of 3D‐layered continua is derived. Based on the use of a scaling line instead of a scaling centre, a suitable scaled boundary transformation is proposed. The derivation of the corresponding scaled boundary finite element (SBFE) equations in displacement and stiffness is presented in detail. The latter is a nonlinear differential equation with respect to the radial coordinate, which has to be solved numerically for each excitation frequency considered in the analysis. Various numerical examples demonstrate the accuracy of the new method and its correct implementation. These include rigid circular and square foundations embedded in or resting on the surface of layered homogeneous or inhomogeneous 3D soil deposits over rigid bedrock. Hysteretic damping is assumed in some cases. The dynamic stiffness coefficients calculated using the proposed method are compared with analytical solutions or existing highly accurate numerical results. Copyright © 2011 John Wiley & Sons, Ltd.     

ITERATIVE SOLUTION OF COUPLED FE/BE DISCRETIZATIONS FOR PLATE–FOUNDATION INTERACTION PROBLEMS

In the present paper, a scheme is developed for the coupled FE/BE analysis of a plate–foundation interaction problem, in which the boundary element equations of the foundation are not explicitly assembled with the finite element equations of the plate, but instead an iterative procedure is proposed to obtain the final coupled solution. This iterative scheme preserves the nature of the BE and FE approaches and the coupled procedure can be easily implemented within an integrated FEM/BEM software environment. The scheme also reduces the computer storage requirement and avoids the error introduced by symmetrization of the BE equations. In addition, some important issues related to the scheme, such as convergence conditions and parameter selection, are discussed. A numerical example is provided to illustrate pthe benefits of the scheme. It is noted, however, that the overall performance of the proposed scheme when compared with the conventional direct solution of the unsymmetric equations arising from the explicit coupling of the FE and BE equations, depends on the choice of a free parameter and a matrix contained in the scheme.     

A high‐order approach for modelling transient wave propagation problems using the scaled boundary finite element method

A high‐order time‐domain approach for wave propagation in bounded and unbounded domains is proposed. It is based on the scaled boundary FEM, which excels in modelling unbounded domains and singularities. The dynamic stiffness matrices of bounded and unbounded domains are expressed as continued‐fraction expansions, which leads to accurate results with only about three terms per wavelength. An improved continued‐fraction approach for bounded domains is proposed, which yields numerically more robust time‐domain formulations. The coefficient matrices of the corresponding continued‐fraction expansion are determined recursively. The resulting solution is suitable for systems with many DOFs as it converges over the whole frequency range, even for high orders of expansion. A scheme for coupling the proposed improved high‐order time‐domain formulation for bounded domains with a high‐order transmitting boundary suggested previously is also proposed. In the time‐domain, the coupled model corresponds to equations of motion with symmetric, banded and frequency‐independent coefficient matrices, which can be solved efficiently using standard time‐integration schemes. Numerical examples for modal and time‐domain analysis are presented to demonstrate the increased robustness, efficiency and accuracy of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.