共查询到19条相似文献,搜索用时 171 毫秒
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《地震工程与工程振动》2017,(2)
本文依据波速有限物理概念,从一维波动方程柯西初值问题的解析解出发,推广应用一种在空间域上采用Lagrange多项式内插、时间域内精确积分的显式方法;并基于包含7个节点的3层网格离散模型,通过权衡精度和稳定性的要求,构建出时空离散精度皆为6阶的稳定递推格式,且具有显式和时空解耦特性。最后,通过算例进行与本文同源的低阶格式(2阶显式格式、4阶显式格式)的对比分析,验证该6阶显式格式的精度和稳定性等理论结果,指出高阶公式对提高计算效率的价值。 相似文献
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动力方程求解的显式积分格式及其稳定性与适用性 总被引:12,自引:0,他引:12
文献(1)给出了一种求解有阻尼体系动力方程的显式积分格式,文中以数值表格的形式给出了格式的稳定性条件,本文对该格式的稳定性问题作了进一步的分析,并给出了其计算稳定性条件的表示式。本文还着重讨论了基于这一显式积分格式的推导过程而派生出的另一形式的积分格式的稳定性,并指出了该派生格式的适用性问题。 相似文献
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推导出了分析二维粘及弹性场地地形对地震动影响的显式有限元-有限差分方法.这一方法中,首先利用人工边界及有限元离散方法,给出问题分析的有限元离散网格计算力学模型,并利用一种类似于差分方法的有限元方法,建立局部网格节点的动力方程,而后利用笔者提出的有阻尼体系动力方程求解的显式差分格式,及推广的多次透射边界公式,给出网格节点运动量计算的时域显式逐步积分公式.利用计算机程序实现这一方法的计算具有所需计算机内存量小及计算时间量小的优势,而且,这一方法适用于任意地形情况,具有较高的计算精度及较好的计算稳定性. 相似文献
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如何更精确高效地模拟大型、复杂系统内域的波动是发展和完善近场波动数值模拟技术的一个重要研究课题。内域波动的数值模拟通常采用计算量较小的显式方法,但现有的时空解耦显式有限元方法的精度只有二阶;低精度不仅影响数值模拟的精度,而且制约着计算效率的提高。鉴于此,本文旨在探索内域波动数值模拟具有更高精度且稳定的显式方法。作者发展了内域波动数值模拟的现有显式有限元解耦技术,提出了一种高精度且稳定的显式数值模拟方法。 相似文献
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本文将小波有限元法引入到流体饱和多孔隙介质二维波动方程的正演模拟中,以二维Daubechies小波的尺度函数代替多项式函数作为插值函数,构造二维张量积小波单元.引入一类特征函数解决了Daubechies小波没有显式解析表达式所带来的基函数积分值计算问题,并推导出计算分数节点上Daubechies小波函数值的递推公式,从而构造出由小波系数空间到波场位移空间的快速小波变换.数值模拟结果表明该方法是有效的. 相似文献
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本基于有限差分交叠格式和解耦有限元方法的基本概念,以应力-速度为变量,提出了求解波动的应力-速度有限元解耦交叠格式,这一格式不仅时空解耦,而且为显式,它适合于线性及非线性波动问题的数值模拟,已有的应力-速度有限元交叠格式(即格子法)为本的特例。通过解析解数值检验表明,本建议的方法具有较高的精度,而格子法计算精度较低。 相似文献
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有限差分方法因其操作简单、计算消耗低而成为地震勘探领域中最为常用的数值模拟方法之一,然而用离散的显式差分算子数值逼近地震波动方程中的连续导数容易导致数值频散,并且基于正方形网格离散形式的有限差分方法对不同地质模型的适应性较低.针对一阶变密度声波方程的数值模拟,本文发展了一种适用于矩形网格离散形式的时间高阶空间隐式有限差分格式,可以有效压制时间和空间频散,同时灵活的网格剖分增强了其应用的广泛性.基于本文矩形交错网格时间高阶空间隐式有限差分格式的时空域频散关系和变量替换的思想,首先采用泰勒级数展开方法求解不同方向的非轴上时间差分系数及轴上空间差分系数,使本文差分格式可以获得任意偶数阶时间和空间精度.为了进一步提高本文差分格式在更大波数区域的空间模拟精度,我们采用线性优化方法来求取新的轴上空间差分系数用于一阶变密度声波方程的波场迭代求解中.频散、稳定性分析及数值模拟算例表明:相比于传统十字形空间域隐式有限差分格式,本文矩形交错网格时间高阶空间隐式有限差分格式在精度、稳定性和效率方面均具有优势. 相似文献
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地震波传播过程本质上是能量在传播过程中逐步损耗直至殆尽的过程,而在实际应用中,常在无能量损耗假设下,用弹性波动方程或标量波动方程描述它.在哈密顿(Hamilton)体系表述下,地震波传播过程即为一个无限维的哈密顿系统随时间的演化过程.若不计能量损耗,波场演化过程实质上为一个单参数连续的辛变换,因而对应的数值算法应为辛几何算法.本文首先从地震波标量方程出发,给出哈密顿体系下地震波传播的表述,即任意两个时刻的波场是通过辛变换联系起来的.随后,把波场在时间和相空间离散化后,给出了用于波场计算的一些辛格式,如显式辛格式、隐式辛格式和蛙跳辛格式.并进一步讨论了有限差分格式和辛格式的异同.然后,应用显式辛格式和同阶的有限差分方法给出了同一理论速度模型下的波场和Marmousi速度模型下的单炮记录.数值结果表明,辛算法是一类可行的波场模拟的数值算法.在时间步长较小时,有限差分方法是辛算法的一个很好近似.文中的理论和方法,为地震波传播理论及实际应用研究提供了新的途径. 相似文献
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Implementation and application of the unconditionally stable explicit parametrically dissipative KR‐α method for real‐time hybrid simulation 下载免费PDF全文
Chinmoy Kolay James M. Ricles Thomas M. Marullo Akbar Mahvashmohammadi Richard Sause 《地震工程与结构动力学》2015,44(5):735-755
In real‐time hybrid simulations (RTHS) that utilize explicit integration algorithms, the inherent damping in the analytical substructure is generally defined using mass and initial stiffness proportional damping. This type of damping model is known to produce inaccurate results when the structure undergoes significant inelastic deformations. To alleviate the problem, a form of a nonproportional damping model often used in numerical simulations involving implicit integration algorithms can be considered. This type of damping model, however, when used with explicit integration algorithms can require a small time step to achieve the desired accuracy in an RTHS involving a structure with a large number of degrees of freedom. Restrictions on the minimum time step exist in an RTHS that are associated with the computational demand. Integrating the equations of motion for an RTHS with too large of a time step can result in spurious high‐frequency oscillations in the member forces for elements of the structural model that undergo inelastic deformations. The problem is circumvented by introducing the parametrically controllable numerical energy dissipation available in the recently developed unconditionally stable explicit KR‐α method. This paper reviews the formulation of the KR‐α method and presents an efficient implementation for RTHS. Using the method, RTHS of a three‐story 0.6‐scale prototype steel building with nonlinear elastomeric dampers are conducted with a ground motion scaled to the design basis and maximum considered earthquake hazard levels. The results show that controllable numerical energy dissipation can significantly eliminate spurious participation of higher modes and produce exceptional RTHS results. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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IntroductionThe analysis of dynamic soil-structure interaction for important engineering project is still based on linear model (including equivalent linear model) with complex damping, and traditional frequency domain method (Lysmer, et al, 1975, 1981; DING, et al, 1999). Namely, first calculating frequency domain solution by Fourier transform, and then calculating time domain solution by Fourier inverse transform. The motion equation of a system in frequency domain is usually written as (… 相似文献
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Shuenn-Yih Chang 《地震工程与结构动力学》1997,26(9):917-929
There is no second-order accurate, dissipative, explicit method in the currently available step-by-step integration algorithms. Two new families of second-order accurate, dissipative, explicit methods have been successfully developed for the direct integration of equations of motion in structural dynamics. These two families of methods are numerically equivalent and possess the desired numerical dissipation which can be continuously controlled. These two families of algorithms are very useful for pseudodynamic tests since the favourable numerical damping can be used to suppress the spurious growth of high-frequency modes due to the presence of numerical and/or experimental errors in performing a pseudodynamic test. © 1997 by John Wiley & Sons, Ltd. 相似文献
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Newm ark-更新精细积分法是动力方程求解的隐式的时域逐步积分法,其稳定性条件非常容易满足。与隐式方法相比较,显式积分方法不需要求解耦联的方程组,可以有效地减少内存占用和机时耗费。因此,根据显式积分方法的特点和优点,基于Newm ark-更新精细积分法的基本思想,提出其显式积分格式。对显式积分方法的精度与稳定性进行了初步的分析,指出该显式积分方法具有极好的稳定性,其精度比隐式积分方法的精度稍低。随着时间步长的增加,其精度优于传统的方法。 相似文献
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The step-by-step modal time history integration methods are developed for dynamic analysis of non-classically damped linear structures subjected to earthquake-induced ground motions. Both the mode displacement and mode acceleration-based algorithms are presented for the calculation of member and acceleration responses. The complex-valued eigenvectors are used to effect the modal decoupling of the equations of motion. However, the recursive step-by-step algorithms are still in terms of real quantities. The numerical results for the acceleration response and floor response spectra, obtained with these approaches, are presented. The mode acceleration approach is observed to be decidedly better than the mode displacement approach in as much as it alleviates the so-called missing mass effect, caused by the truncation of modes, very effectively. The utilization of the mode acceleration-based algorithms is, thus, recommended in all dynamic analyses for earthquake-induced ground motions. 相似文献
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瑞利阻尼介质有限元离散模型动力分析的数值稳定性 总被引:12,自引:0,他引:12
本文针对几种有一般阻尼的动力系数数值积分的显式方法,讨论了阻尼对稳定性的影响,并建议了瑞利阻尼介质有限元离散模型中动力分析数值稳定性的实用稳定判别方法。 相似文献