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汪梦甫 《地震工程与工程振动(英文版)》2007,6(1):57-64
The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm. 相似文献
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为提高变截面梁地震动力求解的计算效率,提出了基于离散时间传递矩阵法的时程分析方法。首先,从欧拉梁的偏微分振动方程出发,基于逐步时间积分法的线性化方法并结合张量变换原理,建立了变截面梁的动力时程计算方法;其次,考虑地震动激励的非一致输入效应,采用数值迭代求解的方式建立了变截面梁地震动力时程分析的离散时间传递矩阵算法;最后,编制了数值仿真计算程序,并结合具体算例进行了算法的有效性和高效性验证。算例结果表明:在采用相同计算模型的前提下,离散时间传递矩阵法不仅能够在计算精度方面与有限元法保持一致,同时还拥有更高的计算效率。 相似文献
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重力勘探中复杂条件下的三维正演计算量大存储要求高,使得这种条件下重力勘探高效、精细正反演变得困难.针对这一问题,提出一种空间-波数混合域数值模拟方法,该方法将空间域引力位积分进行水平方向二维傅里叶变换,将三维空间域卷积问题转换为多个不同波数之间相互独立的空间垂向一维积分问题,一维积分垂向可离散为多个单元积分之和,每个单元采用二次形函数表征密度变化,可得出单元积分的解析表达式.该方法计算量和存储需求少,算法高度并行;保留垂向为空间域,优势之一在于可根据实际情况合理调整单元疏密程度,准确模拟任意复杂地形和密度异常体的重力异常,兼顾计算精度与计算效率;优势之二在于用形函数拟合求得积分的解析解,计算精度和效率高;充分利用一维形函数积分的高效和高精度,不同波数之间一维积分高度并行性及快速傅里叶变换的高效性,实现重力异常场三维数值模拟.设计棱柱体模型,通过数值解和解析解对比验证了该方法的正确性、适用性和高效性.针对任意复杂地形条件下的重力场及其张量的模拟问题,提出一种快速算法,对其有效性进行了验证.探究标准FFT法的截断效应对计算精度的影响,对比分析Gauss-FFT法和标准FFT扩边法两种方法的计算精度和效率,总结了二者的选取策略,结果表明选用标准FFT扩边法计算效率更高.实际地形的数值模拟表明本文算法适用于任意复杂地形的高效计算. 相似文献
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Real‐time hybrid simulation is a viable experiment technique to evaluate the performance of structures equipped with rate‐dependent seismic devices when subject to dynamic loading. The integration algorithm used to solve the equations of motion has to be stable and accurate to achieve a successful real‐time hybrid simulation. The implicit HHT α‐algorithm is a popular integration algorithm for conducting structural dynamic time history analysis because of its desirable properties of unconditional stability for linear elastic structures and controllable numerical damping for high frequencies. The implicit form of the algorithm, however, requires iterations for nonlinear structures, which is undesirable for real‐time hybrid simulation. Consequently, the HHT α‐algorithm has been implemented for real‐time hybrid simulation using a fixed number of substep iterations. The resulting HHT α‐algorithm with a fixed number of substep iterations is believed to be unconditionally stable for linear elastic structures, but research on its stability and accuracy for nonlinear structures is quite limited. In this paper, a discrete transfer function approach is utilized to analyze the HHT α‐algorithm with a fixed number of substep iterations. The algorithm is shown to be unconditionally stable for linear elastic structures, but only conditionally stable for nonlinear softening or hardening structures. The equivalent damping of the algorithm is shown to be almost the same as that of the original HHT α‐algorithm, while the period elongation varies depending on the structural nonlinearity and the size of the integration time‐step. A modified form of the algorithm is proposed to improve its stability for use in nonlinear structures. The stability of the modified algorithm is demonstrated to be enhanced and have an accuracy that is comparable to that of the existing HHT α‐algorithm with a fixed number of substep iterations. Both numerical and real‐time hybrid simulations are conducted to verify the modified algorithm. The experimental results demonstrate the effectiveness of the modified algorithm for real‐time testing. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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将Newmark-β法中常平均加速度法的基本假定与精细指数算法结合,根据指数矩阵的Taylor级数展开式,提出了动力方程的显式级数解,并设计了相应的时程积分算法.该算法的精度可根据Taylor级数展开式的项数进行灵活控制.算例的结果表明:在满足稳定性条件的前提下,随着时间步长的增加,其精度优于传统的时程积分法.通过稳定性的分析,指出其稳定性条件是显然满足的. 相似文献
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波形反演是一种利用全波场信息,通过最小化预测波场和实际波场的残差来揭示地下岩性和构造信息的方法.本文首先简述了常规拟牛顿算法的原理,之后利用一种新的拟牛顿公式对Davidon-Fletcher-Powell(DFP)和Broyden-Fletcher-Goldfarb-Shanno(BFGS)算法进行了修正,改进后的BFGS算法在近似Hessian矩阵逆矩阵时,不仅考虑了梯度和模型信息,还加入了目标函数本身的信息,而且对于每次迭代,基本没有增加计算量.数值试验表明,相对常规拟牛顿方法,修正BFGS算法在保证反演精度的同时,明显提高了反演效率. 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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Optimization of a precise integration method for seismic modeling based on graphic processing unit 
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下载免费PDF全文 General purpose graphic processing unit(GPU) calculation technology is gradually widely used in various fields.Its mode of single instruction,multiple threads is capable of seismic numerical simulation which has a huge quantity of data and calculation steps.In this study,we introduce a GPU-based parallel calculation method of a precise integration method(PIM) for seismic forward modeling.Compared with CPU single-core calculation,GPU parallel calculating perfectly keeps the features of PIM,which has small bandwidth,high accuracy and capability of modeling complex substructures,and GPU calculation brings high computational efficiency,which means that high-performing GPU parallel calculation can make seismic forward modeling closer to real seismic records. 相似文献
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Hybrid simulation is a powerful test method for evaluating the seismic performance of structural systems. This method makes it feasible that only critical components of a structure be experimentally tested. This paper presents a newly proposed integration algorithm for seismic hybrid simulation which is aimed to extend its capabilities to a wide range of systems where existing methods encounter some limitations. In the proposed method, which is termed the variable time step (VTS) integration method, an implicit scheme is employed for hybrid simulation by eliminating the iterative phase on experimental element, the phase which is necessary in regular implicit applications. In order to study the effectiveness of the VTS method, a series of numerical investigations are conducted which show the successfulness of the VTS method in obtaining accurate, stable and converged responses. Then, in a comparative approach, the improved accuracy of the VTS method over commonly used integration methods is demonstrated. The stability of the VTS method is also studied and the results show that it provides conditional stability; however, its stability limit is well beyond the accuracy limit. The effect of time delay on the VTS method results is also investigated and it is shown that the VTS method is quite successful in handling this experimental error. 相似文献
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Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those
of the constant average acceleration method (AAM) for linear elastic systems, except that the capability to capture dynamic
loading was not explored. It was found that there were different quadrature equations to predict the next step displacement
increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement
was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method,
in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition
to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods. 相似文献
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In the complex mode superposition method, the equations of motion for non-classically damped multiple-degree-of-freedom （MDOF） discrete systems can be transferred into a combination of some generalized SDOF complex oscillators. Based on the state space theory, a precise recurrence relationship for these complex oscillators is set up; then a delicate general solution of non-classically damped MDOF systems, completely in real value form, is presented in this paper. In the proposed method, no calculation of the matrix exponential function is needed and the algorithm is unconditionally stable. A numerical example is given to demonstrate the validity and efficiency of the proposed method. 相似文献
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对于时间域航空电磁法二维和三维反演来说,最大的困难在于有效的算法和大的计算量需求.本文利用非线性共轭梯度法实现了时间域航空电磁法2.5维反演方法,着重解决了迭代反演过程中灵敏度矩阵计算、最佳迭代步长计算、初始模型选取等问题.在正演计算中,我们采用有限元法求解拉式傅氏域中的电磁场偏微分方程,再通过逆拉氏和逆傅氏变换高精度数值算法得到时间域电磁响应.在灵敏度矩阵计算中,采用了基于拉式傅氏双变换的伴随方程法,时间消耗只需计算两次正演,从而节约了大量计算时间.对于最佳步长计算,二次插值向后追踪法能够保证反演迭代的稳定性.设计两个理论模型,检验反演算法的有效性,并讨论了选择不同初始模型对反演结果的影响.模型算例表明:非线性共轭梯度方法应用于时间域航空电磁2.5维反演中稳定可靠,反演结果能够有效地反映地下真实电性结构.当选择的初始模型电阻率值与真实背景电阻率值接近时,能得到较好的反演结果,当初始模型电阻率远大于或远小于真实背景电阻率值时反演效果就会变差. 相似文献
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A general formulation and solution procedure are proposed for harmonic response of rigid foundation on multilayered half-space. It is suitable for isotropic as well as anisotropic soil medium. The wave motion equation is formulated in frequency wave-number domain in the state space. A hybrid approach is proposed for its solution, where the precise integration algorithm (PIA) is employed to carry out the integration. Very high accuracy can be achieved. The mixed variable form of wave motion equation enables the assembly of layers simple and convenient. The surface Green׳s function is regarded as rigorous, because it is free from approximations and discretization errors. The algorithm is unconditionally stable. The numerical implementation is based on algebraic matrix operation. Numerical examples of vibration of rigid foundation validate the efficiency and accuracy of the proposed approach. 相似文献
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A direct time domain boundary element method is presented based on the Stokes fundamental solutions, discretized in both time and space, and an efficient time step-by-step solution that minimizes the accumulation of errors. A non-singular numerical integration procedure, in the Cauchy sense, is proposed for the generation of the associated influence matrices. This methodology is shown to be efficient for the solution of a number of computationally intensive problems in the area of soil–structure interaction. In addition, an algorithm for the direct calculation of the response of massive foundations to externally applied forces and/or obliquely incident seismic waves is introduced. The accuracy and computational efficiency of the proposed methodologies is established through a number of comparison studies. 相似文献
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Retracted: Discussion of paper ‘Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation’ by Chinmoy Kolay and James M. Ricles,Earthquake Engineering and Structural Dynamics 2014; 43:1361–1380 下载免费PDF全文
下载免费PDF全文 Shuenn‐Yih Chang 《地震工程与结构动力学》2015,44(8):1325-1328
It seems that the explicit KR‐α method (KRM) is promising for the step‐by‐step integration because it simultaneously integrates unconditional stability, explicit formulation, and numerical dissipation together. It was shown that KRM can inherit the numerical dispersion and energy dissipation properties of the generalized‐α method (GM) for a linear elastic system, and it reduces to CR method (CRM) if ρ∞ = 1is adopted, where ρ∞ is the spectral radius of the amplification matrix of KRM as the product of the natural frequency and the step size tends to infinity. However, two unusual properties were found for KRM and CRM, and they might limit their application to solve either linear elastic or nonlinear systems. One is the lack of capability to capture the structural nonlinearity, and the other is that it is unable to realistically reflect the dynamic loading. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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在Newmark精细直接积分法的基础上,应用高斯积分与精细指数运算,提出该方法的两种逐步积分格式。文中对两种积分格式的稳定性和精度进行了分析。经过分析比较,第1种逐步积分格式计算精度较高,其稳定性明显地满足算法稳定性分析的条件;而第2种积分格式计算精度相对较差,且是不稳定的。因此本文将第1种积分格式应用于结构的地震反应分析中。算例表明,该逐步积分格式对地震作用有很好的适应性。 相似文献
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This paper deals with an explicit numerical integration method for real‐time pseudo dynamic tests. The proposed method, termed the MPC‐SSP method, is suited to use in real‐time pseudo dynamic tests as no iteration steps are involved in each step of computation. A procedure for implementing the proposed method in real‐time pseudo dynamic tests is described in the paper. A state‐space approach is employed in this study to formulate the equations of motion of the system, which is advantageous in real‐time pseudo dynamic testing of structures with active control devices since most structural control problems are formulated in state space. A stability and accuracy analysis of the proposed method was performed based on linear elastic systems. Owing to an extrapolation scheme employed to predict the system's future response, the MPC‐SSP method is conditionally stable. To demonstrate the effectiveness of the MPC‐SSP method, a series of numerical simulations were performed and the performance of the MPC‐SSP method was compared with other pseudo dynamic testing methods including Explicit Newmark, Central Difference, Operator Splitting, and OS‐SSP methods based on both linear and non‐linear single‐degree‐of‐freedom systems. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献