结构动力方程的高斯精细时程积分法

对线性定常结构动力系统提出的精细积分方法,能够得到在数值上逼近于精确解的结果,但是对于非齐次动力方程涉及到矩阵求逆的困难,计算精度取决于非齐次项的拟合精度等问题。提出将高斯积分方法与精细积分方法中的指数矩阵运算技巧结合起来,在实施精细积分过程中不必进行矩阵求逆,整个积分方法的精度取决于所选高斯积分点的数量。这种方法理论上可实现任意高精度,而且计算效率较高,数值例题显示了方法的有效性。     

非线性系统控制方程的齐次扩容精细积分法

基于齐次扩容精细积分法，提出一种新的求解非线性微分方程的高精度预测一校正算法。首先，借助Taylor级数展开，在一个积分步长内将非线性方程转化为线性非齐次方程，然后利用齐次扩容方法，进。一步将其化为线性齐次方程组，便于用精细积分算法求解。为了避免繁琐的导数推导和计算，采用修正Euler法作为预测步、齐次扩容精细积分法进行多次校正计算的方案，获得了较高精度的计算结果。所提出的方法算法简单，编程容易，且避免了系统矩阵的求逆计算，具有更加广泛的应用范围，适用于多自由度、强非线性非保守系统的求解。     

基于对偶神经网络的动力方程精细积分法EI北大核心CSCD

针对一般动力学方程,提出了一种用于求解具有任意非齐次项动力学方程的对偶神经网络精细积分算法。在时间域内,对动力学非齐次方程求解中涉及到的积分运算,选用一组神经网络同时逼近被积函数和原函数,然后通过牛顿莱布尼茨公式实现积分项的求解。该方法利用神经网络的函数拟合优势,具有对时间步长不敏感,不需要对矩阵求逆,不对非齐次项进行假设等优点。通过算例与精细积分法、威尔逊-θ、广义精细积分法等方法进行比较,计算结果表明该方法精度较高、适用范围广。     

结构动力方程的一种自适应步长增维精细积分法EI北大核心CSCD

增维精细积分法是一种求解结构动力方程的高精度逐步积分算法,其步长的选取会对计算精度产生极大的影响,在实际应用中存在难以确定合适步长的问题。为满足实际工程中对计算精度和效率的要求,提出了一种计算误差的估计方法,并以估计误差和迭代收敛速度为基准,建立了一种自适应步长增维精细积分法。针对三种结构动力方程的算例结果表明,在计算各类线性及非线性振动问题时,该方法均可以在保证计算精度的前提下快速有效地控制算法的计算步长,并且仅需较少的额外计算消耗,显著提高了增维精细积分法的计算效率,使该方法在求解结构动力方程时更具计算优势和实用价值。     

结构动力方程的增维分块精细积分法

在增维精细积分法的基础上,对矩阵进行分块计算.考虑非齐次项的特点,减小了矩阵的维数,实现简化计算,提高了计算效率,同时算法仍然具有增维精细积分法的原有优点.数值算例表明本方法在保持精度的同时提高了计算效率,在处理大型问题时将有着很大的优势.     

线性动力分析的一种通用积分格式

针对线性动力状态方程■,结合泰勒级数展开式和广义精细积分法,提出了一种避免状态矩阵求逆的线性动力分析的通用积分格式。将非齐次项在t_(i+1)=(i=0, 1, 2,…,n)时刻利用泰勒公式将其展开成幂级数形式;结合广义精细积分法中的递推公式即可求解出非齐次项的动力响应。该方法计算格式统一,易于编程,通过选取幂级数的项数,可得到不同的计算精度。与传统的数值积分法相比,该方法具有很高的精度、稳定性及适当的效率,可用于求解任意激励下结构的动力响应。     

基于动力特征分区的显式-精细混合积分法

大型动力系统中常因局部的高频振动及非线性等特性限制了系统的积分步长而导致整体计算量激增，针对此问题提出一种分区域异步长显式-精细混合积分方法。在特性复杂的局部区域采取显式积分法，根据精度和稳定性要求取较小的时间步长求解；在其余常规区域则应用精细积分方法，采取可以跨越显式积分区周期的大积分步长求解。对于精细积分区域边界荷载，提出一种基于离散FFT变换的线性项与主频谐波项的组合表示方法，并给出了此种荷载形式下的精细积分计算格式。数值算例结果表明该法能够明显提高计算效率，在显式积分区域和精细积分区域都有很高的精度。     

应用精细积分法的结构MBC状态方程求解

基于市场机制控制(Market-Based Control,MBC)属于分散控制,以往求解状态方程都采用差分类的近似,有时由于计算存在较大误差,不能得到结构真实状态的精确响应。精细积分法以其高精度、无条件稳定等优点被广泛的应用。文中引入两种精细积分方法,将精细积分的思想运用到基于市场机制(MBC)控制算法的求解中,推导了两种基于MBC控制状态方程的精细递推格式,大大提高了计算的精度及算法的稳定性,并且比较了两种精细积分方法的优缺点。最后通过算例,说明了采用精细积分方法计算MBC控制的必要性及有效性。     

基础隔震结构地震响应时程分析新方法

针对隔震层恢复力模型为折线型的层间剪切动力方程，研究了基础隔震结构在地震作用下的弹塑性时程反应。通过多种方法比较，说明了各种方法的优缺点。采用把结构特性和外部激励分开进行精细积分的增维分块精细积分法，避免了每一步迭代过程中的指数矩阵精细积分求解，在保持计算精度的同时，提高了计算效率；考虑地震作用特点后，增维分块精细积分法的计算效率有所提高。因此，增维分块积分法在计算基础隔震结构地震响应上是非常有效的。     

求解水下非圆弹性环声散射问题的一种半解析方法

基于传递矩阵法、齐次扩容精细积分法和复数矢径虚拟边界谱方法 ,提出了一种求解水下非圆弹性环声散射问题的半解析方法。该方法具有以下几个优点 :(1)采用复数矢径虚拟边界谱方法 ,不仅能保证在全波数域内Helmholtz外问题解的唯一性 ,而且由于虚拟源强密度函数采用 Fourier级数展开 ,克服了用单元离散解法不能用于较高频率范围的缺点 ;(2 )采用齐次扩容精细积分法求解非圆弹性环的状态微分方程 ,其计算结果具有很高的精度 ;(3)耦合方程不需要交错迭代求解 ,提高了计算效率。文中给出了两个典型非圆弹性环在平面声波激励下的声散射算例 ,计算结果表明本文方法是一种求解二维非圆弹性环声散射问题非常有效的半解析法。     

Krylov precise time‐step integration method

An efficient precise time‐step integration (PTI) algorithm to solve large‐scale transient problems is presented in this paper. The Krylov subspace method and the Padé approximations are applied to modify the original PTI algorithm in order to improve the computational efficiency. Both the stability and accuracy characteristics of the resultant algorithms are investigated. The efficiency can be further improved by expanding the dimension to avoid the computation of the particular solutions. The present algorithm can also be extended to tackle nonlinear problems without difficulty. Two numerical examples are given to illustrate the highly accurate and efficient algorithm. Copyright © 2006 John Wiley & Sons, Ltd.     

结构动力微分方程的一种高精度摄动解

将结构的位移及速度响应作为状态变量,把结构动力方程转化为状态方程,采用摄动方法求解状态方程,推出一种级数形式的摄动解,同时给出了该文算法的迭代格式和计算步骤。该算法无需对转换矩阵求逆,也无须作指数矩阵运算,仅做矩阵向量相乘及向量求和运算,计算稳定而且效率高,收敛速度快,解的级项数及精度可由允许误差参数直接控制,很容易达到任意精度要求,该方法兼具线性加速法的高效率和精细积分法的高精度,可应用于结构大型稀疏线性动力方程组的求解。最后通过典型算例进一步验证了该文算法的精度和效率。     

An adaptive fast multipole boundary face method with higher order elements for acoustic problems in three-dimension

An adaptive fast multipole boundary face method using higher order elements based on the well-known Burton-Miller equation is presented in this paper for solving the large-scale three-dimensional exterior acoustic wave problems. The fast multipole boundary face method is referred to as FMBFM. In the FMBFM, the boundary integration and field variables approximation are both performed in the parametric space of each boundary face exactly the same as the B-rep data structure in standard solid modeling packages. In this FMBFM, higher order elements are employed to improve the computational accuracy and efficiency, and an adaptive tree structure is constructed to improve the efficiency of the FMBFM. Numerical examples for large-scale acoustic radiation and scattering problems in this paper demonstrated the accuracy, efficiency and validity of the adaptive FMBFM. Comparison study showed that the FMBFM with high order elements out-performs the FMBFM with constant elements respect to accuracy and CPU time at the same number of the nodes. In addition, the CAD models, even with complicated geometry, are directly converted into the FMBFM models, thus the present method provides a new way toward automatic simulation.     

hp Fast multipole boundary element method for 3D acoustics

A fast multipole boundary element method (FMBEM) extended by an adaptive mesh refinement algorithm for solving acoustic problems in three‐dimensional space is presented in this paper. The Collocation method is used, and the Burton–Miller formulation is employed to overcome the fictitious eigenfrequencies arising for exterior domain problems. Because of the application of the combined integral equation, the developed FMBEM is feasible for all positive wave numbers even up to high frequencies. In order to evaluate the hypersingular integral resulting from the Burton–Miller formulation of the boundary integral equation, an integration technique for arbitrary element order is applied. The fast multipole method combined with an arbitrary order h‐p mesh refinement strategy enables accurate computation of large‐scale systems. Numerical examples substantiate the high accuracy attainable by the developed FMBEM, while requiring only moderate computational effort at the same time. Copyright © 2016 John Wiley & Sons, Ltd.     

A study on time schemes for DRBEM analysis of elastic impact wave

 The precise integration and differential quadrature methods are two new unconditionally stable numerical schemes to approximate time derivative with more than the second order accuracy. Recent studies showed that compared with the Houbolt and Newmark methods, they produced more accurate solutions with large time step for the problems where response is primarily dominated by low and intermediate frequency modes. This paper aims to investigate these time schemes in the context of the dual reciprocity BEM (DRBEM) formulation of various shock-excited scalar elastic wave problems, where high modes have important affect on traction response. The Houbolt method was widely recommended in many literatures for such DRBEM dynamic formulations. However, this study found that the damped Newmark algorithm was the most efficient and accurate for impact traction analysis in conjunction with the DRBEM. The precise integration and differential quadrature methods are shown inapplicable for such shock-excited problems due to the absence of numerical damping. On the other hand, we also found that to achieve the same order of accuracy, the differential quadrature method required much less computing effort than the precise integration method due to the use of the Bartels–Stewart algorithm solving the resulting Lyapunov matrix analogization equation. Received 6 November 2000     

Fully variational 6th order elastodynamic formulation for the treatment of blast or fast impulsive forces

A new variational space-time formulation is used to treat elastodynamic problems with impulsive loads that propagate at fast velocities, as blasts or explosions. Based on the new formulation, a new family of fully variational time integration algorithms for elastodynamic problems is formulated. In the framework of this new family of algorithms, a conditionally stable time integration algorithm of the 6th order and the variational treatment of impulsive forces propagating at high speeds are developed. The time integration algorithm is based on Hermite’s polynomials, with independent field of velocities, and discontinuous time derivative of the displacement field. Numerical examples are performed to test the computational efficiency of the new approach to treat fast dynamic impulsive forces.     

基于改进MCMC方法的有限元模型修正研究

针对马尔可夫链蒙特卡罗(MCMC)模型修正方法在待修正参数维数较高时不易收敛和计算效率低下的问题,建立了融合自适应算法和相关向量机的快速模型修正方法。基于广义无偏见先验分布,推导了待修正参数的后验分布;在标准MCMC方法的基础上,引入延缓拒绝算法以提高新样本接受概率;引入自适应算法以自主调整建议分布的带宽。通过相关向量机建立待修正参数与有限元模型理论计算值之间的回归模型,以提高模型修正的计算效率。数值模拟和试验结构的模型修正结果表明,该方法的收敛速度较快,计算效率优于传统的一阶优化模型修正方法,为解决不确定性模型修正中的计算效率提供了一种新手段。     

一种多自由度阻尼体系动力问题的高阶分析方法

传统动力时程直接积分法多采用低阶数值格式,需要选择非常小的时间步距才能获得满足精度要求的动力分析结果.该文将结构动力时程分析的积分求微法推广至多自由度情形,发展了一种具有较高计算效率的多自由度阻尼体系的动力时程高阶分析方法.将相邻的ρ个时步组成一个待求解时段,基于多自由度体系动力响应积分解,以精细积分法结合秦九韶算法计...     

基于隔离非线性的实体单元模型与计算效率分析

实体有限元模型计算中往往需要较多的计算单元与结点数量,且这些单元状态判定以及大规模的刚度矩阵分解将消耗大量的计算资源,计算效率低。该文基于隔离非线性法理论建立了线性四面体与六面体等参单元分析模型,采用直接积分格式的6积分点替代六面体等参单元的8高斯点作为非线性应变插值点,能够在保证计算精度的同时提高单元状态判定效率。控制方程采用Woodbury公式与组合近似法联合求解,使得整个求解过程只有矩阵回代以及矩阵与向量的乘积,进一步提高了求解效率。基于时间复杂度的计算效率分析表明:随着结点自由度数目的增加,该文方法的计算效率相对传统变刚度法显著提高,数值算例验证了实体单元模型的正确性以及算法的高效性。