多体系统动力学方程的基于离散零空间理论的Newmark积分算法

考虑到多体系统动力学方程的数值计算方法是系统动力学分析的基础,提出一种基于离散零空间理论的Newmark积分算法。应用Newmark积分框架对多体系统动力学方程在时域上进行离散,通过离散零空间矩阵消去动力学方程中的拉格朗日乘子项,建立离散的达朗贝尔动力学方程,采用局部结点参数化进一步获得降维的达朗贝尔动力学方程。以空间双摆为算例,数值结果表明:该算法能够在实现系统降维、提高计算效率的同时,进行有效的数值分析,约束违约很小。     

Probabilistic modeling of seismically triggered landslides using Monte Carlo simulations

The 2004 Chuetsu earthquakes of Niigata (Japan) triggered numerous landslides, and the most widespread types of landslides were highly disrupted, relatively shallow slides and soil (debris) flows. This paper presented a method to evaluate slope instability using Newmark displacement on a pixel-by-pixel basis in a given area. The proposed method was able to integrate Newmark displacement modeling and Monte Carlo simulations within geographical information systems. In the modeling, an empirical attenuation relationship was utilized to calculate Arias intensity over this study area, and the variability of geotechnical parameters was taken into account to calculate coseismic landslide displacement. Before deriving the displacement from related inputs, the Monte Carlo simulations ran 1,500 times and generated 1,500 displacement values for each grid cell, and then means and standard deviations of displacement were calculated and probabilistic distributions can be obtained. Finally, given 10 cm as a threshold value of displacement, estimated probabilities of displacement exceeding 10 cm were shown as a map of seismic landslide hazards. The resulting hazard map was classified into four categories from very low to high level.     

气流激振力作用下离心叶轮的瞬态响应分析

为研究流场中离心叶轮受气流激振的瞬态响应问题,利用叶盘结构的循环对称性编制计算程序,实现了使用单扇区模型计算非循环对称力作用下离心叶轮的受迫振动。应用时间倾斜方法计算非等栅距情况下导叶/叶轮干涉的非定常流场,将叶片表面的气动力数据由流体网格插值到结构网格。使用FEAST求解器计算基本扇区各节径下的振型数据,并将其由基本扇区展开至所有扇区,根据各扇区所受周期激励的时间差建立载荷矢量,结构动力方程的时域积分使用Newmark方法完成。以一半开式径向叶轮为例,进行了两种转速下叶盘结构的瞬态响应分析。单扇区模型与整体模型计算的位移响应结果符合较好,两个潜在共振点附近激振频率的振动响应均呈现出近于发散变化的趋势,表明了算法的正确性和预测气流激励导致共振的有效性。     

Overlapping Schwarz and Spectral Element Methods for Linear Elasticity and Elastic Waves

The classical overlapping Schwarz algorithm is here extended to the spectral element discretization of linear elastic problems, for both homogeneous and heterogeneous compressible materials. The algorithm solves iteratively the resulting preconditioned system of linear equations by the conjugate gradient or GMRES methods. The overlapping Schwarz preconditioned technique is then applied to the numerical approximation of elastic waves with spectral elements methods in space and implicit Newmark time advancing schemes. The results of several numerical experiments, for both elastostatic and elastodynamic problems, show that the convergence rate of the proposed preconditioning algorithm is independent of the number of spectral elements (scalability), is independent of the spectral degree in case of generous overlap, otherwise it depends inversely on the overlap size. Some results on the convergence properties of the spectral element approximation combined with Newmark schemes for elastic waves are also presented.     

Selection of ground motion time series and limits on scaling

A procedure to select time series for use in non-linear analyses that are intended to result in an average response of the non-linear system is proposed that is not based simply on magnitude, distance, and spectral shape. A simple model of a yielding system is used as a proxy for the non-linear behavior of a more complicated yielding system. As an example, Newmark displacements are used as a proxy for more complex slope-stability models. The candidate scaled time series are evaluated to find those that yield a response of the simple non-linear system that is near the expected response for the design event. Those scaled time series with responses near the expected value are selected as the optimum time series for defining average response even if the scale factors are larger than commonly accepted (e.g. scale factors >factor of 2).     

用局部Petrov-Galerkin方法分析弹性杆振动问题

提出一维弹性动力问题的局部Petrov -Galerkin方法 ,这是一种真正的无网格方法。这种方法采用移动最小二乘函数来近似解变量 ,并且采用移动最小二乘近似函数的权函数作为加权残值法的权函数。文中对形成的离散动力学方程用Newmark方法求解 ,计算实例表明 :局部Petrov -Galerkin方法是一种很有效的求解弹性动力学问题的方法。     

黄土斜坡地震动时程分析

应用地震危险性分析理论和地震动人工合成技术，给出Newmark法中所需的地震动时程，解决了斜坡稳定性分析Newmark法中难以选取合适地震动时程的难题。通过对黄土斜坡实例计算，给出了坡体中地震动峰值加速度与深度的关系；在计算坡体位移时，提出了等效峰值加速度的概念；对比了使用地面地震动时程和使用坡体内等效地震动时程的计算结果。     

地震动作用下滑坡稳定性分析

应用地震危险性分析理论和地震动人工合成技术,给出Newmark法中所需的地震动时程。通过滑坡实例计算,得出了坡体中地震动峰值加速度与深度存在负指数关系;坡体对地震动放大倍数与坡体厚度近似呈线性关系。通过对Ne wmark法中不同地震动时程作用位置的计算对比,发现使用地面地震动时程得到的结果虽有些偏于安全,但基本是合理的。     

基于Newmark法的三角形板单元局部效应修正

在一般有限元法的基础上推导了三角形板单元局部效应修正公式,利用Newmark逐步积分法在不同荷载激励下对结构进行动力响应分析。计算结果表明,考虑局部效应可以使动内力计算结果更为准确。在进行大型复杂结构的动力响应分析时,通过考虑局部效应,可在计算模型大大简化的同时,获得较为精确的计算结果。     

Time‐domain integration methods of exponentially damped linear systems

In this paper, three new kinds of time‐domain numerical methods of exponentially damped systems are presented, namely, the simplified Newmark integration method, the precise integration method, and the simplified complex mode superposition method. Based on the traditional Newmark integration method and transforming the equation of motion with exponentially damping kernel functions into an equivalent second‐order equation of motion by using the internal variables technique, the simplified Newmark integration method is developed by using a decoupling technique to reduce the computer run time and storage. By transforming the equation of motion with exponentially damping kernel functions into a first‐order state‐space equation, the precise integration technique is used to numerically solve the state‐space equation. Based on a symmetric state‐space equation and the complex mode superposition method, a delicate and simplified general solution of exponentially damped linear systems, completely in real‐value form, is developed. The accuracy and efficiency of the developed numerical methods are compared and discussed by two benchmark examples.