基于辛格式的谱元法及其在横向各向同性介质波场模拟中的应用

基于分部的Runge-Kutta离散形式,给出了一种新的三阶辛积分算法,数值试验表明,长时程计算时该算法具有好的控制误差累积的能力;与有限差分法进行空间域离散相结合,通过数值试验进一步说明算法的有效性.注意到位移波动方程通过谱元离散后的微分方程组,完全符合新推导的三阶辛算法离散所需形式,因此将该三阶辛算法与谱元法结合具有很好的优势,并通过对横向各向同性介质弹性波场的模拟,结果显示不但成功模拟了波的传播特性,而且相对于传统算法,优势明显.     

半解析高阶有限谱元法及其在波导介质层PBG结构滤波器优化设计中的应用

本文采用高阶有限谱单元对分层结构的横截面进行半解析离散．将结构中沿纵向均匀的区段视为子结构，运用基于Riccati方程的精细积分算法求出其出口刚度阵．网格拼装后即可对分层介质问题进行求解．半解析高阶谱单元的采用可以避免著名的龙格现象，该算法的数值精度能随着基函数的阶数的增加呈指数级提高．即高阶有限谱单元能够达到任意需要的精度．数值算例证明这种方法具有很高的精度与效率．在高精度高效率分析的基础上建立了滤波器的优化设计模型，利用遗传算法对优化模型进行全局优化，得到了PBG结构滤波性能全局最优的设计参数．     

基于曲率模态振型的刚架结构损伤检测

结构损伤前后动力特性的变化来快速、直接、方便地判定损伤的存在、程度及位置．本文采用曲率模态对刚架结构的损伤检测进行了研究．首先用有限元法计算出结构的位移模态振型,然后用差分法计算出曲率模态振型．数值模拟结果表明：曲率模态振型对结构的损伤敏感,可同时确定结构损伤的存在、程度和位置,并且可以用于结构多位置损伤的检测．实验结果证实了数值模拟结论．     

二维非线性反应扩散方程的局部间断Galerkin谱元法

本文提出了二维非线性反应扩散方程的局部间断Galerkin谱元法.在空间方向上采用了Legendre-Galerkin Chebyshev谱配置法,即在每个子区域上,该格式按Legendre-G alerkin谱方法形成,子区域交界面处的跳跃项利用数值流量进行处理,非线性项采用在Chebyshev-GaussLobatto点上的插值进行计算.时间方向上采用四阶低存储Runge-Kutta方法.文中给出了半离散格式下的稳定性和收敛性分析,以及单区域和多区域算法的数值算例,并与间断Galerkin有限元方法进行比较.     

一种宇航继电器冲击响应谱等效计算方法的研究

宇航继电器抗冲击性能试验是其力学可靠性评价的关键要素,研究和分析试验时域波形与冲击响应谱的等效算法,将有效提升器件实际应用过程冲击边界条件评估的准确程度,增强冲击环境下器件使用安全性.回溯了国内外公开的冲击响应谱计算方法的研究历史,概览了通用算法及应用效果.依据军用继电器冲击试验评价方法,建立规定时域曲线,在斜坡不变理论基础上,推导单自由度系统传递函数关系表达式,通过Matlab软件,建立起始频率与终止频率之间加速度峰值谱与时域函数之间的等效对应数值关系,并设计数字滤波器用于推算等效冲击响应谱.利用该算法实现了典型半正弦冲击条件的等效冲击响应谱计算,并与某器件冲击边界条件对比,可为后续继电器设计、生产及试验过程中冲击量级确定提供理论依据.     

基于比例边界问断谱元法的无穷域亚音速圆柱绕流数值模拟

将比例边界坐标插值方法引入谱元法,构成比例边界谱单元;为了增加计算的稳定性,将节点布置在单元内部;用若干无限谱元离散计算域,用间断有限元方法对无穷域Euler方程亚音速圆柱绕流问题进行了数值模拟;计算结果的误差很小,显示了计算方法的可行性.     

基于GPU的图形学加速算法在离散元法中的应用

颗粒离散元法是一种广泛应用于研究颗粒物料力学行为的数值模拟方法,而计算效率是制约其发展和应用的主要因素之一。通过Pro/E软件建立了料斗模型,利用Stream DEM软件对料斗的颗粒充填过程进行离散元法模拟研究,并对基于CPU和GPU加速算法的运算过程和结果进行对比。结果表明,基于GPU的计算机图形学加速算法可大幅提高颗粒离散元法模拟过程的运算效率。当填充颗粒数量达到13万时,其运算效率比基于CPU的运算效率提高了10倍以上。     

具有细观结构新材料跨尺度分析的细观元法

建议一种适用于具有细观结构新材料宏细观间跨尺度分析的细观元方法.细观元法在结构的常规有限元内部设置密集细观单元以反映材料细观构造,又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度,再上机计算.此方法可实现材料细观结构到构件宏观响应的直接过渡分析,而计算单元与自由度又等同一般常规有限元,为解决具有细观结构新材料与构件跨尺度分析提供一种新的有力工具.研究了直接从制备时给定的材料组分分布及网状细观结构图形出发计算功能梯度板件宏观响应,给出了不同边界条件功能梯度板件的力学量三维分布形态以及细观结构局部突变引起宏观等应力线图的畸变.     

求解周期结构中声波传播问题的一种边界元法

本文应用边界积分方程方法(边界元法)求解无限长周期结构中声波的传播问题,根据散射体的周期排布方式,将无限个散射体对应无限个边界积分方程的求解问题转化为在某一个单位块中有限个边界积分方程的求解,从而使得该问题的数值求解变得简单可行.然后将该方法应用于声子晶体能量禁带的预测中,通过对数值算例的求解以及与其他方法求解结果的比较,验证了本文所提出方法的可行性和准确性.     

基于能量谱的时域波形再现瞬态振动环境试验方法

利用外场瞬态振动时间历程数据获得能量谱包络,借鉴振动台控制理论中随机信号产生原理获得具有包络能量谱幅值特性以及典型外场试验数据相位信息的时域波形,并用振动台波形再现的方式进行产品瞬态振动环境试验;该方法为今后直接使用能量谱控制的瞬态振动振动台试验方法提供技术支撑.     

混合基函数勒让德谱元方法

针对勒让德谱元方法,构造了一类混合局部基函数,并证明了其线性无关特点.在此基础上,给出了一种勒让德谱元计算格式:在元素端点采用局部拉格朗日基函数,在元素内部采用调整后的局部勒让德多项式.进行了正确性和精度测试,数值实验结果表明该方法能够有效地实现高计算精度,且其计算矩阵比经典谱元方法更为简单,并具有良好的数据重用性和稀疏特点.     

Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation

This paper presents a method for the dynamic analysis of structures with stochastic parameters to random excitation. A procedure to derive the statistical characteristics of the dynamic response for structure is proposed by using dynamic Neumann stochastic finite element method presented herein. Random equation of motion for structure is transformed into a quasi-static equilibrium equation for the solution of displacement in time domain. Neumann expansion method is developed and applied to the equation for deriving the statistical solution of the dynamic response of such a random structure system, within the framework of Monte Carlo simulation. Then, the results from Neumann dynamic stochastic finite element method are compared with those from the first- and second-order perturbation stochastic finite element methods and the direct Monte Carlo simulation with respect to accuracy, convergence and computational efficiency. Numerical examples are examined to show that the approach proposed in this paper has a very high accuracy and efficiency in the analysis of compound random vibration.     

A truncated Legendre spectral method for solving numerical differentiation

A numerical differentiation problem for a given function with noisy data is discussed in this paper. A truncated spectral method has been introduced to deal with the ill-posedness of the problem. The theoretical analysis shows that the smoother the genuine solution, the higher the convergence rate of the numerical solution by our method. Numerical examples are also given to show the efficiency of the method.     

Legendre spectral method for solving integral and integro-differential equations

A new spectral approximation of an integral based on Legendre approximation at the zeros of the first term of the residual is presented. The method is used to solve integral and integro-differential equations. The method generates approximations to the lower order derivatives of the function through successive integrations of the Legendre polynomial approximation to the highest order derivative. Numerical results are included to confirm the efficiency and accuracy of the method.     

An efficient method for solving elliptic boundary element problems with application to the tokamak vacuum problem

A method for regularizing ill-posed Neumann Poisson-type problems based on applying operator transformations is presented. This method can be implemented in the context of the finite element method to compute the solution to inhomogeneous Neumann boundary conditions; it allows to overcome cases where the Neumann problem otherwise admits an infinite number of solutions. As a test application, we solve the Grad–Shafranov boundary problem in a toroidally symmetric geometry. Solving the regularized Neumann response problem is found to be several orders of magnitudes more efficient than solving the Dirichlet problem, which makes the approach competitive with the boundary element method without the need to derive a Green function. In the context of the boundary element method, the operator transformation technique can also be applied to obtain the response of the Grad–Shafranov equation from the toroidal Laplace n=1 response matrix using a simple matrix transformation.     

Modeling gap discontinuity in coplanar waveguide using quasistatic spectral domain method

An efficient computer technique based on the spectral domain method is presented to solve the problem of modeling coplanar gap discontinuity. Comparison with available published data is done to confirm the accuracy of the method. © 2000 John Wiley & Sons, Inc. Int J RF and Microwave CAE 10: 150–158, 2000.     

Laguerre谱方法在地震勘探中的应用

从大深度地震勘探一维波动方程出发,采用Laguerre谱方法对其正问题进行求解,给出了求解的离散过程,利用高斯-牛顿法对参数进行反演,并给出了数值模拟。结果表明该方法对于大深度地震勘探具有较好的效果。     

谱方法求解水声传播问题的优化与并行

水声传播数值计算的效率是各类水声学应用关心的核心因素之一,谱方法作为求解微分方程的一种数值方法,具有精度高、收敛速度快等优点,因此,近年来利用简正波-谱方法求解水声传播方程引起了许多学者的关注;然而,谱方法计算量更大,计算时间更长,在求解大范围海域声传播问题时,难以满足实时性的需求.因此,需要借助现代高性能计算机系统,...     

The NCAR spectral element climate dynamical core: Semi-implicit eulerian formulation

A prototype dynamical core for the Community Atmospheric Model (CAM) component of the Community Climate System Model (CCSM) is presented. The 3D governing primitive equations are specified in curvilinear coordinates on the cubed-sphere combined with a hybrid pressureη vertical coordinate. The horizontal space discretisation is based on a ℙ _N − ℙ _N spectral element variational formulation. A semi-implicit time integration scheme is derived in order to circumvent the severe time step restrictions associated with gravity waves. Eigen-mode decomposition of the vertical structure matrix results in a set of decoupled 2D modified Helmholtz problems which are solved using a preconditioned conjugate gradient iteration. An idealized climate simulation is presented, where the semi-implicit scheme permits a much larger time step.