曲面拟合在拉格朗日反分析方法中应用的探讨

把一组不同位置的速度(应变)波形构筑的x-t域离散成8节点或9节点单元,每个单元的插值函数为10或12参数多项式,利用拉格朗日反分析可以得到相应的应力(速度)波形。正如路径线法,曲面拟合反分析的某一单元函数值计算需要利用前一单元与该单元交界点的计算值,因而误差生成和发展有时很难预测、控制。文中对不同位置、不同数量量计线情况下,拉格朗日反分析中的曲面拟合法及路径线法误差生成、发展进行了分析,分析结果对材料实验中布置速度(应变)传感器的数量及其间距是有一定帮助的。     

等步长高次多项式插值加速度法的局限性

动力时程分析中,在几个相邻的等长时间步之间对加速度的变化规律用多项式插值来描叙,经过推导可求解得到整个时间域上的动力方程的解答.根据泰勒展开原理分析表明,随着所取多项式次数的增加,收敛精度增高,计算步长适当放大,截断误差仍能在容许的范围之内.但是随着所取多项式次数增大,其算法的稳定域减少, 计算步长受到了此小稳定域的限制,收敛精度不再是所取计算步长宽度的决定因素,稳定域大小成了所取计算步长宽度的决定因素.因为一旦步长超出了此小稳定域范围,虽然在每个时间步内的截断误差不大,其传递的误差却会被放大到很多倍,最后导致计算结果严重失真.分析结果显示,多项式插值次数采用到步长的三次时,与一次多项式插值(对应线性加速度法)和二次多项式插值(对应二次加速度法)的分析方法相比,算法的稳定域急剧变窄,为h/T≤0.0099(h为计算步长,T为结构的固有周期),此小稳定域限制了计算步长的选择范围,其收敛精度很高因此可放大计算步长的优势无法施展.本文推导了三次加速度法的求解过程,进行了一个理想单自由度系统的动力时程分析计算,验证了结论的正确性.表明同时考虑收敛精度和稳定域来确定计算步长的宽度时,二次加速度法为优.     

二维Euler方程无网格算法的精度分析

在几种典型的点云布点方案中,分析了文献[3]中的无网格算法的计算精度。分析指出影响无网格算法计算精度的主要因素是点云中点的分布是否平衡;增加点云中节点的数目或者采用高阶曲面拟合都不能提高精度;这里的理论分析为无网格算法的布点提供了重要参考。     

振型叠加法合理振型数目的确定

振型叠加法是常用的动力时程分析方法之一,参与计算的振型数目是影响该方法精度的重要因素。本文揭示了确定振型参与数目的质量参与系数法、振型位移控制法的数学背景及物理含义,分析了两者存在的不足。通过推导振型截断误差估计公式,提出了更合理的确定振型数目范数形式的方法。这种方法基于严密的理论推导,适用于任意动力荷载形式。计算结果表明,振型位移控制法所确定的振型数目过大,质量参与系数法提供的振型数目偏少,而本文方法更有优势。     

用灰关联分析方法确定影响岩体爆破质量的主要因素

用灰关联分析方法确定影响岩体爆破质量的主要因素。在简介灰关联分析原理及其计算方法后,通过实例计算与分析,得到各影响因素的主次关系。并且发现:节理裂隙岩体中的爆破块度指标主要受爆区内节理裂隙分布特征的控制;其次,也与均质岩体中的爆破一样,影响块度分布的主要因素是炮孔间距、排距和最小抵抗线等。     

基于微机械陀螺的MIMU关键技术

针对基于微机械陀螺的MIMU关键技术，对其进行研究和解决。参加美国JDAM性能指标和导航精度要求，计算陀螺性能参数：采用多级大容量的滤波器及有源电流限制电路，同时电源的输入端接入EMC滤波器，以提高电磁兼容性，并能抵抗浪涌和拉偏的能力；DSP实现信号实时采集，采用高次多项式拟合预处理去除数据野值；根据GJB729评估方法，利用利用蒙特卡罗方法仿真进行精度评估；最后按照GJB813进行可靠性分析。     

地下洞室开挖过程中洞周损伤分布的时变反演

洞室开挖过程中，洞周围岩的损伤场是时间和空间的函数。本文由建立的岩体时变损伤本构模型，基于位移反演理论，依据各步开挖后洞周及深部测线量测位移，对地下洞室由开挖引起的时变损伤分布情况进行辨识。通过构造损伤分布拟合函数直接反演洞周损伤分布的时变过程，尝试了用拟合函数法实现动态分布参数的反分析。在对某直墙半园拱顶隧道进行反演时，将洞室边界映射成单位圆，建立了由衰减函数和傅立叶级数构成的拟合函数，并采用约束优化法反演。最终结果显示，反演得到的区域损伤平均值与真值相比，绝大多数误差较小。本文法在地下工程施工的岩体内部损伤监测中具有一定的参考价值。     

基于单纯形寻优的响应面可靠性分析方法

结构可靠度计算常采用经典的响应面法拟合隐式功能函数或高维功能函数，而对于强非线性功能函数的实际工程问题，尽管其能够计算出结构可靠度的结果，但此时多项式响应面的拟合精度不够，很容易造成不收敛的现象。为了解决上述问题，将响应面法与单纯形寻优的思路进行结合来探求一种有效的计算方法。本文利用单纯形算法对每次迭代的验算点进行优化；再以优化后的设计验算点为中心进行取样，利用响应面法循环迭代计算；最后，沿着真实响应面逐渐逼近最终的验算点。该方法能够解决高维非线性的隐式极限状态方程可靠度计算收敛性的问题，可以提高计算精度和计算效率，具有一定的工程适用性。     

基于动态响应参数的点阵桁架夹芯板脱焊损伤检测数值方法研究

点阵桁架夹芯板作为一种特殊的超轻多孔材料,具有广阔应用前景。针对其加工和服役过程中经常发生的脱焊损伤,本文提出一种基于结构振动特性进行金字塔型点阵桁架夹芯板无损评价的方法。首先,基于有限元理论对夹芯板在不同损伤状态(损伤个数、位置)下的振动特性进行数值模拟;然后基于计算所得振动特性参数,运用切比雪夫多项式逼近法计算相应均布载荷曲面的曲率,进而通过此参数与原始未损伤模型参数作差进行损伤识别;最后运用曲面拟合算法解决该检测方法对原始未损伤模型参数的依赖性问题。数值计算结果表明:四周简支金字塔型点阵桁架夹芯板中存在损伤时,损伤前后结构损伤位置处的均布载荷曲面的曲率差值比较明显,基于此差分方法可精确识别各种损伤状况下夹芯板脱焊损伤的位置和数量;利用曲面拟合算法可以消除损伤结构参数中因损伤造成的尖点,从而不需以原始未损伤模型参数为依据即可精确识别损伤。     

圆管截面齐次广义屈服函数与结构极限承载力

为克服圆管截面广义屈服准则不满足比例加载条件,导致采用弹性模量调整法求解该类结构极限承载力时存在计算结果受荷载初值影响、计算精度受损等问题,利用回归分析和最小二乘法研究建立了圆管截面广义屈服函数的齐次多项式,通过误差分析确定了齐次化多项式的阶次;据此定义了圆管截面薄壁构件的单元承载比、承载比均匀度和基准承载比,为高承载比薄壁单元的判别及其弹性模量调整提供了动态判据,进而依据能量守恒准则建立了以单元承载比为基本参数的模量调整公式,结合下限原理提出了圆管截面薄壁结构极限承载力分析的弹性模量缩减法。研究表明,选取齐次化多项式的广义屈服函数能更加准确地考虑各项内力对结构极限承载力的综合影响,具有良好的计算精度和效率,可应用于复杂圆管截面薄壁结构的极限承载力分析中。     

结构优化半解析灵敏度及误差修正改进算法

提出结构半解析灵敏度分析及其针对刚体位移的误差修正方法的改进算法, 构建灵敏度分析与误差修正项可分离形式. 该方法实现简便, 数值精度不受摄动步长与单元数目的影响. 首先从总体角度推得静力问题的误差修正半解析灵敏度分析方法, 提出了位移误差修正灵敏度列式, 并给出算法实施途径; 然后将此思路推广于自振频率、屈曲临界载荷问题, 提出了相应的计算步骤. 随后, 给出梁单元与壳单元误差修正项的具体推导方法, 并分别使用两种单元构建有限元模型进行算例测试. 结果表明, 该方法适用于多种分析类型, 数值精度不受单元数目与摄动步长的影响. 由于灵敏度分析与误差修正项可以分开计算, 该方法支持将误差修正项直接叠加于灵敏度求解结果进行误差修正, 使已有灵敏度分析程序得到充分利用. 尤其对于复杂工程结构的优化设计, 特别是形状优化设计以及尺寸、形状混合优化设计, 相比于原误差修正方法, 实现更为简便, 效率有所提升, 能为半解析灵敏度分析方法及其程序实现提供新的思路.      

Impact of truncation error and numerical scheme on the simulation of the early time growth of viscous fingering

The truncation error associated with different numerical schemes (first order finite volume, second order finite difference, control volume finite element) and meshes (fixed Cartesian, fixed structured triangular, fixed unstructured triangular and dynamically adapting unstructured triangular) is quantified in terms of apparent longitudinal and transverse diffusivity in tracer displacements and in terms of the early time growth rate of immiscible viscous fingers. The change in apparent numerical longitudinal diffusivity with element size agrees well with the predictions of Taylor series analysis of truncation error but the apparent, numerical transverse diffusivity is much lower than the longitudinal diffusivity in all cases. Truncation error reduces the growth rate of immiscible viscous fingers for wavenumbers greater than 1 in all cases but does not affect the growth rate of higher wavenumber fingers as much as would be seen if capillary pressure were present. The dynamically adapting mesh in the control volume finite element model gave similar levels of truncation error to much more computationally intensive fine resolution fixed meshes, confirming that these approaches have the potential to significantly reduce the computational effort required to model viscous fingering.     

Meshing Requirements for Tidal Modeling in the Western North Atlantic

This paper presents an a posteriori approach to unstructured mesh generation via a localized truncation error analysis and applies it to the Western North Atlantic Tidal (WNAT) model domain. The WNAT model domain encompasses the Gulf of Mexico, the Caribbean Sea, and the North Atlantic Ocean east to the 60°W Meridian. Herein, we pay particular attention to the area surrounding the Bahamas.

A bathymetric data set with fine resolution is employed in seven separate linear, harmonic simulations of shallow water tidal flow for seven different tidal-forcing constituents. Each set of simulation results is used to perform a truncation error analysis of a linear, harmonic form of the depth-averaged momentum equations for each of the seven different tidal-forcing frequencies. Truncation error is then driven to a more uniform, domain-wide value by solving for local node spacing requirements. The process is built upon successful research aiming to produce unstructured grids for large-scale domains that can be used in the accurate and efficient modeling of shallow water flow. The methodology described herein can also be transferred to other modeling applications.     

矩形槽内水体大幅晃动分析中截断误差影响范围判断方法探讨

液体大幅晃动是目前CFD研究中一个热点。在CFD中,偏微分方程离散所产生的截断误差是主要的误差来源,且与网格尺度密切相关。本文首先从理论上介绍了截断误差的产生过程,由此过程可知截断误差与物理粘性的作用具有类似性。以此概念为基础,根据液体晃动动力响应的特点提出了在液体大幅晃动分析中,如何通过对物理粘性系数的参数敏感性分析,判断截断误差的作用范围从而判断计算精度是否满足要求的方法,最后与现有试验资料进行对比校核,验证了该方法的实用性。     

2D unstructured mesh generation for oceanic and coastal tidal models from a localized truncation error analysis with complex derivatives

A method for computing target element size for tidal, shallow water flow is developed and demonstrated. The method, Localized truncation error analysis with complex derivatives (LTEA-CD) utilizes localized truncation error estimates of the linearized shallow water momentum equations consisting of complex derivative terms. This application of complex derivatives is the chief way in which the method differs from a similar existing method, LTEA. It is shown that LTEA-CD produces results that are essentially equivalent to those of LTEA (which in turn has been demonstrated to be capable of producing practicable target element sizes) with reduced computational cost. Moreover, LTEA-CD is capable of computing truncation error and corresponding target element sizes at locations up to and including the boundary, whereas LTEA can be applied only on the interior of the model domain. We demonstrate the convergence of solutions over meshes generated with LTEA-CD using an idealized representation of the western North Atlantic Ocean, Caribbean Sea and Gulf of Mexico.     

惯性导航系统的误差估计

惯性导航系统（INS）以其自主的工作能力广泛应用于军事武备的导航、制导与控制系统和国民经济的诸多领域。它的主要缺点是定位误差随其工作时间的增长而增大。对惯导系统的误差进行估计和补偿是在保证性能价格比的前提下，提高惯性导航系统精度的有效途径。目前，对惯导系统的误差修正均采用外信息（如GPS的输出信息）校正，即在INS工作的全部时间内，定期地利用GPS输出的速度和位置信息与INS输出的相应信息的差值作为观测量，对INS误差进行估计和补偿。Kalman滤波的方法广泛地应用于惯导系统的误差修正初始对准。本研究了当地水平惯导系统的误差估计和补偿问题。分析结果表明，采用Kalman滤波的方法，可以精确地估计惯导系统的误差（包括陀螺漂移和加速度计零偏），误差估计的精度高，并且估计的方差阵收敛快。     

Variable penalty method for finite element analysis of incompressible flow

A new scheme is applied for increasing the accuracy of the penalty finite element method for incompressible flow by systematically varying from element to element the sign and magnitude of the penalty parameter λ, which enters through ?.v + p/λ = 0, an approximation to the incompressibility constraint. Not only is the error in this approximation reduced beyond that achievable with a constant λ, but also digital truncation error is lowered when it is aggravated by large variations in element size, a critical problem when the discretization must resolve thin boundary layers. The magnitude of the penalty parameter can be chosen smaller than when λ is constant, which also reduces digital truncation error; hence a shorter word-length computer is more likely to succeed. Error estimates of the method are reviewed. Boundary conditions which circumvent the hazards of aphysical pressure modes are catalogued for the finite element basis set chosen here. In order to compare performance, the variable penalty method is pitted against the conventional penalty method with constant λ in several Stokes flow case studies.     

An estimation of the sensitivity of numerical error norm using adjoint model

A posteriori estimation of the numerical error sensitivity to the local truncation error is addressed using adjoint model endowed with the information on the error field. The numerical error is estimated from the solution of the linear tangent model (LTM) or from a Richardson extrapolation. The local truncation error used in the LTM is obtained by the action of a high‐order finite‐difference stencil on the field computed by the main (low‐order accuracy) algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Incorporating spatially variable bottom stress and Coriolis force into 2D,a posteriori,unstructured mesh generation for shallow water models

An enhanced version of our localized truncation error analysis with complex derivatives (LTEA?CD ) a posteriori approach to computing target element sizes for tidal, shallow water flow, LTEA+CD , is applied to the Western North Atlantic Tidal model domain. The LTEA + CD method utilizes localized truncation error estimates of the shallow water momentum equations and builds upon LTEA and LTEA?CD‐based techniques by including: (1) velocity fields from a nonlinear simulation with complete constituent forcing; (2) spatially variable bottom stress; and (3) Coriolis force. Use of complex derivatives in this case results in a simple truncation error expression, and the ability to compute localized truncation errors using difference equations that employ only seven to eight computational points. The compact difference molecules allow the computation of truncation error estimates and target element sizes throughout the domain, including along the boundary; this fact, along with inclusion of locally variable bottom stress and Coriolis force, constitute significant advancements beyond the capabilities of LTEA. The goal of LTEA + CD is to drive the truncation error to a more uniform, domain‐wide value by adjusting element sizes (we apply LTEA + CD by re‐meshing the entire domain, not by moving nodes). We find that LTEA + CD can produce a mesh that is comprised of fewer nodes and elements than an initial high‐resolution mesh while performing as well as the initial mesh when considering the resynthesized tidal signals (elevations). Copyright © 2008 John Wiley & Sons, Ltd.