解三维摩擦接触问题的一个二阶锥线性互补法

针对三维摩擦接触问题的求解,给出了一种基于参变量变分原理的二阶锥线性互补法. 首先,基于三维Coulomb摩擦锥在数学表述上属于二阶锥的事实,利用二阶锥规划对偶理论,建立了三维Coulomb摩擦接触条件的参变量二阶锥线性互补模型,它是二维Coulomb摩擦接触条件参变量线性互补模型在三维情形下的自然推广;随后,利用参变量变分原理与有限元方法,建立了求解三维摩擦接触问题的二阶锥线性互补法. 较之于将三维Coulomb摩擦锥进行显式线性化的线性互补法,该方法无需对三维Coulomb摩擦锥进行线性化,因而在保证精度的前提下所解问题的规模要小很多. 最后通过算例展示了该方法的特点.      

基于三级多源信息融合结构的SINS性能测试综合评估算法

针对SINS性能测试存在指标多、不确定性等问题,提出了一种基于三级多源信息融合结构的SINS性能测试综合评估算法。给出了包括精度测试、稳定性测试和可靠性测试等三大性能测试指标和16个性能测试底层子指标构成的SINS性能测试指标体系,并构建SINS测试评估结构框架。利用多个专家对底层性能测试子指标进行评估给出相应性能子指标的模糊评价,并构造基本置信指派组成多个证据;利用基于局部冲突分配的组合规则进行三级证据融合,得到性能测试指标的综合评价结果。仿真实验结果表明:与传统的证据理论融合方法相比,该算法可以较为全面地很好地评估SINS性能,而且结果更为合理。     

正交各向异性摩擦接触分析的一个二阶锥线性互补法

建立了用于各向异性摩擦接触分析的一个新型互补模型:二阶锥线性互补模型.通过与弹塑性力学的类比,并引入"线性二阶锥互补"的概念,将正交各向异性摩擦接触定律表达为一个二阶锥线性互补模型.在此基础上,在参变量变分原理的框架下,建立了正交各向异性摩擦接触问题的有限元列式.由于避免了对摩擦锥的显式线性化,使得该文模型的变量个数较线性互补模型小很多,而解的精度又高很多.文末通过算例,说明了方法对于正交各向异性摩擦接触分析的有效性.     

关于壳体的一般理论的一个经典错误及其修正

在经典力学发展的历史中,对于特征方程有重根的二阶线性微分方程的初值问题的解,在一个很长的历史时期内被当成发散的,致使许多有关的力学问题被错误的给出答案。虽然这一错误早在拉格朗日时代已被更正,然而在符拉索夫所著的“壳体的一般理论及其在工程中的应用”一书中,在讨论壳体的无力矩理论     

关于壳体的一般理论的一个经典错误及其修正

在经典力学发展的历史中,对于特征方程有重根的二阶线性微分方程的初值问题的解,在一个很长的历史时期内被当成发散的,致使许多有关的力学问题被错误的给出答案。虽然这一错误早在拉格朗日时代已被更正,然而在符拉索夫所著的"壳体的一般理论及其在工程中的应用"一书中,在讨论壳体的无力矩理论...     

解Drucker-Prager塑性问题的二阶锥互补法

基于经典弹塑性理论中多数屈服准则具有凸锥数学结构的事实,将在大规模计算中更具潜力的锥规划法引入弹塑性分析。考虑到弹塑性流动理论有关联与非关联之分,本文提出利用锥型互补法求解弹塑性问题。具体以Drucker-Prager弹塑性模型为例,首先利用最大塑性功耗散原理和圆锥对偶理论等工具,建立了弹塑性本构方程的等价二阶锥互补模型;然后,基于参变量变分原理和有限元技术,建立了弹塑性增量分析的二阶锥线性互补模型;最后,利用一类半光滑Newton算法求解。数值算例表明了本文方法的有效性。     

一般非对称非经典结构响应的二阶实振子精确解耦法

为使现代一般非对称非经典结构的分析和设计法等同于基于物理意义明确的二阶标准振子传统经典结构,对该类结构响应的二阶标准实振子精确解耦法进行了系统研究。首先,运用复模态法对具有一般非对称质量和刚度矩阵及非对称非经典阻尼矩阵结构的响应进行精确解耦;其次,构造复响应量与实响应量的变换关系,运用拉氏变换,通过实矩阵坐标变换法,将一般非对称非经典结构及被动减震结构的位移与速度响应精确解耦为系列二阶标准实振子位移与速度响应及地震位移与速度响应的线性组合,并使系列标准振子的广义荷载仅为原始荷载的实数线性组合;最后,对实振子与实模态解耦法进行了对比分析。结果表明:实模态解耦法是实振子解耦法的特殊情况;当一般非对称非经典结构退化为经典结构时,实矩阵坐标变换法退化为实模态坐标变换法,实振子解耦法退化为实模态解耦法。此外,运用本文所建立的方法,可将现有的成熟经典结构体系的分析与设计法直接推广到一般非对称非经典复杂结构体系。     

线性哈密顿系统的本征摄动法

利用哈密顿算子辛自共轭的特点讨论了保守哈密顿体系的摄动问题,给出了哈密顿矩阵的本征值与本征向量的二阶摄动分析方法。即当系统在哈密顿框架下进行较小修改时,不重复求解大型哈密顿矩阵的本征问题,只需在原系统的模态参数基础上进行模态分析即可,这种矩阵摄动法给出了修改后矩阵的二阶本征值和本征向量,为一般线性保守体系的本征摄动求解提出了一个新方法。     

非惯性坐标系中的边界层方程

本文用匹配渐近展开法导出二维翼型在非惯性坐标系中的一阶和二阶边界层方程,消去压强项后,一阶边界层方程与经典边界层方稃相同;惯性力的作用在二阶边界层中才出现。     

二阶非定常多宗量热传导反问题的正则解

引入Bregman距离函数及其加权函数作为正则项，应用Tikhonov正则 化方法，对二阶非定常多宗量热传导反问题进行求解. 利用测量信息和计算信息构造最小二 乘函数，将多宗量反演识别问题转化为一个优化问题. 空间上采用8节点等参元进行离散， 时域上采用时域精细算法进行离散，建立了二阶非定常多宗量热传导问题的有限元正/反演数 值模型. 该模型不仅考虑了非均质和参数分布的影响，而且也便于正反演问题的敏度分析， 可对导热系数和边界条件等宗量进行有效的单一和组合识别. 给出了相关的数值验证，对信 息测量误差以及不同正则项的计算效率作了探讨. 数值结果表明，该方法能够对二阶非定常 多宗量热传导反问题进行有效的求解，并具有较高的计算精度.     

Robustness of the hybrid DRP‐WENO scheme for shock flow computations

This paper describes a new variant of hybrid scheme that is constructed by a wave‐capturing scheme and a nonoscillatory scheme for flow computations in the presence of shocks. The improved fifth‐order upwind weighted essentially nonoscillatory scheme is chosen to be conjugated with the seven‐point dispersion‐relation‐preserving scheme by means of an adaptive switch function of grid‐point type. The new hybrid scheme can achieve a better resolution than the hybrid scheme which is based on the classical weighted essentially scheme. Ami Harten's multiresolution analysis algorithm is applied to density field for detecting discontinuities and setting point values of the switch function adaptively. Moreover, the tenth‐order central filter is applied in smooth part of the flow field for damping dispersion errors. This scheme can promote overall computational efficiency and yield oscillation‐free results in shock flows. The resolution properties and robustness of the new hybrid scheme are tested in both 1D and 2D linear and nonlinear cases. It performs well for computing flow problems with rich structures of weak/strong shocks and large/small vortices, such as the shock‐boundary layer interaction problem in a shock tube, which illustrates that it is very robust and accurate for direct numerical simulation of gas‐dynamics flows. Copyright © 2011 John Wiley & Sons, Ltd.     

抗差自适应插值粒子滤波及其在组合导航中的应用

针对粒子滤波存在的粒子退化和重要性密度函数难以选取的问题,在吸收抗差自适应滤波、二阶插值滤波和粒子滤波算法优点的基础上,提出了一种新的抗差自适应插值粒子滤波算法。该算法利用二阶插值滤波算法得到重要性密度函数,通过抗差自适应因子实时控制动力学模型误差及观测异常对导航解的影响。将该算法应用于SINS/CNS/SAR组合导航系统进行计算仿真,并与经典的粒子滤波算法进行比较分析。结果表明,提出的滤波算法得到的姿态误差控制在[-0.3′,+0.3′],速度误差控制在[-0.4 m/s,+0.4 m/s],位置误差控制在[-5 m,+5 m],性能明显优于经典的粒子滤波算法。新的滤波算法不但能够有效地抑制粒子退化,而且能够有效地控制动力学模型误差及观测异常的影响,提高了组合导航的滤波精度。     

Vibration reduction in a flexible-link mechanism through synthesis of an optimal controller

In this paper, reduction of vibration of a flexible planar mechanism is achieved through synthesis of an optimal controller. A finite element model, based on the equivalent rigid-link system theory, is used to accurately describe the dynamic behavior of the system. The model, which accounts for geometric and inertial nonlinearities of the mechanism, has been fully validated through experimental tests. In order to be able to employ the classical optimal control theory, a suitable linear model has been derived from the original one by means of a suitable linearization procedure. Vibration reduction can then be obtained by first defining an adequate performance index, which accounts for vibration amplitude, then by solving Riccati’s equation in order to find the controller that minimizes the performance index, i.e. the optimal controller. The results of several tests that have been carried out are also reported, to show the effectiveness of the synthesized control system.     

Moment Lyapunov exponent for three-dimensional system under real noise excitation

The pth moment Lyapunov exponent of a two-codimension bifurcation system excited parametrically by a real noise is investigated. By a linear stochastic transformation, the differential operator of the system is obtained. In order to evaluate the asymptotic expansion of the moment Lyapunov exponent, via a perturbation method, a ralevant eigenvalue problem is obtained. The eigenvalue problem is then solved by a Fourier cosine series expansion, and an infinite matrix is thus obtained, whose leading eigenvalue is the second-order of the asymptotic expansion of the moment Lyapunov exponent. Finally, the convergence of procedure is numerically illustrated, and the effects of the system and the noise parameters on the moment Lyapunov exponent are discussed.     

非稳态Hamilton-Jacobi方程的7阶加权紧致非线性格式

Hamilton-Jacobi (HJ) 方程是一类重要的非线性偏微分方程, 在物理学、流体力学、图像处理、微分几何、金融数学、最优化控制理论等方面有着广泛的应用. 由于HJ方程的弱解存在但不唯一, 且解的导数可能出现间断, 导致其数值求解具有一定的难度. 本文提出了非稳态HJ方程的7阶精度加权紧致非线性格式 (WCNS). 该格式结合了Hamilton函数的Lax-Friedrichs型通量分裂方法和一阶空间导数左、右极限值的高阶精度混合节点和半节点型中心差分格式. 基于7点全局模板和4个4点子模板推导了半节点函数值的高阶线性逼近和4个低阶线性逼近, 以及全局模板和子模板的光滑度量指标. 为避免间断附近数值解产生非物理振荡以及提高格式稳定性, 采用WENO型非线性插值方法计算半节点函数值. 时间离散采用3阶TVD型Runge-Kutta方法. 通过理论分析验证了WCNS格式对于光滑解具有最佳的7阶精度. 为方便比较, 经典的7阶WENO格式也被推广用于求解HJ方程. 数值结果表明, 本文提出的WCNS格式能够很好地模拟HJ方程的精确解, 且在光滑区域能够达到7阶精度; 与经典的同阶WENO格式相比, WCNS格式在精度、收敛性和分辨率方面更优, 计算效率略高.      

一种提高车载定位定向系统定位精度的方法

在车载定位定向系统中,通常采用停车修正或引入GPS等外信息校正系统,这会降低陆地武器装备的战场生存能力和自主性。基于上述情况,分析了惯导系统以及与里程计构成的航位推算系统的误差模型,得出了惯导系统短时间内定位精度高以及航位推算系统定位误差随时间增长缓慢的规律。据此推导并提出了一种提高系统定位精度的方法,该方法不需要停车或外部信息,首先利用惯导系统对航位推算系统进行校正,估计出里程计标度因数误差和载车的安装误差并进行补偿;之后利用航位推算系统对惯导系统进行校正;采用加权函数对系统位置输出进行加权优化处理。理论分析和仿真实验表明利用此方法在2 min内能估计出里程计标度因数误差和载车的安装误差,估计精度在90%以上;加权后的位置输出精度在0.2%D(D为里程)以上。     

Weighted averaged equations for modeling velocity profiles of 1D steady open channel flows

A new mathematical algorithm is proposed to address the essential details of vertical distributions of horizontal velocity for one‐dimensional steady open‐channel flow. This new algorithm comprises a system of weighted averaged equations developed from corresponding Reynolds equations by performing weighted average operations instead of conventional depth average operations. It is the system of weighted averaged equations, instead of the vertical grids, that allows for more hydraulic coefficients identifiable. It can be thought of as an extension of the St. Venant equations to address the vertical distributions of horizontal velocities, as well as the water surface profiles. To avoid the difficult expansion of governing partial differential equations in high order, an indirect scheme is proposed to solve hydraulic variables through their weighted average values. The governing partial differential equations are generated by using a variety of weight functions, and the weighted averages of relevant hydraulic variables are taken as the unknown independent variables to be solved first. Then, on the basis of the values and polynomial expansions of these weighted averaged velocities, a system of linear algebraic equations is generated and the unknown hydraulic variables or their coefficients are easily solved. Note that the new model is not proposed to compete with any three‐dimensional models in modeling accuracy or accommodation ability to all conditions. It just provides a valuable option to study the vertical structure of flow in open channels where only essential detail and reasonable accuracy of vertical distributions are required, and the data availability and other conditions limit the application of fully three‐dimensional models. The performance of the model is evaluated with experimental data of flows in two different flumes. It is shown that the model well predicted the velocity profiles of sections along the centerlines of these flumes with reasonable accuracy and essential details of vertical distributions of horizontal velocity. Copyright © 2013 John Wiley & Sons, Ltd.     

An efficient algorithm for elasto-viscoplastic vibrations of multi-layered composite beams using second-order theory

An efficient time-domain algorithm for plane non-linear flexural vibrations of multi-layered composite beams, which are driven into the inelastic range by severe transverse loadings, is presented. The influence of an axial static preload is considered in the sense of the quasi-linear second-order theory of structures. The inelastic parts of strain are treated as additional sources of selfstress in the linear elastic background-structure, driving the elastic response into the inelastic one. The efficiency of this exact formulation lies in the fact that linear solution techniques can be used in their most powerful form: Rubin's useful formulation for the quasi-static second-order transfer-matrix of linear elastic structures is applied in combination with modal analysis. Having in mind multi-metal beams, the classical lamination theory is assumed to be valid. Beams with overhang composed of ideal elastic-plastic and viscoplastic layers are studied as example structures. The fictitious sources of selfstress are calculated from the different material laws of the layers in a numerical time-stepping procedure, where a generalized midpoint-rule in combination with Crisfield's secant-Newton procedure is used.     

黏弹夹芯板的有限元建模及实验研究

从有限元分析和数值模拟及实验验证的角度研究了黏弹夹芯板的频率依赖振动特性。夹芯板中间层为黏弹性材料，其刚度和阻尼的频率依赖性行为直接影响系统的模态频率和阻尼，并导致振动模式求解的复杂化。采用三阶七参数Biot模型描述黏弹性材料频率相关的黏弹性行为。开发了三层四节点28自由度的夹芯板单元，基于经典板理论和哈密顿原理建立了黏弹夹芯板的有限元动力学方程。通过引入辅助耗散坐标，将Biot模型和黏弹夹芯板的有限元动力学模型结合起来，并将其转化为常规二阶线性系统形式，极大简化了求解非线性振动特性的过程。对一边固定、另三边自由的黏弹夹芯板进行了前三阶固有频率和损耗因子的预测，并与实验结果对比。数值模拟结果和实验结果吻合良好，说明所提有限元方法是正确有效的。