Analysis of an arbitrarily loaded shell of revolution based on the finite element method in a mixed formulation

The volume finite element in the form of hexahedron with nodal unknowns as components of the displacement vector and stress tensor has been developed to analyze the shells of revolution. The displacement vector components for the inner point of the finite element and the components of its stress tensor are expressed through the nodal unknowns using the method of vector and tensor fields interpolation by the trilinear shape functions; that provides taking into account the finite element displacement as a whole solid. The variational principle in a mixed formulation is applied to form the matrix of hexahedron deformation. The efficiency of the proposed method for approximating the values being sought as vector and tensor fields in comparison with the traditional method for approximating the values being sought as scalar fields is confirmed by a numerical example.     

扰动线运动对惯性系粗对准影响分析及优化方法

针对扰动线运动对惯性系粗对准精度影响较大的问题，通过分析惯性体坐标系下重力加速度积分矢量的物理含义，给出了受扰动线运动影响的惯性系粗对准的误差分析。并在此基础上提出了基于位移积分矢量构造定姿矢量矩阵的抗扰动粗对准算法，利用对速度积分矢量进一步积分得到的3个时间点的位移积分矢量构建姿态解算矩阵，抑制扰动线运动对粗对准精度的影响。仿真结果表明，该算法可有效减小扰动线运动影响下的对准结果振动幅值，能够快速收敛到满足精对准使用的精度范围，从而提高武器装备环境适应性。     

扰动线运动对惯性系粗对准影响分析及优化方法

针对扰动线运动对惯性系粗对准精度影响较大的问题,通过分析惯性体坐标系下重力加速度积分矢量的物理含义,给出了受扰动线运动影响的惯性系粗对准的误差分析。并在此基础上提出了基于位移积分矢量构造定姿矢量矩阵的抗扰动粗对准算法,利用对速度积分矢量进一步积分得到的3个时间点的位移积分矢量构建姿态解算矩阵,抑制扰动线运动对粗对准精度的影响。仿真结果表明,该算法可有效减小扰动线运动影响下的对准结果振动幅值,能够快速收敛到满足精对准使用的精度范围,从而提高武器装备环境适应性。     

改进型SVM在轴向磁轴承转子位移自检测中的应用

磁轴承采用位移自检测技术能够减少磁轴承体积、降低成本和提高可靠性。提出了一种基于混合核函数最小二乘支持向量机(LSSVM)预测模型的磁轴承自检测技术。介绍了轴向主动磁轴承的工作原理并推导了其悬浮力的数学模型;在混合核函数LSSVM回归原理的基础上,建立了控制线圈电流与转子位移之间的非线性预测模型,并优化了LSSVM参数,实现了无位移传感器控制。构建了轴向主动磁轴承系统自检测仿真模型,针对所提自检测方法进行了仿真研究,仿真结果表明该模型能够准确预测转子轴向位移。进一步的试验结果表明,该方法具有良好的轴向位移自检测性能,实现了轴向主动磁轴承无位移传感器下稳定悬浮运行。     

Analysis of geometrically nonlinear shells of revolution based on the finite element method with the vector interpolation of desired quantities

In this paper, we present an algorithm for geometrically nonlinear finite element analysis of the shells of revolution. Use is made of the most proper algorithms for vector interpolation of displacements through the nodal unknowns and an efficient algorithm for obtaining the stress-strain increment relation at a step of loading. By comparing the results of analyzing a geometrically nonlinear shell of revolution obtained on the basis of the ANSYS software with the scalar interpolation of displacements with those obtained on the basis of an author-developed finite element, it has been shown that application of the FEM vector displacement interpolation leads to increasing the accuracy of the finite element solutions in analyzing the stress-strain state of the geometrically nonlinear shells.     

Strapdown inertial navigation using dual quaternion algebra: error analysis

In a strapdown inertial navigation system (INS), the general displacement of a rigid body is traditionally separately modeled and analyzed, i.e., direction cosine matrix or quaternion for rotation analysis and vector for translation analysis. As a subsequent work of a companion paper (Wu et al., 2005), this paper adopts dual quaternion algebra, a most concise and unified mathematical tool for representing the general displacement of a rigid body, to analyze error characteristics of the strapdown INS. Two new error models in terms of quaternion algebra are developed: the additive dual quaternion error (ADQE) model and multiplicative dual quaternion error (MDQE) model. Both are expected to facilitate the future inertial navigation-based integrated navigation filter.     

Auto-normalization algorithm for robotic precision drilling system in aircraft component assembly

A novel approach is proposed to detect the normal vector to product surface in real time for the robotic precision drilling system in aircraft component assembly, and the auto-normalization algorithm is presented based on the detection system. Firstly, the deviation between the normal vector and the spindle axis is measured by the four laser displacement sensors installed at the head of the multi-function end effector. Then, the robot target attitude is inversely solved according to the auto-normalization algorithm. Finally, adjust the robot to the target attitude via pitch and yaw rotations about the tool center point and the spindle axis is corrected in line with the normal vector simultaneously. To test and verify the auto-normalization algorithm, an experimental platform is established in which the laser tracker is introduced for accurate measurement. The results show that the deviations between the corrected spindle axis and the normal vector are all reduced to less than 0.5°, with the mean value 0.32°. It is demonstrated the detection method and the auto-normalization algorithm are feasible and reliable.     

The finite element analysis of shells of revolution with a branching meridian

We present an algorithm for calculating the shells of revolution with the branching meridian using the triangular finite elements, the rigidity matrices of which are formed based on the vector method of displacement interpolation [1]. The correct kinematic and static conditions of shell conjugation on the line of their coupling have been developed. The shell structure consisting of a cylinder and adjacent shells is calculated under various conditions of support.     

二元推力矢量喷管导流板的设计研究

在某型飞机进行二元推力矢量改装时，为了获得俯仰方向的矢量推力，必须对飞机尾喷口气流进行导向，以便实现推力方向的改变。本文将喷口导流板设计成由矩形板部分和三角形部分组合成的一个几何体，利用有限元软件Patran对导流板进行了应力强度分析和变形分析，得出不同的三角形高度和不同的矩形宽度组成的导流板的应力分布场和变形位移场不同。通过对不同宽度的矩形板和不同高度的三角形板组成的导流板的分析计算得出，导流板最大应力和最大位移随三角形高度变化曲线，从而确定最佳的三角形高度和矩形板宽度。     

机动转弯条件下转子有限元建模方法

为了使机动转弯条件下转子动力学模型更加精确,考虑梁单元的转动惯量和剪切变形,对有限元Timoshenko梁模型的相关理论进行推导;考虑到机动转弯载荷对转子响应的影响,对机动转弯条件下梁单元、刚性圆盘单元的机动载荷向量和重力载荷向量进行推导。利用以上推导结果建立了1套机动转弯条件下转子有限元的建模方法,利用该方法建立的模型进行机动转弯过程中含弹性支承双盘转子的振动响应计算,结果表明:机动转弯产生的附加载荷会使转子模型产生一定的静位移。     

飞机结构加筋壁板参数化有限元模型的实现

提出一种基于MSC.Nastran/Patran的加筋板结构有限元模型自动生成方法.方法对加筋条位置、加筋条几何尺寸、底板几何尺寸、材料物性以及网格密度完全参数化,给出标量参数、向量参数、字符参数及动态数组在PCL函数中的具体应用,载荷、约束以及材料特性全部施加于几何体以实现网格密度的自动疏密控制.实例表明,对于帽型加筋板,张角为60°时壁板位移最小.     

Stress-strain state analysis of shells of revolution based on the triangular discretization element with the Lagrange multipliers

The present paper sets forth an algorithm of analyzing thin shells with significant gradients of meridian curvature based on the Kirchhoff-Love hypothesis and finite element method. As a discretization element use is made of a triangular fragment of the middle surface with the Lagrange multipliers in additional nodes arranged in the triangle side middles. We apply the vector method of displacement interpolation that has a number of advantages over the conventional interpolation procedure. The high efficiency of the algorithm developed is confirmed by the numerical examples.     

交互式棱柱网格生成中翘曲现象形成机制及消除算法

在基于径向基函数插值的交互式棱柱网格生成中,当物面网格单元空间法矢变化范围较大或变化剧烈时,棱柱网格生成会发生翘曲问题,降低棱柱网格质量。针对该问题,首先采用DLR-F6机翼外形算例对翘曲现象进行了介绍和初步分析,并结合平板外形棱柱网格生成,通过不同波长推进位移扰动模拟法矢变化对推进位移的影响,研究棱柱网格翘曲现象的形成机制。不同位移扰动下平板棱柱网格生成结果证实边界棱线网格点推进位移不光滑会通过空间插值放大,引起棱柱网格发生翘曲,且网格翘曲的表现形式与推进位移的分布有关。从而间接表明棱柱网格生成中翘曲现象是由法矢变化带来推进位移分布不光滑引起的。然后从翘曲现象的形成机制出发,基于拉普拉斯方法发展了推进位移光顺技术,并通过DLR-F6机翼算例进行了验证。测试结果表明,光顺技术能够完全消除棱柱网格的翘曲,获得光顺的高质量棱柱网格。最后通过DLR-F6翼身组合体外形棱柱网格生成,展示了添加光顺技术的棱柱网格生成算法的应用潜力。     

Optimization and verification of free flight separation similarity law in high-speed wind tunnel

Based on the similarity of separation time, a similarity law optimization method for high-speed weapon delivery test is derived. The typical separation state under wind load is simulated by the numerical method. The real separation data of aircraft, separation data of previous test methods, separation data of ideal wind tunnel test of previous methods, and simulation data of the proposed optimization method are obtained. A comparison of the data shows that the method proposed can improve the performance of tracking. Similarity law optimization starts with the development of motion equations and dynamic equations in the windless state to address the problems of mismatching between vertical and horizontal displacement, and to address the problems of separation trajectory distortion caused by insufficient gravity acceleration of the scaling model of existing light model. The ejection velocity of the model is taken as a factor/vector, and is adjusted reasonably to compensate the linear displacement insufficiency caused by the insufficient vertical acceleration of the light model method, so as to ensure the matching of the vertical and horizontal displacement of the projectile, and to improve the consistency between the test results of high-speed projection and the actual separation trajectory. The optimized similarity law is applicable to many existing free-throwing modes of high-speed wind tunnels. The optimized similarity law is not affected by the ejection velocity and hanging mode of the projectile. The optimized similarity law is suitable not only for the launching of the buried ammunition compartment and external stores, but also for the test design of projectile launching and gravity separation.     

二元推力矢量喷管导流管的设计研究

针对某型飞机进行二元推力矢量改装时对发动机出口的气流进行过渡转换的问题，设计了喷管导流管，将导流管气流截面由圆形过渡到长方形。本文利用有限元软件PATRAN对导流管进行了应力强度分析和变形分析，得出导流管的应力分布场和变形位移场，通过对不同厚度的导流管的分析计算得出导流管最大应力和最大位移随管壁厚度变化曲线，从而确定最佳的管壁厚度。研究了导流管最大应力和最大位移沿轴向的变化曲线，并对导流管的结构进行了优化设计，给出两种优化设计方案，得到较为理想的结构。     

轴对称推力矢量喷管载荷变形的控制补偿

研究了温度场和气动载荷联合作用下的轴对称矢量喷管出口面积和偏转角度误差的补偿问题.建立了扩张调节片位姿参数与其悬挂机构尺度之间的关系,导出了悬挂机构关节角位移增量与构件长度增量之间的微分方程,得到喷管出口面积误差和矢量偏转角误差与负载变形之间的解析表达式.利用矢量偏转角度和面积与轴对称矢量喷管转向驱动机构动平台位姿之间的关系,建立了受温度场和气动载荷联合作用下的动平台位姿补偿方程.研究表明,补偿后的矢量偏转角度和面积的相对误差不大于1%.      

采用壳体应变—应力状态的体—壳过渡元

由于初始热应变表达式不当及不能完全实现泊松效应,以往建立的体-壳过渡元会导致不真实的大应力。本文采用壳体应变-应力状态作为过渡元中的应变应力状态,给出~种新的15节点体-壳过渡元列式,从而解决了以上两个方面的问题。算例表明了这种过渡元的有效性与实用性。本文方法既适用于其它类型的过渡元,对于其它处理体-壳组合结构的方法也有重要参考价值。     

MPT方法中的纳米粒子识别技术

多粒子追踪（MPT）是测量粒子布朗运动的一种方法。在200nm粒子扩散系数实验测量中,对MPT方法中的粒子识别和粒子匹配两个重要环节提出改进：在粒子识别时,通过调节灰度阈值并检测光斑面积的改变,可有效分别真实粒子和光晕引起的＂伪粒子＂;在粒子匹配中,将手动追踪和程序追踪得到的粒子单步位移用矢量法表示,可直观显示不同追踪方法的粒子匹配效果。实验结果表明,在MPT方法中增加上述措施后,手动追踪和程序追踪获得的实验扩散系数之间的偏差由8%~13%减小为2%~8%,说明基于阈值敏感性的＂伪粒子＂剔除方法合理、有效。     

计入离心力影响的直升机旋翼翼型结冰数值模拟

建立了一套计入离心力影响的直升机旋翼翼型结冰的数值模拟方法.首先生成围绕翼型的贴体正交网格,然后用Navier-Stokes（N-S）方程求解黏性绕流流场.在此基础上,利用拉格朗日法建立水滴运动方程.其中,为提高计算效率,提出了结合位移矢量的水滴所处单元寻觅方法.最后,结合桨叶工作特点,发展了一种计入离心力影响的三维结冰模型.通过与桨叶结冰实验的对比,验证了本文结冰预测方法的可靠性.对比常规结冰模型,桨叶结冰量减少22.3%;若考虑桨叶的挥舞运动影响,桨叶结冰量进一步减少,表明了离心力及桨叶运动在结冰数值模拟中的重要性.通过不同剖面间的结冰量和冰形对比,分析并获得了桨叶结冰特征.结果表明离心力的影响程度随径向位移的增加而增加,下翼面结冰量随挥舞角的增加而减少.      

灾害天气下大跨屋盖多模态随机离散风致响应研究

研究了具有空间相关性随机风荷载有色噪声过程的数学模型,讨论了用随机白噪声过程滤波生成脉动风荷载的方法。高阶振型对大跨屋盖随机风致响应的贡献不可忽略。本文根据模态解耦原理并结合精细时程积分法,提出了多模态随机离散精细积分法,推导了大跨屋盖风致响应与风效应系数的计算公式。通过大跨屋盖刚性和气弹模型风洞试验,计算了屋盖随机风致动力响应时程。同时研究了大跨屋盖的荷载风效应系数和位移风效应系数的分布情况,结果与有限元分析较吻合,验证了多模态随机离散精细积分法的正确性,证实了该方法是一种简便、快速、准确的大跨屋盖风致响应计算方法。