一般硬化材料弹塑性轴对称圆柱壳的工程解法

在小弹塑性变形条件下，首先将应力写成应变的奇次四项式的幂函数形式，使其相当精确地拟合材料的拉伸曲线，然后，应用线弹性轴对称圆柱壳的位移模态和一待定系数构成弹塑性壳的位移场，再应用最小势能原理确定该系数，从而得到封闭解。     

矩形薄板线弹性变曲的一般解析解

基于Kirchhoff薄板理论，从板的控制微分方程出发，得到了双以前文献中的更加完全的解函数，因此能够求解更多的不同边界条件矩形板问题。本文求争三边固定一边自由矩形板和两对边固定两对边自由矩形板， 并同有限元结果可进行比较。     

一类非线性椭圆型方程的非平凡广义解

给出了相应的拟线性方程的定解问题的集中列紧引理 ,利用这一结果得到了方程在无界区域中非平凡解的存在性。最后给出了这一结论的一个应用     

四种粘弹性地基上弹性地基板的自由振动解

本文首先推出了四种粘弹性地基上弹性薄板在时间域上的动力学方程，并给出了三元件和Kelvin粘弹性地基上矩形薄板的固有频率的解析解，然后对振动特性进行了分析和比较，最后给出了算例和结果讨论。     

两端固支深梁弯曲问题的解析解

引入单位脉冲函数和Dirac函数之后，从平面应力基本方程出发，建立了两端固支深梁静力问题的状态方程，还给出了问题的解析解。算例分析表明，本文方法计算效率和计算精度相当好。     

奇异摄动与鸭解

鸭解是近年来在奇异摄动方程的研究中发现并开始研究的，它是一种新的分支现象，关于这方面的结果不是很多，且在大多数文献中多采用非标准方法，本文则利和渐近分析法，微分方程定性理论及不动点方法，对一类特殊的单参数奇异摄动方程鸭解的存在性进行研究。给出了鸭解存在的充分条件及其所对应参数的估计；并给出了鸭解的近似表达式，利用这些结果可以清楚地描述这类方程当参数变化时相图的变化情况。     

Analytical redundancy of variable cycle engine based on variable-weights neural network

In this paper, variable-weights neural network is proposed to construct variable cycle engine’s analytical redundancy, when all control variables and environmental variables are changing simultaneously, also accompanied with the whole engine’s degradation. In another word, variable-weights neural network is proposed to solve a multi-variable, strongly nonlinear, dynamic and time-varying problem. By making weights a function of input, variable-weights neural network’s nonlinear expressive capability is increased dramatically at the same time of decreasing the number of parameters. Results demonstrate that although variable-weights neural network and other algorithms excel in different analytical redundancy tasks, due to the fact that variable-weights neural network’s calculation time is less than one fifth of other algorithms, the calculation efficiency of variable-weights neural network is five times more than other algorithms. Variable-weights neural network not only provides critical variable-weights thought that could be applied in almost all machine learning methods, but also blazes a new way to apply deep learning methods to aeroengines.     

9自由度混联微创外科机器人的正反解

针对北京航空航天大学机器人研究所最新开发的用于胸腹部冷冻穿刺手术的9自由度"5R+4T"混联机器人,基于指数积公式,利用反变换法和逆矩阵的特性,提出了一种在单约束条件下,得到该机器人解析形式正反解的新算法.通过数值算例验证了正反解的互推性,即算法的有效性,并经过对算例的分析给出了修正方案,扩大了算法的适用范围.该方法克服了因为混联机器人自由度多、结构复杂而带来的难以完成正反解计算的困难,为多自由度混联机器人的运动学求解提供了一种新的思路.      

轨道交会、悬停及绕飞控制的解析解方法

面向航天器交会对接、编队伴飞以及在轨操控等空间应用的需求,分别对近圆、椭圆轨道上航天器间的相对运动进行了分析与建模,在常值推力作用假设下进行了相对运动的解析求解。采用模型预测的方法获得航天器相对位置和相对速度的预期偏差。通过广义逆变换构造关于预期偏差的最小范数、最小二乘全状态反馈控制器。提出了一种普遍适用于近圆、椭圆轨道,可以实现轨道交会、相对悬停保持和循迹绕飞,对相对位置和相对速度进行同步控制的高精度、高稳定度相对制导律。仿真结果校验了方法的可行性和有效性。     

Nonlinear bending analysis of a 3D braided composite cylindrical panel subjected to transverse loads in thermal environments

The aim of this study is to investigate nonlinear bending for a 3-Dimensional(3D)braided composite cylindrical panel which has transverse loads on its finite length. By refining a micro-macro-mechanical model, the 3D braided composite can be treated as a representative average cell system. The geometric structural properties of its components deeply depend on their positions in the section of the cylindrical panel. The embedded elastic medium of the panel can be described by a Pasternak elastic foundation. Via using the shell theory of the von Ka′rma′nDonnell type of kinematic nonlinearity, governing equations can be established to get higherorder shear deformation. The mixed Galerkin-perturbation method is applied to get the nonlinear bending behavior of the 3D braided cylindrical panel with a simply supported boundary condition.Based on the analysis of the braided composite cylindrical panel with variable initial stress, geometric parameter, fiber volume fraction, and elastic foundation, serial numerical illustrations are archived to represent the appropriate nonlinear bending responses.