关于旋转周期结构设计的注记

基于离散Fourier变换，在解析方程的层次上将旋转周期结构的问题化为若干个关于局部结构的问题，指出旋转周期结构计算的另一途径。     

周期旋转对称结构的动力特征

本文根据离散化的周期旋转对称结构的刚度阵、质量阵形式,给出了一个确定其固有频率的快速算法,并证明这种结构有一系列重频率存在。在此基础上,本文最后讨论了在实际应用中如何更有效地确定该种结构的前几阶最低频率的问题.     

虚边界元法中的旋转周期对称结构

本文证明具有旋转周期对称性的结构,在对称适应的指标架下,其虚边界元方程的系数矩阵具有块循环的形式,给出一种分解算法（即将原问题分解成一系列相互独立的子问题的求解法）,适于任意形式的载荷分布。     

主惯导旋转调制对传递对准性能的影响

旋转调制技术在调制惯性器件常值误差,有效提高惯导系统长航时导航精度的同时,也引入了由系统旋转而造成的速度误差以旋转周期和旋转周期二倍频波动,这种波动对以速度为匹配量的传递对准有一定的影响。从旋转调制系统的误差特性出发,分析了旋转调制对以速度为匹配量传递对准的有利和不利影响,并针对不同的旋转调制周期进行了仿真验证,仿真结果表明当旋转周期远大于舒勒周期时,旋转调制引起的不利和有利影响都很小,可忽略不计;当旋转周期远小于舒勒周期时,旋转调制可提高子惯导的方位对准精度,但延长了系统的传递对准时间。例如,当旋转周期为3(°)/s时,水平对准时间由3 min延长到4 min,而对准精度由1.2′提高到0.2′;方位对准时间由10 min延长到16 min,而对准精度由2.2′提高到0.4′。     

周期变速旋转运动电流变夹层梁的参激振动

采用多尺度法对周期变速旋转运动电流变夹层梁的动力稳定性进行了研究. 假设电流变夹层梁绕固定轴线做随时间变化的简谐周期运动,将变速度转动梁作为一个时变参激振动系统,分析了不同结构和控制参数对失稳区域的影响. 仿真结果表明,改变外加控制电场强度的大小和梁的结构参数,可改变旋转电流变夹层梁发生动力失稳的临界角速度和失稳区域. 故在一定的条件下,可以通过控制作用于电流变夹层梁的电场强度来调节旋转运动柔性梁的振动特性,提高结构的动力稳定性.      

边界元法中的周期旋转对称

本文证明具有周期旋转对称性的结构，在对称适应的座标架下，其边界元方程的系数矩阵具有块循环的形式，给出分块的系列子问题求解方法，适于任意形式的载荷分布。     

蜂窝夹芯圆环的拓扑优化设计及尺度效应研究

采用尺度关联的一体化设计方法开展了旋转周期圆环结构的拓扑优化设计研究，以宏观 结构的最大刚度为目标，研究了材料表征体胞尺度、构型以及不同载荷作用形式对蜂窝夹芯 圆环结构优化结果的影响. 所提出的无量纲结构构型因子实现了优化结构的结构效率量化评 估. 结合SIMP材料模型和周长控制方法，实现了宏观结构和细观表征体胞的优化设计，获得 清晰的材料分布. 数值算例表明，尺度关联的一体化设计方法能有效地完成圆环结构的拓扑 优化设计，设计结果充分反映体胞尺度效应对旋转周期圆环结构夹芯构型的影响.     

日地系统L_2点Halo轨道绳系卫星编队动力学

研究平动点附近周期轨道上旋转多体绳系卫星编队系统的非线性耦合动力学问题。编队系统为各卫星质量接近的轮辐状结构,位于日地系统第二平动点附近,整个系统的旋转保持系绳处于张紧状态,建立Hill限制性三体问题的绳系编队系统动力学模型。针对处于留位阶段的典型对称三星编队,在位于较大Halo轨道上无控制力作用的情况下,进行母卫星轨道运动与系绳摆动耦合运动的动力学模拟,分析轨道方向、卫星质量比、系绳长度以及初始旋转速度对编队系统整体稳定性的影响。     

基于拉格朗日乘子法和群论的具有任意位移边界条件的旋转周期对称结构有限元分析

对任意位移边界条件下的旋转周期对称结构，由拉格朗日乘子法建立有限元方程。在对称适应的坐标系下，由结构刚度矩阵的块循环性质，利用群变换给出一种新的求解方法。数值验证给出令人满意的结果。     

质量周期分布对偏心旋转环状结构自由振动的影响

工程实际中，某些旋转对称设计结构由于存在制造安装误差常呈现偏心旋转状态，进而影响结构稳定性.针对该类环状周期结构，考虑其偏心运动，研究附加质量周期分布参数以及偏心率对系统固有频率与动力稳定性的影响.首先，在环状结构上建立随动坐标系，利用Hamilton原理建立动力学模型.其次，采用经典振动理论求解系统的特征值，分析不同参数组合下的模态特性和不稳定性.最后，利用数值法计算系统的动态响应，并与解析结果进行对比.结果表明，当附加质量个数与波数满足一定关系时，固有频率发生分裂；对于不同的偏心率和周期分布特征，系统在不同转速下动力性能差异较大，适当提高偏心率、选取合适的附加质量个数及大小可有效抑制不稳定性.此研究有助于分析工程实际中该类结构的动力学稳定性，为其振动控制提供借鉴.     

Numerical analysis of bifurcation buckling for rotationally periodic structures under rotationally periodic loads

By considering the characteristics of deformation of rotationally periodic structures under rotationally periodic loads, the periodic structure is divided into some identical substructures in this study. The degrees-of-freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain conditions of the whole structure are obtained by solving the elastic static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method is used to get the bifurcation buckling load and mode for the whole rotationally periodic structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. The finite element (FE) formulation of shell element of relative degrees of freedom (SERDF) in the buckling analysis is derived. Different measures of tackling internal degrees of freedom for different kinds of buckling problems and different stages of numerical analysis are presented. Some numerical examples are given to illustrate the high efficiency and validity of this method.     

THE ROTATIONALLY PERIODIC SYMMETRY IN BEM

Rotationally periodic symmetry is exploited in 2-D elastostaticcalculation using the BEM.It is proved that the coefficient matrices of the globalboundary element equations for the rotationally periodic system are block-circulant solong as a kind of symmetry-adapted reference coordinate system is adopted.Furthermore,an efficient algorithm,which partitions the original problem of solvingthe boundary element equations into a series of subproblems,is proposed.The methodpermits arbitrary load distribution for stress analysis problems.     

复合材料弹塑性多尺度分析模型与算法

对材料非线性多尺度分析的计算模型与算法进行研究.在构建周期分布单胞分析算法的基础上,发展针对复合材料结构材料非线性多尺度分析的一般有限元方法.方法的特点是将所建立的单胞分析过程作为有限元分析的子程序嵌入到总程序系统当中,完成对应的高斯点应力计算,因而使所发展的方法具有实现方便的特点.给出数值计算结果,验证了方法与所发展的多尺度有限元分析程序的正确与有效性.     

Solving viscoelastic problems with cyclic symmetry via a precise algorithm and EFGM

The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method (EFGM) for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables at a discretized time interval, the variations of variables can be described more precisely, and iteration is not required for non-linear cases. A space-time domain coupled problem with initial and boundary values can be converted into a series of linear recursive boundary value problems, which are solved by a group theory based on EFGM. It has been proved that the coefficient matrix of the global EFG equation for a rotationally periodic system is block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted, and then a partitioning algorithm for facilitating parallel processing was proposed via a completely orthogonal group transformation. Therefore instead of solving the original system, only a series of independent small sub-problems need to be solved, leading to computational convenience and a higher computing efficiency. Numerical examples are given to illustrate the full advantages of the proposed algorithm. The project supported by the National Natural Science Foundation of China ((10421002, 10472019 and 10172024); NKBRSF (2005CB321704) and the Fund of Disciplines Leaders of Young and Middle Age Faculty in Colleges of Liaoning Province. The English text was polished by Yunming Chen.     

Mechanics of fish skin: A computational approach for bio-inspired flexible composites

Natural materials and structures are increasingly becoming a source of inspiration for the design novel of engineering systems. In this context, the structure of fish skin, made of an intricate arrangement of flexible plates growing out of the dermis of a majority of fish, can be of particular interest for materials such as protective layers or flexible electronics. To better understand the mechanics of these composite shells, we introduce here a general computational framework that aims at establishing a relationship between their structure and their overall mechanical response. Taking advantage of the periodicity of the scale arrangement, it is shown that a representative periodic cell can be introduced as the basic element to carry out a homogenization procedure based on the Hill-Mendel condition. The proposed procedure is applied to the specific case of the fish skin structure of the Morone saxatilis, using a computational finite element approach. Our numerical study shows that fish skin possesses a highly anisotropic response, with a softer bending stiffness in the longitudinal direction of the fish. This softer response arises from significant scale rotations during bending, which induce a stiffening of the response under large bending curvature. Interestingly, this mechanism can be suppressed or magnified by tuning the rotational stiffness of the scale-dermis attachment but is not activated in the lateral direction. These results are not only valuable to the engineering design of flexible and protective shells, but also have implications on the mechanics of fish swimming.     

功能梯度材料构件三维分析的细观元模型

提出一种新颖的功能梯度构件分析的细观元法,给出了方法模型、基本算式及特点与功能。细观元法对构件的常规有限单元内部设置密集细观单元以反映材料特性梯度变化,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。这种细观元法既能充分反映材料功能梯度及组分变化特性,而其计算单元与自由度又与常规有限元一样,是一种针对功能梯度构件分析的有效数值方法。算例表明了细观元法对不同情况下功能梯度构件分析的适应性与精度。     

Multi-scale FE computation for the structures of composite materials with small periodic configuration under condition of coupled thermoelasticity

In this paper, the multi-scale computational method for a structure of composite materials with a small periodic configuration under the coupled thermoelasticity condition is presented. The two-scale asymptotic (TSA) expression of the displacement and the increment of temperature for composite materials with a small periodic configuration under the condition of thermoelasticity are briefly shown at first, then the multi-scale finite element algorithms based on TSA are discussed. Finally the numerical results evaluated by the multi-scale computational method are shown. It demonstrates that the basic configuration and the increment of temperature strongly influence the local strains and local stresses inside a basic cell. The project supported by the National Natural Science Foundation of China (19932030) and Special Funds for Major State Basic Research Projects