基于渐近均匀化方法的准周期梁结构等效刚度数值实现方法研究

相比周期梁结构,准周期梁结构沿轴向梯度变化,具有更大的设计自由度,能够获得更好的结构性能。由于其非均质性,一般将其均匀化为具有等效性质的均质梁结构,但现有工作很少涉及准周期梁结构等效性质的计算。本文针对由周期梁结构映射而成的准周期梁结构,通过引入雅可比矩阵,基于渐近均匀化方法推导的单胞方程及其等效性质计算列式,并建立了其单胞方程及等效刚度的有限元求解列式。该方法可以处理沿轴向变形的任意微单胞构型,数值算例验证了其正确性和有效性。     

周期性点阵类桁架材料等效弹性性能预测及尺度效应

比较了Dirichlet型和Neumann型边界条件下的代表体元法及均匀化方法对具有周期性结构的点阵类桁架材料等效弹性性能的预测结果.数值结果表明,Dirichlet型和Neumann型边界条件下的代表体元法所得结果随着参与模拟的单胞(微结构的最小周期)个数的增加,分别从上下界逼近均匀化方法的结果.对于一类具有特殊微结构的桁架材料,只需一个单胞即可充分逼近均匀化结果.指出产生尺度效应的判据是,对Dirichlet型边界条件下的代表体元法,单胞公共边界处的节点支反力是否平衡;对Neumann型边界条件下的代表体元法,单胞边界间变形是否协调.最后,我们证明了对于一类均匀化方法求解中没有广义自由度的桁架材料,其均匀化结果就是各构件性能按照体积份数加权平均得到.     

基于半波法的双向张弦梁结构索力测试试验研究

双向张弦梁结构的索力测试是预应力张拉结构健康监测的核心内容,精确测试拉索的索力关系到整个结构的安全.双向张弦梁结构中拉索长径比较小,且是双向多跨拉索,拉索的撑杆边界条件比较复杂,传统的索力计算方法难以精确地识别出这类拉索的索力.针对这类拉索的索力识别问题,进行了双向张弦梁结构试验模型的索力测试试验研究.利用模态试验给出了模型拉索的模态信息,利用半波法索力识别技术测试了不同长径比的拉索索力.试验结果表明,基于半波法能够精确地测试出双向张弦梁结构拉索的索力,并且采用高阶模态信息计算的索力比低阶模态信息计算的索力要精确.为在役预应力张拉结构的健康监测提供了新的途径.     

结构拓扑优化研究方法综述

结构拓扑优化研究方法目前有解析方法和数值方法两大类.首先介绍了解析方法中的Michell理论,它在结构拓扑优化领域研究较早,影响最为深远.随后着重讨论了杆系和连续体结构拓扑优化的数值方法.杆系结构常采用基结构方法,通过删除部分杆件达到结构拓扑优化的目的.连续体结构一般要划分为有限单元,通过删除单元形成带孔的连续体,以实现拓扑优化.介绍了连续体结构拓扑优化常采用的材料模型:各向同性、各向异性和带微结构材料.并对连续体结构(0-1)拓扑优化中的数值计算不稳定问题的机理进行了分析,给出了解决方法.此外,对应力约束问题存在解的奇异性现象也作了简要介绍.最后,对数值方法中的主要数学求解方法进行了简单介绍.     

多刚体离散化方法在杆梁结构的屈曲与后屈曲分析中的应用

提出了杆梁结构的多刚体弹簧。铰链系统的离散化模型，推导了求解杆梁结构屈曲时的临界力与失稳曲线的多刚体模型的屈曲特征方程及后屈曲平衡方程。最后，给出了几个算例，并与分析解进行了比较，说明了该方法的有效性与优越性。     

基于人工弹簧模型的周期结构带隙计算方法研究

能量法具有将求解微分方程边值问题转化为泛函极值问题的优点,故而在结构动力学分析中被广泛使用, 近年来也被引入到周期结构带隙计算中. 然而,由于周期结构边界条件相对复杂,采用传统能量法(如Rayleigh-Ritz法)分析时位移函数构造难度大;且由于位移函数中包含波数项,扫描波数计算带隙的过程中质量、刚度矩阵需不断重算, 导致计算量较大. 鉴于此,本文对传统能量法进行改进,通过引入人工弹簧来模拟包含周期边界在内的各类边界条件,可将边界约束转化为人工弹簧的弹性势能,故而各能量分部中仅有周期边界弹性势能包含波数项,扫描波数时仅需重新计算与其对应的刚度矩阵,其余的质量、刚度矩阵只需要计算一次, 继而显著降低了计算量. 研究结果表明,本文方法准确、可靠, 且相较于传统能量法, 本文方法的计算效率更高,随着结构质量、刚度矩阵的维度增大, 或者扫描波数点数的增多,本文方法计算效率优势更加明显. 此外, 人工弹簧模型使用灵活、便捷,可进一步地拓展到更为复杂的周期性组合结构带隙分析中.     

悬臂梁弯曲共振法自由阻尼结构试件设计研究

用悬臂梁弯曲共振法测量阻尼材料动态力学参数时,试件设计是否合理直接决定了测量结果的可信度.考虑到复合试件基底层材料阻尼的影响,本文对测量理论进行了改进,得到了考虑基底层阻尼影响的悬臂梁弯曲共振法测量方程.仿真结果表明忽略基底层阻尼将会导致杨氏模量和损耗因子测量精度降低,并且损耗因子测量误差对基底层阻尼变化更敏感.这为基底材料的选用提供了一定的理论依据.本文还结合误差放大因子的概念,对试件设计若干关键参数进行了灵敏度分析,得到了一组对悬臂梁弯曲共振法自由阻尼结构试件设计具有指导意义的结论.     

基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响, 通过合理设计复合材料微观结构可以得到期望的宏观性能. 均质化方法作为一种有效的设计方法, 它从微观结构的角度出发, 利用均匀化的概念, 实现了对复合材料宏观力学性能的预测和设计. 而当考虑非线性因素, 均质化的实现就非常困难. 本文利用双渐近展开方法, 将位移按照宏观位移和微观位移展开, 推导了非线性弹性均质化方程. 通过直接迭代法, 对非线性弹性均质化方程进行了求解, 并给出了具体的迭代方法和实现步骤. 本文基于迭代步骤和非线性弹性均质化方程编写MATLAB 程序, 对3种典型本构关系的周期性多孔材料平面问题进行了计算, 对比细致模型的应变能、最大位移和等效泊松比, 对程序及迭代方法的准确性进行了验证. 之后对一种三元橡胶基复合材料进行多尺度均质化, 将其分为芯丝尺度和层间尺度. 用线弹性的均质化方法得到了芯丝尺度的等效弹性参数, 并将其作为层间尺度的材料参数. 在层间尺度应用非线性弹性均质化方法对结构进行计算, 得到材料的宏观等效性能, 并以实验结果为基准进行评价.      

型钢连接装配式混凝土梁等效抗弯刚度研究

型钢连接装配式混凝土梁截面抗弯刚度因构造做法差异而相差较大。基于小变形叠加原理,提出了该类构件在荷载作用下的挠度计算方法,根据等挠度原则,推导了构件的等效抗弯刚度计算公式,并与试验研究结果进行了比较,验证了公式的有效性。在此基础上,分析了型钢混凝土梁参数变化对变刚度构件整体抗弯刚度的影响。研究结果表明,型钢连接方式增大了装配式混凝土梁的抗弯刚度,减小了构件在荷载作用下的挠度变形,对构件和结构受力更为有利。     

Two-scale finite element method for piezoelectric problem in periodicstructure

The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element...     

Novel numerical implementation of asymptotic homogenization method for periodic plate structures

The present paper develops and implements finite element formulation for the asymptotic homogenization theory for periodic composite plate and shell structures, earlier developed in  and , and thus adopts this analytical method for the analysis of periodic inhomogeneous plates and shells with more complicated periodic microstructures. It provides a benchmark test platform for evaluating various methods such as representative volume approaches to calculate effective properties. Furthermore, the new numerical implementation (Cheng et al., 2013) of asymptotic homogenization method of 2D and 3D materials with periodic microstructure is shown to be directly applicable to predict effective properties of periodic plates without any complicated mathematical derivation. The new numerical implementation is based on the rigorous mathematical foundation of the asymptotic homogenization method, and also simplicity similar to the representative volume method. It can be applied easily using commercial software as a black box. Different kinds of elements and modeling techniques available in commercial software can be used to discretize the unit cell. Several numerical examples are given to demonstrate the validity of the proposed methods.     

基于均匀化理论的多孔板弯曲问题新解

由于密集型分布孔的存在,通常的有限元法不能有效地分析多孔板的弯曲问题.该文基于均匀化理论建立了该类问题的新解法.对含密集型分布的阶梯型圆孔板的分析结果,说明了该文方法是有效的.     

Periodic and Chaotic Motions of a Rotor-Active Magnetic Bearing with Quadratic and Cubic Terms and Time-Varying Stiffness

In this paper, we use the asymptotic perturbation method to investigate nonlinear oscillations and chaotic dynamics in a rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The stiffness in the AMB is considered as the time varying in a periodic form. Because of considering the weight of the rotor, the formulation on the electromagnetic force resultants includes the quadratic and cubic nonlinearities. The resulting dimensionless equations of motion for the rotor-AMB system with the time-varying stiffness in the horizontal and vertical directions are a two-degree-of-freedom nonlinear system with quadratic and cubic nonlinearities and parametric excitation. The asymptotic perturbation method is used to obtain the averaged equations in the case of primary parametric resonance and 1/2 subharmonic resonance. It is found that there exist period-3, period-4, period-6, period-7, period-8, quasiperiodic and chaotic modulated amplitude oscillations in the rotor-AMB system with the time-varying stiffness. It is seen from the numerical results that there are the phenomena of the multiple solutions and the soft-spring type and the hardening-spring type in nonlinear frequency-response curves for the rotor-AMB system. The parametric excitation, or the time-varying stiffness produced by the PD controller is considered to be a controlling force which can control the chaotic response in the rotor-AMB system to a period n motion.     

The dynamic modelling of elastic wavy plates

Summary The aim of the contribution is to formulate an engineering theory describing the dynamic behaviour of periodically waved shell-like elements, called wavy plates. On the basis of the proposed theory, the effect of coupling between free macro- and micro-vibrations of a wavy plate is investigated. It is also shown that the homogenized model of wavy plates (obtained by scaling down the wavelength parameters) cannot be applied in the analysis of dynamic problems.The research was sponsored by KBN, Warsaw, under grant No 333109203.