多分辨率Timoshenko梁单元

基于Timoshenko梁的假定,通过基本节点形函数的扩展,并在梁区域上进行伸缩和平移,本文构建了基函数系,由此生成相互嵌套、逐级包含的位移空间序列,最后,采用最小势能原理,得到梁的平衡方程,从而构造了多分辨率Timoshenko梁单元。该单元具有如下特性：1．可通过自由调节单元分辨率的大小来增减单元的网格节点数量,从而调整单元的计算精度,其精度与相同网格划分条件下任意多个传统梁单元计算的相一致;2．经重新划分网格后的单元整体刚度、质量矩阵及等效节点荷载向量可直接获得,不像传统梁单元那样需要重新生成;3．与传统梁单元一样可以很方便地处理各种边界条件。本文首次将多分辨率概念引入到传统的Timoshenko梁单元中,并构建了梁结构网格划分的数学依据—位移空间序列,同时,揭示了共同节点可以采用人工叠加方法形成整体刚阵的缘由—连续的节点扩展形函数。     

基于等效黏性弹簧的黏弹性Timoshenko裂纹梁弯曲解析解

考虑裂纹的缝隙和黏性效应,将梁中横向裂纹等效为黏弹性扭转弹簧,利用广义Delta函数,给出了Laplace变换域内裂纹梁的等效抗弯刚度,得到了具有任意开闭裂纹数目且满足标准线性固体黏弹性本构的Timoshenko梁在时间域内的弯曲变形显式解析通解．在此基础上,通过两个数值算例,分析了时间、梁跨高比和裂纹深度等参数对黏弹性Timoshenko开裂纹梁弯曲变形的影响．结果表明：裂纹黏性对Timoshenko裂纹梁的弯曲具有显著的影响．相比于裂纹的弹性扭转弹簧模型,考虑裂纹黏性效应的黏弹性Timoshenko裂纹梁在裂纹处挠度尖点和转角跳跃现象十分明显．另外,由于横向剪切引起的附加变形,Timoshenko裂纹梁的稳态挠度与Euler-Bernoulli梁挠度的差值为常数,其大小与裂纹模型、梁跨高比或裂纹深度无关,这些结果对梁裂纹无损检测具有指导意义．     

Winkler地基上裂纹Timoshenko梁的弯曲解析解

将梁中裂纹等效为无质量线性扭转弹簧,研究了温克勒(Winkler)基础上具有任意开裂纹数目Timoshenko梁的弯曲变形．利用Delta广义函数和Heaviside函数以及Laplace变换,给出了Winkler基础上具有任意裂纹数目Timoshenko梁弯曲变形的解析通解．在此基础上,研究了Winkler基础上受均布荷载作用简支裂纹Timoshenko梁的弯曲变形,数值分析了裂纹数目和位置以及深度、梁剪切刚度和基础反力系数等对裂纹Timoshenko梁弯曲变形的影响．结果表明：在裂纹处,梁挠度存在尖点,转角存在跳跃;梁挠度随着裂纹深度和数目的增加而增加,但横截面弯矩和转角减小;随着基础反力系数的增加,梁挠度、弯矩和转角减小;随着剪切刚度的增加,梁挠度减少,弯矩和转角增大．     

无约束修正Timoshenko梁的冲击问题

介绍了修正后的Timoshenko梁运动方程,并比较了修正Timoshenko梁与经 典Timoshenko梁的运动方程. 推导了考虑剪切变形引起的转动惯量的修正Timoshenko 梁的正交条件,推导了集中质量对无约束修正Timoshenko梁的正碰撞对梁所引起的瞬态冲 击响应公式,并用算例进行了分析,且与集中质量对经典的无约束Timoshenko梁的正碰撞 对梁所引起的冲击响应进行了比较,另外还用算例分析了梁的刚度的变化和冲击质量比对其 冲击响应产生的影响.     

任意边界条件下Timoshenko梁及其修正理论的自振特性分析

提出一种求解任意边界条件下经典Timoshenko梁以及修正Timoshenko梁自振频率和振型的新方法。利用改进的傅立叶级数消除传统傅立叶级数的边界不收敛问题,然后通过Rayleigh-Ritz法导出Timoshenko梁的拉格朗日泛函,根据Hamilton原理将原问题转化为求解矩阵广义特征值问题。通过与解析解对比,本文采用的方法具有较好的收敛性以及较高的计算精度;通过数值计算发现,经典Timoshenko梁的自振频率略高于修正的Timoshenko梁,随着振型阶数的提高,经典Timoshenko梁的计算结果逐渐偏离文献解和有限元结果,而修正的Timoshenko梁能够保持较好的一致性;对于不同边界条件下修正Timoshenko梁的计算结果均能与有限元的计算结果吻合得很好。最后运用MATLAB编程软件将程序设计为App,对于不同情形的梁只需要修改参数即可,可为实际工程提供高效便捷的计算方案和可靠理论依据。     

变截面Timoshenko梁动力反应的半解析法

为研究移动荷载下截面剪切变形和转动惯量影响,在推导变截面Timoshenko梁振型正交性的数学表达式的基础上,建立了任意荷载作用下Timoshenko梁动力响应的模态叠加法.然后,将模态摄动法和模态叠加法结合起来,提出了变截面Timoshenko梁动力反应计算的公式.在此基础上,基于矩形截面梁,比较分析了简支Timoshenko梁理论和Euler梁理论动力反应随移动荷载速度、长细比和截面衰减率的变化规律的区别.计算结果表明:由于剪切变形和转动惯量的影响,Timoshenko梁的动力反应将大于Euler梁.当长细比小于10时,Timoshenko梁跨中位移比Euler梁增加25%以上,当长细比大于30后,可采用Euler梁理论进行简化分析.     

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将理性有限元法引入到Timoshenko梁问题中,提出了一种理性Timoshenko梁单元,克服了 剪切锁死现象. 在推导控制方程时,与传统有限元方法采用Lagrange插值不同, 理性有限元法用Timoshenko梁弯曲问题的基本解逼近单元内部场. 运用该梁单元分析 Timoshenko梁时,无需缩减积分,就能避免剪切锁死,并且极大地提高了计算精度,说明 理性有限元法具有广泛的应用前景.     

饱和多孔弹性Timoshenko梁的大挠度分析

基于微观不可压饱和多孔介质理论和弹性梁的大挠度变形假设,考虑梁剪切变形效应,在梁轴线不可伸长和孔隙流体仅沿轴向扩散的限定下,建立了饱和多孔弹性Timoshenko梁大挠度弯曲变形的非线性数学模型.在此基础上,利用Galerkin截断法,研究了两端可渗透简支饱和多孔Timoshenko梁在突加均布横向载荷作用下的拟静态弯曲,给出了饱和多孔 Timoshenko梁弯曲变形时固相挠度、弯矩和孔隙流体压力等效力偶等随时间的响应.比较了饱和多孔Timoshenko梁非线性大挠度和线性小挠度理论以及饱和多孔 Euler-Bernoulli梁非线性大挠度理论的结果,揭示了他们间的差异,指出当无量纲载荷参数q＞l0时,应采用饱和多孔Timoshenko梁或Euler-Bernoulli梁的大挠度数学模型进行分析,特别的,当梁长细比λ＜30时,应采用饱和多孔Timoshenko梁大挠度数学模型进行分析.     

轴向随动分布载荷作用下FGMs Timoshenko梁的后屈曲特性

研究了Timoshenko功能梯度材料梁在随动分布载荷作用下的后屈曲问题。在考虑轴线伸长和一阶横向剪切变形基础上,建立了在轴向分布随动载荷作用下一端简支一端固定Timoshenko功能梯度梁的过屈曲控制方程。其中假设功能梯度材料性质只沿厚度方向变化,并以成分含量的幂指数函数形式变化。采用打靶法求解了所得线性常微分两点边值问题,获得了随动载荷作用下Timoshenko功能梯度梁的过屈曲平衡路径和平衡构形。对比了Timoshenko梁和Euler梁的后屈曲行为,并分析了材料的体积分数指数和长细比对梁屈曲行为的影响。结果表明:考虑剪切变形的Timoshenko梁的后屈曲行为与Euler梁的后屈曲行为明显不同;体积分数指数一定时,随着长细比的增加,梁的临界载荷减小;长细比一定时,随着体积分数指数的增加,梁的临界载荷也减小。     

分数阶黏弹性Pasternak地基上两端固支Timoshenko梁的动力响应

本文研究了放置在黏弹性Pasternak地基上的Timoshenko梁在移动载荷作用下的动力响应行为．首先,引入分数阶导数,将整数阶标准固体黏弹性地基模型推广为分数阶标准固体黏弹性模型．对于Pasternak地基,考虑压缩层是黏弹性的而剪切层仍是弹性的情况,给出了地基反作用力．然后,求解了Timoshenko梁的自由振动解,获得含黏性耗散信息的复固有频率及振型函数．在此基础上用振型叠加法分析了在移动简谐荷载作用下梁的位移响应．在数值算例中,给出了不同分数阶导数、地基黏性系数以及载荷移动速度下梁的动态响应,讨论了黏弹性地基对梁的动态响应的影响规律．     

Analysis of wave propagation in a functionally graded nanobeam resting on visco-Pasternak's foundation

Wave propagation analysis for a functionally graded nanobeam with rectangular cross-section resting on visco-Pasternak's foundation is studied in this paper. Timoshenko's beam model and nonlocal elasticity theory are employed for formulation of the problem. The equations of motion are derived using Hamilton's principals by calculating kinetic energy, strain energy and work due to viscoelastic foundation. The effects of various parameters such as wavenumber, non-homogeneous index, nonlocal parameter and three parameters of foundation are performed on the phase velocity of the nanobeam. The obtained results indicate that some parameters such as non-homogeneous index, nonlocal parameter and wavenumber have significant effect on the response of the system.     

Dynamical behaviors of nonlinear viscoelastic thick plates with damage

Based on the deformation hypothesis of Timoshenko's plates and the Boltzmann's superposition principles for linear viscoelastic materials, the nonlinear equations governing the dynamical behavior of Timoshenko's viscoelastic thick plates with damage are presented. The Galerkin method is applied to simplify the set of equations. The numerical methods in nonlinear dynamics are used to solve the simplified systems. It could be seen that there are plenty of dynamical properties for dynamical systems formed by this kind of viscoelastic thick plate with damage under a transverse harmonic load. The influences of load, geometry and material parameters on the dynamical behavior of the nonlinear system are investigated in detail. At the same time, the effect of damage on the dynamical behavior of plate is also discussed.     

复合材料层合梁的屈曲

本文在铁摩辛柯梁理论基础上,利用迭合刚度方法及Hamilton原理建立了层合梁屈曲问题控制方程,并用此控制方程求解了在具体边界条件下层合梁的屈曲问题,得出了无论在什么边界条件下层合梁的最小屈曲载荷不会大于等效剪切刚度系数C的结论.     

风浪联合发电系统水动力学研究进展

随着化石能源枯竭和全球变暖等环境问题的日益严重,海洋可再生能源(海上风能、波浪能和潮流能)成为研究热点. 为了有效开发海洋可再生能源,降低成本,多种能源综合开发成为现阶段的趋势. 海上风能与波浪能结合具有广阔的应用前景,联合发电系统不断创新. 水动力性能是联合发电系统与波浪相互作用的重要基础. 本文简要介绍多种应用在联合发电系统上的水动力学数值模拟方法,包括线性频域、线性时域、势流非线性方法标识码基于 Navier-Stokes 方程的黏性方法,对现有文献的水动力学数值模拟方法进行综述,从计算效率和精度标识码析其优缺点,且进一步阐述水动力控制优化的技术原理与实验技术主要科研难点,为联合发电系统的水动力设计提供依据. 得到以下主要结论:从计算效率上看,线性频域方法最优,其次为线性时域、势流非线性、黏性方法,从计算精标识码,与前者恰好相反;综合考虑计算效率和精度,采用考虑黏性修正的势流方法来研究是一个切实可行的方案;模标识码方法和优化控制技术目前还不够成熟,尚处于探索阶段.      

Pseudo-beam method for compressive buckling characteristics analysis of space inflatable load-carrying structures

This paper extends Le van＇s work to the case of nonlinear problem and the complicated configuration. The wrinkling stress distribution and the pressure effects are also included in our analysis. Pseudo-beam method is presented based on the inflatable beam theory to model the inflatable structures as a set of inflatable beam elements with a prestressed state. In this method, the discretized nonlinear equations are given based upon the virtual work principle with a 3-node Timoshenko＇s beam model. Finite element simulation is performed by using a 3-node BEAM189 element incorporating ANSYS nonlinear program. The pressure effect is equivalent included in our method by modifying beam element cross-section parameters related to pressure. A benchmark example, the bending case of an inflatable cantilever beam, is performed to verify the accuracy of our proposed method. The comparisons reveal that the numerical results obtained with our method are close to open published analytical and membrane finite element results. The method is then used to evaluate the whole buckling and the loadcarrying characteristics of an inflatable support frame subjected to a compression force. The wrinkling stress and region characteristics are also shown in the end. This method gives better convergence characteristics, and requires much less computation time. It is very effective to deal with the whole load-carrying ability analytical problems for large scale inflatable structures with complex configuration.     

Strain gradient plasticity modeling of the cyclic behavior of laminate microstructures

Two recently proposed Helmholtz free energy potentials including the full dislocation density tensor as an argument within the framework of strain gradient plasticity are used to predict the cyclic elastoplastic response of periodic laminate microstructures. First, a rank-one defect energy is considered, allowing for a size-effect on the overall yield strength of micro-heterogeneous materials. As a second candidate, a logarithmic defect energy is investigated, which is motivated by the work of Groma et al. (2003). The properties of the back-stress arising from both energies are investigated in the case of a laminate microstructure for which analytical as well as numerical solutions are derived. In this context, a new regularization technique for the numerical treatment of the rank-one potential is presented based on an incremental potential involving Lagrange multipliers. The results illustrate the effect of the two energies on the macroscopic size-dependent stress–strain response in monotonic and cyclic shear loading, as well as the arising pile-up distributions. Under cyclic loading, stress–strain hysteresis loops with inflections are predicted by both models. The logarithmic potential is shown to provide a continuum formulation of Asaro's type III kinematic hardening model. Experimental evidence in the literature of such loops with inflections in two-phased FFC alloys is provided, showing that the proposed strain gradient models reflect the occurrence of reversible plasticity phenomena under reverse loading.     

Variational principles for Cosserat body

Two variational principles are derived for the mixed boundary value problem of Cosserat solid. These principles are a generalization of the stationary principle of potential energy and the stationary principle of complementary energy from non-linear theory of elasticity.     

表面张力液柱中粘性引起的模分裂

本文证明粘性会使得表面张力所维持的无限长液柱运动模发生分裂(或称分叉),结果是每个轴对称模一次分裂为无穷个。这种现象类似于原生物理学中的 Zeemen 和 Stark效应。无粘条件下的不稳定模分裂后还出现可数无穷个负势能的稳定模,这是关于连续系统模稳定性的 Hare 和 Chandrasekhar 势能判据的一个反例,并解释其物理意义。     

A review on flow energy harvesters based on flapping foils

This article presents an overview of the state of the art investigations on the recently developed oscillating foil energy converters. A summary of available knowledge and up-to-date progress in the application of such bio-inspired systems for renewable energy devices is provided. Starting from concepts and achieved results in three distinguishable categories, various parametric studies are reviewed, along with an in-depth discussion on the potential device performance enhancement via flow control mechanisms. Finally, potential future research directions are discussed.     

NUMERICAL ANALYSIS OF THE LARGE DEFLECTION OF AN ELASTIC-PLASTIC BEAM

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