大变形薄壁复合材料旋转梁静动态特性分析

该文研究了大变形薄壁复合材料旋转梁的静、动态特性以及复合材料旋转梁不同铺层角、转速对固有频率的影响变化规律。在梁截面上设立翘曲节点引入翘曲变形,假设应变沿薄壁厚度呈二次曲线形式变化;由Hamilton原理,推导了复合材料梁的大变形公式;建立了考虑剪切、翘曲薄壁复合材料大变形梁静、动态分析的有限元模型,并编写了相应的计算程序。分析了复合材料薄壁梁大变形状态下的静态变形行为;在旋转状态下,考虑哥氏力影响,不同转速、不同铺层角对复合材料梁动态特性的影响。计算结果表明:能够用该文建立的模型计算复合材料梁的静动态特性,与相关文献计算结果进行比较,说明了模型的优越性。     

基于n阶GBT初始轴向载荷影响下FGM梁的振动特性

研究了初始轴向载荷影响下弹性地基功能梯度材料(FGM)梁的振动特性。基于一种拓展的n阶广义剪切变形梁理论(n-GBT),以轴向位移、剪切变形挠度与弯曲变形挠度为基本未知函数,应用Hamilton原理,建立了该系统自由振动问题力学模型的控制方程。引入边界控制参数,采用一种改进型广义微分求积(MGDQ)法获得了FGM梁的静动态响应。通过算例验证并给出了GBT阶次n的理想取值,丰富梁理论的同时,可供验证或改进其它各种剪切变形梁理论;提供的数值分析方法切实可行,拓展了GDQ法的使用范围。最后,着重讨论并分析了初始轴向载荷、边界条件、梯度指标、地基刚度、跨厚比等参数对FGM梁振动特性的影响。     

考虑剪切变形时刚性地基梁的非线性弯曲

本文研究了考虑剪切变形时刚性地基梁的非线性弯曲，以地基反力和挠度作为未知量，通过解析求解建立起地基反力和挠度的线性互补方程，利用Ｌｅｍｋｅ方法得到梁的位移和内力，最后给出了二个算例，表明剪切变形对于梁挠度和弯矩影响。     

基于变长度单元ANCF的轴向伸展悬臂梁振动分析

伸展悬臂梁系统中含有刚体运动和大变形运动,属于时变刚柔耦合非线性动力学问题。采用Shabana提出的绝对节点坐标法(ANCF),建立了一种变长度的Euler-Bernoulli梁单元模型。从大变形条件下准确的曲率和Green-Lagrangian正应变出发,基于考虑惯性力的虚功原理,得到了轴向伸展悬臂梁的单元非线性动力学方程组,以及组装后的伸展悬臂梁系统的非线性动力学方程组。最后,通过算例分析了材料特性参数(弹性模量、密度)和伸展规律(匀速伸展、匀加速伸展)对伸展悬臂梁系统的末端非线性挠度响应的影响。     

悬臂梁支座附近表层嵌入FRP筋后性能研究

对悬臂梁支座附近受弯面和侧面表层嵌入FRP筋材后的性能开展了试验研究,探讨了FRP筋类型、试验梁侧面开槽嵌粘方式和初始荷载对悬臂梁性能影响,分析了试验梁的特征荷载、悬臂端挠度、钢筋和FRP筋材的应变。试验结果显示,内嵌FRP筋能够提高悬臂梁的开裂荷载、屈服荷载和极限荷载,试验梁的极限荷载提高范围为48.9%~64.2%;内嵌FRP筋有效地抑制悬臂端挠度,控制了悬臂梁的变形,持续荷载作用下试验梁加固后特征荷载要比其它无初载作用的加固试验梁略低,变形略大,不过,加固效果仍很明显。由此可见,悬臂梁采用FRP筋嵌粘是一种有效的加固方法。     

基于铁木辛柯梁理论的工字梁剪切变形计算方法研究

飞机机翼通常采用工字梁作为支撑结构,然而由于工字梁的几何参数改变,理论计算会受到影响,梁理论的选择会直接影响计算结果。目前,现有的工字梁挠度计算主要基于欧拉-伯努利梁理论,未充分考虑梁弯曲时存在的剪切变形。因此,本文提出了一种基于铁木辛柯梁理论的考虑剪切作用的工字梁计算方法,用于针对受集中力影响的工字梁进行计算。通过表征剪切变形对梁变形的影响,获得了剪切变形对梁的作用规律,并解释了剪切变形在梁中的变形机制。研究表明,当工字悬臂梁靠近固定端一定范围内以及梁的跨高比小于5时,计算时应考虑剪切变形的影响。该计算方法得出的内力计算理论结果与仿真及电测法结果基本一致,可以应用于实际工程计算中。     

钢-混凝土预制混合梁变形性能研究

基于两端固定边界条件下预制混合梁的静力受弯试验,研究了此类预制构件在跨中集中荷载作用下的变形性能。采用奇异函数法建立了预制混合梁的挠曲线计算公式,分析了钢梁与混凝土梁抗弯刚度比、长跨比以及高跨比对变形性能的影响。结果表明:各试件考虑剪切变形影响的挠度计算值与试验值吻合较好,与预制混凝土梁相比,剪切变形对预制混合梁变形性能影响更为显著;由剪切变形引起的附加挠度与总挠度比值随长跨比增加呈线性增长趋势,相同长跨比下其比值随高跨比的增加而增大;建议预制混合梁在高跨比大于1/12时考虑剪切变形的影响。     

波形钢腹板组合槽型梁剪切挠度计算方法与试验研究

为了提出适用于波形钢腹板组合槽型梁的剪切挠度的计算方法,分析了荷载作用下组合梁的受力特点和截面上的剪应力分布规律,推导了剪应变的几何方程,提出了支反力-荷载分段函数的计算模式,通过对几何方程进行积分,建立了波形钢腹板组合槽型梁的剪切挠度计算公式。该公式能够计算多个集中荷载和均布荷载同时作用下的剪切挠度,并适用于波形钢腹板组合梁的其它截面形式。通过4片波形钢腹板组合槽型梁和1片波形钢腹板组合工形梁的静载试验和有限元分析,验证了剪切挠度计算公式的准确性。试验研究表明:对于5片缩尺试验梁,不考虑剪切变形的影响,挠度值偏小约20%,而采用该文考虑剪切变形影响的挠度公式计算的理论值与实测值吻合良好。     

湿-热-机-弹耦合FGM梁的稳定性及振动特性

研究了初始轴向机械载荷作用下Winkler-Pasternak弹性地基上功能梯度材料（FGM）梁在湿-热环境中的稳定性及振动特性。假设温度和湿度沿梁厚度方向稳态分布,材料的物性依赖于温度且按Voigt混合幂律模型连续分布。首先,基于一种扩展的n阶广义梁理论,应用Hamilton原理,统一建立了以轴向位移、弯曲变形项挠度及剪切变形项挠度为基本未知函数FGM梁的屈曲及自由振动方程,采用Navier解法获得了FGM简支梁静动态响应的精确解。其次,通过算例验证并给出了该广义梁理论阶次n的理想取值,丰富梁理论的同时,可供验证或改进其他各种剪切变形梁理论。最后,着重探讨了3种湿-热分布下湿度与温度增加、初始轴向机械载荷、跨厚比、地基刚度、梯度指标等诸多参数对FGM梁稳定性和振动特性的影响。     

作大范围运动的柔性梁的动力学分析

对附着在空间运动体上的柔性悬臂梁的动力学进行了研究，利用微元法建立了中心刚体作任意三维大位移运动时柔性悬臂梁作横向和纵向振动的动力学方程，此动力学方程计及了动力刚化效应。在对柔性梁离散求解时考虑了横向弯曲对纵向变形的影响，最后通过几个例子分析了运动基上柔性梁的动力学行为。     

复合材料梁的几何精确非线性建模及非经典效应

基于Hodges的广义Timoshenko梁理论对具有任意剖面形状、任意材料分布及大变形的复合材料梁进行几何精确非线性建模,采用旋转张量分解法计算梁内任意一点的应变,采用变分渐近法确定梁剖面的任意翘曲,采用平衡方程由二次渐近精确的应变能导出广义Timoshenko应变能,采用广义Hamilton原理建立梁的几何精确非线性运动方程。将所建模型用于复合材料梁的静动力分析,通过与实验数据的对比,验证了建模方法的准确性,并进一步研究了剖面翘曲及横向剪切变形非经典效应对复合材料梁的影响。研究表明,剖面翘曲对复合材料梁的静变形和固有频率有显著影响,横向剪切变形对复合材料梁的静变形和固有频率的影响与梁的长度/剖面高度比有关。     

The large rigid-plastic deformation of a circular cantilever beam subjected to impulsive loading

A quadrantal circular beam subjected to radial impact in its own plane at its tip by a rigid mass is studied on the basis of a large deformation formulation. The procedure for computing this dynamic response is given and numerical examples are shown in order to make a comparison with the results on the basis of small deformation formulation of the same problem.     

《薄壁Timoshenko梁弯扭耦合振动的动态有限元法》

通过直接求解单对称均匀薄壁Timoshenko梁单元弯扭耦合振动的运动微分方程,推导了其精确的动态刚度矩阵。在本文研究中考虑了弯扭耦合、翘曲刚度、转动惯量和剪切变形的影响。针对某弯扭耦合的薄壁梁算例,应用本文推导的动态刚度矩阵,采用自动Muller法和结合频率扫描法的二分法求解频率特征方程,计算了该薄壁梁的固有特性,并讨论了翘曲刚度、剪切变形和转动惯量对该弯扭耦合薄壁梁的固有频率和模态形状的影响。数值结果验证了本文方法的精确性和有效性,并指出随着模态阶次的增加,剪切变形、转动惯量和翘曲刚度对薄壁梁的固有特性的影响更加显著。     

Investigation of composite box beam dynamics using a higher-order theory

A higher-order composite box beam theory is developed to model beams with arbitrary wall thicknesses. The theory, which is based on a refined displacement field, approximates the three-dimensional elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the tranverse shear stresses through the thickness of each wall while satisfying stress-free boundary conditions on the inner and outer surfaces of the beam. Numerical results are presented for beams with varying wall thicknesses and aspect ratios. The static results are correlated with available experimental data and show excellent agreement. Dynamic results presented show the importance of including inplane and out-of-plane warping deformations in the formulation.     

非对称Bernoulli-Euler薄壁梁的弯扭耦合振动

通过直接求解均匀Bernoulli-Euler薄壁梁单元自由振动的控制运动微分方程,推导了其精确的动态传递矩阵。采用Bernoulli-Euler弯扭耦合梁理论,假定梁横截面没有任何对称性,考虑了薄壁梁在两个方向的弯曲振动及翘曲刚度的影响。动态传递矩阵可以用于计算非对称薄壁梁及其集合体的精确固有频率和模态形状。针对具体的算例,给出了各种边界条件下固有频率的数值结果并与文献中已有的结果进行了比较,还讨论了翘曲刚度对固有频率和模态形状的影响,结果表明如果忽略翘曲刚度的影响,可能得到毫无意义的结果。     

Investigation of composite ☐ beam dynamics using a higher-order theory

A higher-order composite ☐ beam theory is developed to model beams with arbitrary wall thicknesses. The theory, which is based on a refined displacement field, approximates the three-dimensional elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the tranverse shear stresses through the thickness of each wall while satisfying stress-free boundary conditions on the inner and outer surfaces of the beam. Numerical results are presented for beams with varying wall thicknesses and aspect ratios. The static results are correlated with available experimental data and show excellent agreement. Dynamic results presented show the importance of including inplane and out-of-plane warping deformations in the formulation.     

Vibration analysis of rotating composite beams using a finite element model with warping degrees of freedom

A finite element beam formulation that properly takes into account the warping of the cross-sections has been extended to the free vibration analysis of rotating and nonrotating composite beams. The formulation allows transverse shear deformation and the warping effects are incorporated by superimposing warping displacements that are parallel to the beam axis in the deformed configuration. For modeling of thin and moderately thick walled sections, the strain is assumed to be linear through the wall thickness. Numerical tests were conducted to calculate the natural frequencies of cantilever composite beams with various ply layups. Correlations of the calculated natural frequencies with experimentally measured values demonstrate the validity of the present approach. Although only rectangular solid and box beams were considered for numerical tests, the formulation allows modeling of beams with complicated cross-sections, tapers, pretwists and arbitrary planforms.     

The damped transient behaviour of finite beams and plates

The direct Finite Element Analysis which was successfully employed in the solution of dynamic flexural traveling wave problems is extended herein to provide the transient behaviour of finite beams and plates in which shear deformation and rotatory inertia are considered. The particle and angular velocities are exponentially damped so that the static solutions for these problems are obtained with the same analysis which provided the dynamic and transient cases. Three special cases are chosen as examples. In the first, a sinusoidally varying shear force is applied at the tip of a cantilever beam. The resonant characteristics of this beam for both the undamped and damped cases are studied. In the second, a step shear loading is applied to a cantilever beam and its damped dynamic history is studied. Finally, a circular plate whose outer edge is simply supported is impacted at its inner edge by a step moment and its damped transient behaviour is determined. The idea of the methods is potentially applicable to dynamic problems in general.     

A finite element model of shape memory polymer composite beams for space applications

Structures made of shape memory polymer composite (SMPC), due to their ability to be formed into a desired compact loading shape and then transformed back to their original aperture by means of an applied stimulus, are an ideal solution to deployment problems of large and lightweight space structures. In the literature, there is a wide array of work on constitutive laws and qualitative analyses of SMP materials; dynamic equations and numerical solution methods for SMPC structures have rarely been addressed. In this work, a macroscopic model for the shape fixation and shape recovery processes of SMPC structures and a finite element formulation for relevant numerical solutions are developed. To demonstrate basic concepts, a cantilever SMPC beam is used in the presentation. In the development, a quasi‐static beam model that combines geometric nonlinearity in beam deflection with a temperature‐dependent constitutive law of SMP material is obtained, which is followed by derivation of the dynamic equations of the SMPC beam. Furthermore, several finite element models are devised for numerical solutions, which include both beam and shell elements. Finally, in numerical simulation, the quasi‐static SMPC beam model is used to show the physical behaviors of the SMPC beam in shape fixation and shape recovery. Copyright © 2015 John Wiley & Sons, Ltd.