Vibrational behavior of isotropic plate structures in contact with a bounded fluid via unified formulation

This paper presents an analytical solution for free vibration analysis of thick rectangular isotropic plates coupled with a bounded fluid for various boundary conditions. In order to consider displacement theories of an arbitrary order, the Carrera Unified Formulation(CUF) is used. The eigenvalue problem is obtained by using the energy functional, considering plate and fluid kinetic energies as well as the potential energy of the plate. The Ritz method is used to evaluate the displacement variables, and the functions used in the Ritz series can be adjusted to consider any of the classical boundary conditions. The convergence of the solution is analyzed, and a validation of results considering open literature and 3D finite element software is performed. Parametric studies are carried out to obtain natural frequencies as a function of the side-to-thickness ratio, plate aspect ratio, fluid domain size, plate boundary conditions, and fluid-solid density ratio. Pressure and velocity in the fluid domain are evaluated in order to establish the consistency of the solution.Accurate results for thick plates are obtained with a much lower computational cost compared to that of 3D finite element solutions.     

Efficient computation of energy release rates for delaminated beam structures

The often encountered problem of mode partitioning for delaminated, isotropic beam structures is addressed. For the sake of efficiency, solutions that do not require complex continuum solutions – in practise mostly obtained by the finite element method – are examined. Three approaches that meet the postulated efficiency are reviewed and compared. While one method fits consistently into the concept of linear-elastic fracture mechanics, the remaining two deduce mode partitioning hypotheses solely from kinematic quantities of beam theory. The results obtained through these hypotheses are then compared to continuum-based solutions. The latter are generated by the finite element method and are validated by analytical solutions as applicable. Furthermore, mode partitioning solutions for beams, loaded in transverse shear, are given with excellent accuracy. Finally, the conditions for which the different methods comply with or substantially deviate from each other are discussed.     

若干周期性复合材料结构数学均匀化方法的计算精度

数学均匀化方法(MHM)一般需要通过有限元方法(FEM)来实现,摄动阶次和单元阶次直接影响计算结果。在解耦格式中,各阶摄动位移是相应阶次的影响函数和均匀化位移导数的乘积。单元阶次的选取取决于影响函数和均匀化位移的精度要求,而摄动阶次的选取则主要依赖于虚拟载荷的性质和均匀化位移各阶导数的计算精度;针对周期性复合材料杆的静力学问题,在施加不同阶次的载荷时,通过选择合适阶次的单元和摄动阶次得到了精确解。使用类似的方法研究了2D周期性复合材料静力学问题,指出了四边固支作为周期性单胞边界条件以及宏观位移求导精度对计算结果将有很大的影响。强调了二阶摄动对数学均匀化方法计算精度的作用;在数值结果中,应用最小势能原理评估了各阶摄动数学均匀化方法的计算精度,数值比较结果验证了结论的正确性。     

航空发动机滚动轴承的载荷分布研究

滚动轴承载荷分布的研究大多应用基于Hertz接触理论的拟动力学法进行。由于Hertz接触理论半无限空间的边界条件,以及分析时采用刚性套圈假设,拟动力学法的计算结果与实际情况有较大出入。近年来随着有限元、边界元等数值计算方法的发展,使考虑套圈变形和边界条件影响的滚动轴承载荷分布的研究成为可能。建立滚动轴承载荷分布的有限元分析模型,分析载荷参数对轴承接触应力、接触角和变形的影响规律,并将有限元法的计算结果与拟动力学法及实验结果进行分析比较。研究表明:由于有限元法考虑套圈变形以及边界条件的影响,与实验结果更为接近。     

无界区域上理想绕流问题的混合有限元方程

本文讨论无界区域上理想绕流边值问题的有限元近似解。为了克服区域无界性所带来的困难,本文将传统的分析方法与有限元方法相结合,首先将问题化为一个等价的有界区域上的边值问题,然后用有限元方法求得这个等价问题的近似解。作为算例,本文计算了理想不可压缩流体的圆球绕流问题,并给出其近似解的误差分析。     

An advanced five-unknown higher-order theory for free vibration of composite and sandwich plates

Accurate prediction of dynamic characteristics is quite critical to understand the strength of layered structures. Nevertheless, the existing five-unknown higher-order theories encounter difficulties to forecast accurately the dynamic response of sandwich structures. Therefore, a new five-unknown higher-order theory is developed for free vibration analysis of composite and sandwich plates, which possesses the same degree of freedom as those of other five-unknown higher-order theories. The developed model can meet beforehand interlaminar continuity conditions and the free-surface conditions of transverse shear stresses. To assess capability of the proposed model, analytical solution for such composite structures with simply-supported conditions has been presented by employing Hamilton’s principle, which is utilized for analysis of mechanical behaviors of composite and sandwich plates. Compared with the three-dimensional (3D) elasticity solutions, 3D finite element results and the results obtained from the chosen five-unknown higher-order models, the proposed model can yield accurately natural frequencies of composite and sandwich plates. Even for the thick plates, the higher-order frequencies calculated from the proposed model are in good agreement with the 3D finite element results. By studying effect of the thickness/length ratios on natural frequencies, it is found that the proposed model is adaptable to predicting natural frequencies of the sandwich plates with the thickness/length ratios between 1/4 and 1/100. In addition, some factors influencing accuracy of five-unknown higher-order models have been investigated in detail. Finally, by means of numerical analysis and discussion, some conclusions have been drawn as well, which can serve as a reference for other investigators.     

斜削梁协调元素族及其在梁固有振动分析上的应用

本文给出了位移函数为三次、五次、七次幂多项式时斜削梁元素刚度与质量矩阵的显表达式以及计算任意奇次幂高阶斜削梁元素族刚度与质量矩阵显表达式的一般方法。然后应用高阶协调元素计算了六种线性斜削梁在悬臂支持、二端简支、二端固支等情况下的头五阶固有频率及振型。结果表明,在所有情况下,与低阶元素相比,高阶元素均显出有较好的收敛性。但若施加以力的边界条件,则在使用少量元素和梁的斜削度较大的情况下,高阶元素的结果反而不如低阶元素的结果好。     

Determination of thermal expansion coefficients for unidirectional fiber-reinforced composites

In the present work, the coefficients of thermal expansion（CTEs） of unidirectional（UD）fiber-reinforced composites are studied. First, an attempt is made to propose a model to predict both longitudinal and transverse CTEs of UD composites by means of thermo-elastic mechanics analysis. The proposed model is supposed to be a concentric cylinder with a transversely isotropic fiber embedded in an isotropic matrix, and it is subjected to a uniform temperature change. Then a concise and explicit formula is offered for each CTE. Finally, some finite element（FE） models are created by a finite element program MSC. Patran according to different material systems and fiber volume fractions. In addition, the available experimental data and results of other analytical solutions of CTEs are presented. Comparisons are made among the results of the cylinder model,the finite element method（FEM）, experiments, and other solutions, which show that the predicted CTEs by the new model are in good agreement with the experimental data. In particular, transverse CTEs generally offer better agreements than those predicted by most of other solutions.     

表贴式永磁同步电机永磁体偏心气隙磁场解析

采用分区域的方法对表贴式永磁同步电机磁极偏心的气隙磁场进行推导解析。将求解区域分为永磁体区域、气隙区域、定子槽区域和基于分离变量法利用各区域的边界条件得出相关系数,并在计及永磁体偏心的情况下求解电机气隙磁场。解析模型能够计算电机空载和负载气隙磁场的分布。将解析模型计算结果与有限元分析结果进行对比,发现所建立的解析模型具有较高的准确度。     

计及套圈变形的薄壁角接触球轴承性能分析

为了准确计算柔性支承轴承负荷分布,以外圈孤立点支承薄壁角接触球轴承为例,建立了三维有限元分析模型,考虑外圈受载后弯曲变形对滚动体负荷分布的影响,分析不同工况下轴承负荷分布,寿命及刚度等性能的变化规律,并将有限元法的计算结果与拟动力学法及实验结果进行分析比较.结果表明,有限元方法计算结果与实验结果更为接近.      

纤维增强复合材料力学性能预测及试验验证

针对纤维均匀排布的单向纤维增强复合材料结构力学性能预测问题,基于复合材料细观力学有限元方法,研究建立了代表体积元(RVE)模型,并施加周期性边界条件,实现了纤维增强复合材料基本力学性能的预测。通过将应用上述RVE模型所获取的B/Al纤维增强复合材料力学性能预测结果与解析解和试验数据进行对比表明,施加周期性边界条件的RVE模型的力学性能预测结果与解析解和试验数据吻合良好,验证了所建立计算模型的有效性。基于单向连续纤维增强SiC/TC4复合材料板材的力学性能测试试验,获取了不同铺层方案结构的纵向/横向弹性模量和泊松比,得到的纵向/横向弹性模量计算值与各自试验值均值的误差均小于5%,表明弹性力学性能参数基本一致,计算模型具有合理性。      

超音速、小高超音速三元薄翼非定常二次理论的准确度及其适用范围

 本文处理了超音速三元薄翼非定常问题,通过PLK法使二次解均匀有效。首先考虑零攻角或初始攻角时,已知基本定常绕流叠加高-量级的非定常小扰动流,把它线性化。本方法从健全的基本方程出发,使用高马赫数近似,将非定常二次方程化简,其形式与定常二次方程类似,因而有可能利用定常二次理论的方法求解。特解是求解的关键。鉴于精确特解的复杂性,本报告采用了一种近似特解。 本方法适于一般超音速和完全高超音速之间的马赫数区域（约3～8）,折合频率可达至1左右。可较精确地估计厚度,初始攻角对非定常气动力,力矩的影响。 目前据我们所知,还没有有关实验数据,只能和一些理论结果进行比较。为此对低频有初始攻角的超音速前缘平板三角翼进行了计算,在马赫数3～8,与D.D.Liu^[6]比较吻合。计算结果表明,三元薄翼二次理论可用到高超音速相似参数Mδ=1.0。     

受面内非均匀分布载荷的矩形板屈曲分析

薄板线性稳定性分析进行了很多年,发展得较为完善并且有手册可方便查阅。受非均匀面内分布载荷的板因为解析解不易求出,在分析中一般假设应力与边缘处的作用力分布规律相同。实际上此时板内的应力分布却与边缘处的不一样,而且还会产生另外两个应力分量,其影响取决于边界条件。采用有限元法分析非均匀载荷作用时薄板的稳定性问题,给出多种边界条件下的板的屈曲载荷,还给出了相应的基于受均匀载荷薄板屈曲载荷的当量因子。同时发现《飞机设计手册》中薄板受某线性载荷作用时的临界载荷因子不够精确。研究结果为承受非均匀面内分布载荷的板结构设计提供参考依据。     

采用近似边界求解壁板颤振的CBS有限元算法

为了简化Euler方程求解壁板颤振问题,将近似边界条件成功地推广到CBS(characteristic-based split)有限元方法求解壁板颤振领域,把运动壁面的影响转化为Euler方程的边界条件,避免了对动网格的处理.通过对近似边界方法、动网格方法以及3阶活塞理论的数值模拟结果进行对比发现:首先,加载近似边界的CBS有限元方法操作非常简便,且模拟结果与动网格方法完全吻合;其次,Euler方程可以准确捕捉到壁板前后两端不光滑尖点所引起的压力突跳,而3阶活塞理论则无法做到;最后,采用近似边界的CBS有限元方法在求解无黏可压缩流动中细长体小变形的流-固耦合问题上具有潜力和优势.      

一种新的三维四步编织复合材料几何模型及其在宏观弹性性能预测中的应用

 为了准确预测三维四步(1×1)编织复合材料的宏观弹性常数，提出了一种考虑纤维束三维几何结构和纤维束与基体相互作用、便于有限元网格划分的单胞几何模型，该模型精确地反映了纤维体积比。以该几何模型为基础，用六面体单元分别对纤维束和基体进行了网格划分，满足了纤维束与基体界面间的位移连续条件。采用有限元模型计算了编织复合材料的宏观弹性常数，与其他计算结果和实验结果的比较表明，该几何模型和有限元模型比较合理。     

非零压差边界下间隙流动雷诺方程近似解析解

为了获得间隙密封、滑动轴承等的液膜压力分布解析表达式,将间隙流动雷诺方程的解析解表示为特解和通解之和,其中特解表示为周向坐标函数和轴向坐标函数之和,通解表示为周向坐标函数和轴向坐标函数之积,结合分离变量法和非零压差边界条件,推导获得间隙流动雷诺方程的近似解析解。基于近似解析解计算间隙密封的液膜承载力和偏位角等参数,并与采用有限差分法的计算结果对比,其中液膜承载力偏差小于5%,偏位角偏差小于3°,而计算效率提高了数百倍。      

非紧致气动噪声半空间传播基本解的边界积分方法

为了获得低马赫数流动诱发的非紧致气动噪声在半空间内传播的基本解,结合复等效源方法和边界元方法建立了半空间精确格林函数的边界积分方程,当半空间边界为刚度型阻抗边界时可避免奇异性积分。同时基于等效源方法提出一种半空间二维非紧致圆柱声散射模型,推导了静止介质中声散射基本解的理论表达式。对静止介质中的二维圆柱声散射,数值解在研究的频率与观察点处与理论解一致。采用数值方法计算二维圆柱绕流诱发的半空间声场基本解,结果显示半空间边界强化了声源的声辐射能力,小于马赫数0.2的介质运动对声传播的影响可以忽略。     

用边界元-数学规划法解弹塑性接触问题

 本文基于塑性增量理论导出一种不显含应变的矩阵增量物理关系及平面应变问题σ_z的表达式,提出解决无摩擦弹塑性接触问题的边界元-数学规划法。据此编写了用边界元法解二维问题的通用程序,并用之解算了两圆柱体的弹性和弹塑性接触问题,将数值解与现有结果进行了比较。     

基于剖面翘曲修正理论的复合材料叠层梁动态特性分析

 利用复合材料叠层结构剖面翘曲修正理论和瑞利原理，导出了叠层梁的固有振动方程，然后利用升阶谱有限元法作数值计算，给出了叠层梁的动态特性及相应的动应力分布。与一阶剪切理论相比，指出一阶剪切理论在高频计算时有较大的误差     

复合材料叠层结构边缘应力分析的翘曲修正模型

研究复合材料叠层结构在单轴拉伸状态下的边缘应力问题。在厚度方向 ,利用翘曲修正理论 ,推导出了叠层板三个方向的位移分布规律 ;在宽度方向 ,采用升阶谱位移模式 ;应用虚功原理 ,给出了叠层板边缘应力分析的特殊有限元模型。通过典型例题的计算表明 :边缘应力计算结果与精确弹性解符合很好 ,还进行了收敛性的研究。本文方法的自由度度少 ,方法简单 ,优于差分法、常规有限元法 ,适用于解决边缘效应问题