复合材料层合板弯曲振动高阶理论及有限元模型

本文提出了一种新的复合材料层合板高阶弯曲位移模式,此位移模式既考虑横向剪切的影响,又考虑了法向正应力的分布,进而建立的相当于三维弹性理论解的二维有限元模型,具有精度高、计算量并不大的优点。     

基于半理论法预测基础激励下纤维增强悬臂梁结构应变能

提出了半理论法预测基础激励下纤维增强悬臂梁结构应变能。首先,建立了基础激励下纤维增强复合梁结构的应变能分析模型。然后,明确了采用半理论法预测纤维增强悬臂梁应变能的相关原理,并给出预测纤维增强悬臂梁应变能的具体流程。最后,测试获得该类型梁结构在某基础激励幅度下的振动位移响应,验证所建立的应变能分析模型的正确性,可以采用半理论法来分析预测复合梁的应变能,同时还与相同尺寸的铝合金梁的预测结果进行了对比。结果证明:在相同激励幅度下,纤维增强悬臂梁的应变能相对于铝合金梁结构要低于24%~36%,可以利用应变能指标来客观评价复合结构件相对于金属构件的减振能力。      

考虑剪切和翘曲影响的直升机旋翼气弹稳定性分析

在中等变形梁理论的基础上,对桨叶变形体进行有限变形分析,推导出同时考虑剪切和翘曲影响的小应变、中等变形梁应变-位移关系,并构造出一个全新的21自由度梁单元,应用Hamilton原理导出桨叶运动的有限元方程。在此基础上,研究了剪切和翘曲等非经典因素对无铰旋翼桨叶的动特性和悬停时气弹稳定性的影响。数值结果表明:剪切和翘曲对旋转桨叶的固有频率,尤其是高阶频率,有一定的影响,特别是随着转速的提高这种影响会变大;同时对悬停时桨叶的气弹稳定性有相当程度的影响,尤其是在高桨距角下这种影响是不能忽略的。     

一种考虑截面任意变形模式梁的有限元模型

提出了一种考虑截面完整变形的截面插值梁模型,并用于机翼结构的建模与分析。首先引入截面插值函数——拉格朗日函数描述截面形状,以位移向量为未知变量描述截面位移,在此基础上依据插值理论构造梁单元位移场。不同于传统梁单元通过假定的中性轴的挠度和转角来确定梁截面各点位移,该梁模型摒弃了中性轴假设与平截面假设,通过截面插值函数得到梁截面面内、面外变形;然后通过有限元理论推导了梁单元刚度矩阵与质量矩阵;最后利用截面插值梁单元对机翼各部件进行有限元建模,并展开典型工况下的静力学分析以及动力学分析,与Nastran实体单元计算结果进行了对比分析,验证了该梁模型的有效性,为机翼的结构设计和强度分析提供了一种新的简化建模方法。     

考虑耦合变形的无轴承旋翼气弹稳定性分析

无轴承旋翼存在强烈的非线性扭转-弯曲耦合变形。推导了桨叶的非线性应变-位移关系,应用Hamilton原理建立了多路传力的无轴承旋翼桨叶运动的有限元方程,气动力模型采用二维准定常片条理论,考虑了耦合变形对桨叶轴向弹性位移的影响,并构造了一个新的15自由度梁单元,分析了悬停状态下的无轴承旋翼气弹稳定性。数值结果表明：考虑耦合变形对轴向弹性位移的影响可以提高悬停状态下的无轴承旋翼气弹稳定性分析的精度。     

动态优化中的动响应高阶修改及灵敏度分析

本文通过建立设计变量空间到重分析变量空间的映射关系,然后在重分析变量空间,考虑动响应高阶方向导数及动响应修改量的泰勒级数表达式,利用模态分析技术,推导出一套动响应高阶修改和计算动响应梯度的公式。其工作量完全同于一阶导数修改。公式适合于采用模态截断来限制计算代价的大型飞机结构动态优化设计。算例表明公式具有高精度和高效率。     

横Π型梁在风洞应变天平阻力结构上的应用

主要通过对比传统T型梁和横Π型梁,对风洞应变天平的阻力测量梁进行了分析,根据分析结果提出了传统的横Π型阻力测量梁的改进方式,并通过有限元分析软件进行了优化分析,改进后的横Π型阻力测量梁降低了升力对阻力的干扰,并有利于提高天平阻力分量的稳定性。该测量梁结构应用到了某型飞机高速风洞试验测力天平上,天平静态校准结果与理论分析结果吻合,风洞试验时天平状态良好、性能稳定。     

基于位移测量的机翼载荷分布反演方法

机翼载荷的准确获取是决定机翼结构设计的关键,提出了一种基于位移测量的载荷分布反演方法。针对典型机翼结构建立了COMSOL有限元模型并获取了载荷与位移响应的关系,利用MATLAB调用了位移数据,采用Levenberg-Marquardt梯度算法实现了机翼载荷的高效反演。在此基础上,开展了不同载荷初值和位移测量误差对载荷反演结构的影响分析。分析结果表明：不同初值对载荷反演的影响可以忽略,证明方法具有良好的稳定性;位移测量误差对载荷反演结果影响较小,证明本方法具有较好鲁棒性。提出的载荷反演方法在机翼结构强度分析、优化设计和定寿延寿方面具有广阔的应用前景。     

复合材料层板小挠度理论的改进

改进了复合材料层板高阶剪切变形理论。改进后的理论与一阶剪切变形理论同样只有5个独立变量,但考虑了横向剪切应变沿板厚呈二次曲线变化及满足了层间剪应力的连续性。该理论比简单高阶理论计算的位移和应力更为精确,且逼近三维弹性解。     

基于机载模型的轴向柱塞泵动态特性参数辨识及影响分析

针对航空发动机柱塞泵动态特性解析模型复杂、阶次高、计算资源需求大、参数多且难以准确确定的问题，在忽略解析模型高阶特性得出简化的机载模型基础上，提出了基于典型环节特征参数的时域阶跃响应辨识方法，得到柱塞泵的动态参数。仿真分析和试验结果表明，简化模型精度可达95%，计算资源需求少，为柱塞泵机载模型应用奠定了基础。同时，基于动态模型分析了柱塞泵动态响应对伺服控制动态响应的影响，柱塞泵动态特性应在伺服回路动态特性4倍以上，国军标中规定的柱塞泵动态特性要求可满足航空发动机喷口控制要求。     

Static Analysis of Functionally Graded Sandwich Plates Using an Efficient and Simple Refined Theory

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of function-ally graded sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Two common types of functionally graded sandwich plates, namely, the sandwich with functionally graded facesheet and homogeneous core and the sandwich with homogeneous facesheet and functionally graded core, are considered. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinu-soidal loading has been obtained by using the Navier method. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded sandwich plates.     

A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates

A refined trigonometric shear deformation theory (RTSDT) taking into account transverse shear deformation effects is presented for the thermoelastic bending analysis of functionally graded sandwich plates. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, does not require shear correction factor, the displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The sandwich with homogeneous facesheet and FGM core is considered. Material properties of the present FGM core are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The influences played by the transverse shear deformation, thermal load, plate aspect ratio, and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded metal–ceramic plates are investigated. It can be concluded that the proposed theory is accurate and simple in solving the thermoelastic bending behavior of functionally graded plates.     

Higher-order vibration of thick composite and sandwich plates based on an alternative higher-order model

The transverse stretching vibration of thick sandwich plates, which is attributed to largely different stiffness at the adjacent layers, is a challenging issue, and efficient approach for such issue is less reported in the published literature. Thus, natural frequencies corresponding to stretching vibration modes are generally neglected in engineering design, which might impact structural safety as frequencies of the exciting force are close to transverse stretching vibration frequencies. This paper proposes an alternative higher-order model for dynamic analysis corresponding to the higher-order vibration modes. The proposed model is classified in the displacement-based equivalent single-layer theory, as the number of displacement parameters in the proposed model is independent of the layer number. The continuity of displacements and transverse shear stresses can be fulfilled at the interfaces between the adjacent layers of structures. To demonstrate the capability of the proposed model, typical examples are analyzed by utilizing the proposed model, the three-dimensional finite element method and the chosen higher-order models. By comparing with the exact three-dimensional elasticity solutions, it is found that the proposed model can yield more accurate natural frequencies corresponding to the higher-order displacement modes than the selected models. Moreover, the factors influencing reasonable prediction of the higher-order frequencies are investigated in detail, which can provide a reference for the accurate prediction of the higher-order frequencies.     

Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel

In the present article, the linear and the nonlinear deformation behaviour of functionally graded (FG) spherical shell panel are examined under thermomechanical load. The temperature-dependent effective material properties of FG shell panel are evaluated using Voigt’s micro-mechanical rule in conjunction with power-law distribution. The nonlinear mathematical model of the FG shell panel is developed based on higher-order shear deformation theory and Green-Lagrange type geometrical nonlinearity. The desired nonlinear governing equation of the FG shell panel is computed using the variational principle. The model is discretised through suitable nonlinear finite element steps and solved using direct iterative method. The convergence and the val-idation behaviour of the present numerical model are performed to show the efficacy of the model. The effect of different parameters on the nonlinear deformation behaviour of FG spherical shell panel is highlighted by solving numerous examples.     

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.     

基于静强度试验的有限元模型修正技术研究

基于静力响应的有限元模型修正技术广泛应用于工程结构的参数识别中,需要解决软件实现、基准数据与目标函数选取,以及参数的灵敏度分析等问题。利用位移响应信息对损伤位置确定的悬臂梁进行了损伤程度的精确识别,对于损伤位置不能确定的情况,通过引入应变约束条件实现了损伤位置与损伤程度的同时确定。作为实际工程算例,将飞机静强度试验得到的位移响应与内力响应作为基准数据,利用模型修正技术确定飞机方向舵有限元模型边界条件。算例比较了不同目标函数和约束条件对修正效果的影响,并通过增加内力响应信息进一步修正了根部约束参数,为计算分析提供了精确有限元模型。     

一种特殊梯度分布的功能梯度矩形板弯曲问题解析解

研究了一种特殊梯度分布功能梯度材料矩形板弯曲问题。假设材料的弹性模量在板厚度方向上呈幂函数分布,泊松比为常数,引入PLEVAKO解,利用分离变量法,导出四边简支功能梯度材料矩形板弯曲问题的解析解。通过算例分析了材料组分变化时,功能梯度板应力和位移的变化规律。结果显示不同梯度分布板结构中的应力、位移的变化规律是不同的,有时甚至差别很大。该方法为发展针对功能梯度材料特点的数值算法和简化理论提供依据。     

全复合材料主承力梁结构研制与分析验证

根据结构特点和受力特性,研制了一种全复合材料主承力梁结构。给出了主梁的铺层设计,详述了其成形工艺。基于MSC.Patran/Nastran建立了主梁有限元分析模型,采用线性求解器对多级载荷作用下的主梁进行了静强度分析,给出了结构应变与位移结果。同时设计了强度试验方案,对主梁结构进行了静强度试验验证,采集了应变与位移信息,确定了结构的响应。结果表明,全复合材料主承力梁结构满足强度设计要求,为复合材料应用于主承力结构提供了依据。