两种典型缺陷对六边形蜂窝压缩性能的影响

文摘通过数值模拟研究了孔洞和部分填充孔穴这两种典型缺陷对弹性蜂窝(橡胶)和弹塑性蜂窝(金属)的压缩性能的影响规律。结果表明,相对于分散孔洞,集中孔洞对蜂窝材料的力学性能影响更大,且它们的存在完全改变了其变形模式;而对于含填充孔穴的蜂窝材料而言,其弹性模量得到显著增强,弹性蜂窝的屈曲应力也得到增强,但弹塑性蜂窝的塑性坍塌应力则保持不变或有所下降。     

零泊松比十字形混合蜂窝设计分析及其在柔性蒙皮中的应用

柔性机翼变弯度/展/弦长方案需要蒙皮在面内具有一维大变形能力,并且在垂直平面方向能够提供足够的抗压和抗弯刚度。设计了一种零泊松比十字形混合蜂窝,支撑弹性胶膜构成柔性蒙皮结构。研究了十字形混合蜂窝的面内变形机理、蜂窝力学特性与单元形状参数的关系,针对蜂窝的面内单向变形能力进行了参数优化;将蜂窝结构等效为正交各向异性材料,研究了十字形混合蜂窝的面外抗弯能力及其影响因素;根据后缘变弯度机翼柔性蒙皮设计要求,研究了十字形混合蜂窝结构参数的适用性。结果表明这种蜂窝能够满足柔性蒙皮的使用要求,且质量轻、易驱动。     

基于CR理论的大柔性机翼几何非线性结构建模

大柔性机翼在气动载荷的作用下,将产生显著的弹性变形,常规线弹性理论的小变形假设不再成立,需要采用能够考虑几何非线性效应的结构模型进行求解。基于CR(Co-Rotational)共旋转有限元理论,把几何非线性大变形分解为刚体的旋转和平移及局部坐标系下的弹性变形,建立了适用于大柔性机翼几何非线性变形描述的结构模型。以大柔性悬臂梁为例,采用载荷增量法,研究了集中弯矩作用下的非线性变形特征,对静力学方法进行了验证,并讨论了耦合加载几何非线性变形特征;以类"太阳神"太阳能布局无人机(UAV)为例,研究了其几何非线性大变形特性。     

A method of determining effective elastic properties of honeycomb cores based on equal strain energy

A computational homogenization technique (CHT) based on the finite element method (FEM) is discussed to predict the effective elastic properties of honeycomb structures. The need of periodic boundary conditions (BCs) is revealed through the analysis for in-plane and out-of-plane shear moduli of models with different cell numbers. After applying periodic BCs on the represen-tative volume element (RVE), comparison between the volume-average stress method and the boundary stress method is performed, and a new method based on the equality of strain energy to obtain all non-zero components of the stiffness tensor is proposed. Results of finite element (FE) analysis show that the volume-average stress and the boundary stress keep a consistency over different cell geometries and forms. The strain energy method obtains values that differ from those of the volume-average method for non-diagonal terms in the stiffness matrix. Analysis has been done on numerical results for thin-wall honeycombs and different geometries of angles between oblique and vertical walls. The inaccuracy of the volume-average method in terms of the strain energy is shown by numerical benchmarks.     

In-plane corrugated cosine honeycomb for 1D morphing skin and its application on variable camber wing

A novel 0-Poisson’s ratio cosine honeycomb support structure of flexible skin is proposed. Mechanical model of the structure is analyzed with the energy method, finite element method (FEM) and experiments have been performed to validate the theoretical model. The in-plane characteristics of the cosine honeycomb are compared with accordion honeycomb through analytical models and experiments. Finally, the application of the cosine honeycomb on a variable camber wing is studied. Studies show that mechanical model agrees well with results of FEM and experiments. The transverse non-dimensional elastic modulus of the cosine honeycomb increases (decreases) when the wavelength or the wall width increases (decreases), or when the amplitude decreases (increases). Compared with accordion honeycomb, the transverse non-dimensional elastic modulus of the cosine honeycomb is smaller, which means the driving force is smaller and the power consumption is less during deformation. In addition, the cosine honeycomb can satisfy the deform- ing requirements of the variable camber wing.     

考虑机翼几何非线性的气动弹性建模与分析

大展弦比柔性机翼结构重量轻、气动效率高,广泛应用于高空长航时无人机(UAVs)。飞行过程中,这类机翼在气动力作用下发生大变形,线性结构模型不再适用,需要建立考虑几何大变形的结构模型。采用牛顿力学方法推导了考虑结构几何非线性的机翼结构动力学模型,该方法推导过程简洁、物理意义明确,可以与Hodges基于哈密顿原理的推导方法相互补充,相互验证。为了能够更准确地求解大展弦比柔性机翼的非定常气动力,建立了能够考虑机翼三维效应且适用于机翼空间大变形的非定常气动力模型。基于建立的非线性结构模型和非定常气动力模型,采用松耦合方法建立了非线性气动弹性模型,并通过算例验证了气弹模型的准确性。研究结果表明,大展弦比柔性机翼颤振速度对来流迎角和机翼的展长均较为敏感;当来流速度大于颤振速度时,由于几何非线性,机翼振动并未发散而是形成稳定的极限环振荡(LCO);随着来流速度进一步增加,机翼再次穿过临界稳定点,由不稳定系统变为稳定系统,直到随着速度的增加系统再次达到临界稳定状态。     

Geometrically exact nonlinear analysis of pre-twisted composite rotor blades

Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the anisotropic material properties. In this paper, the geometrically exact nonlinear modeling of a generalized Timoshenko beam with arbitrary cross-sectional shape, generally anisotropic material behavior and large deflections has been presented based on Hodges’ method. The concept of decomposition of rotation tensor was used to express the strain in the beam. The variational asymptotic method was used to determine the arbitrary warping of the beam cross section. The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy. The geometrically exact nonlinear equations of motion were established by Hamilton’s principle. The established modeling was used for the static and dynamic analysis of pre-twisted composite rotor blades, and the analytical results were validated based on experimental data. The influences of the transverse shear deformation on the pre-twisted composite rotor blade were investigated. The results indicate that the influences of the transverse shear deformation on the static deformation and the natural frequencies of the pre-twisted composite rotor blade are related to the length to chord ratio of the blade.     

细观力学有限元法预测复合材料宏观有效弹性模量

基于能量等效原理提出了复合材料有效弹性模量的定义，并指出了该定义的基础及前提条件。为从理论上计算复合材料宏观有效弹性模量，建立了通过细观力学有限元法计算复合材料有效弹性模量的方法。复合材料宏观弹性模量，是通过对复合材料细观结构代表性体积元的力学响应的计算来得到，在该计算方法中，给出了施加简便的边界载荷以及恰当的边界变形约束条件的方法。数值计算结果与部分试验结果具有较好的一致性，表明所提出的方法能够较好地计算复合材料的宏观有效弹性模量。     

蜂窝夹芯结构面内等效弹性参数的分析研究

针对Bernoulli Euler梁法计算蜂窝夹芯等效弹性参数的不足,利用3D有限元数值模拟技术,通过对不同材料、不同尺寸的正六边形蜂窝夹芯弹性参数进行数值模拟,给出了芳纶纸面内等效刚度和Poisson比随蜂窝夹芯几何参数变化关系,提出了等效弹性参数的计算公式和一种循环优化设计蜂窝夹芯板厚度的新思想,得到了一些Bernoulli Euler梁法无法得到的重要结论:正六边形蜂窝夹芯结构y方向的弹性模量大于x方向的1.5倍;等效Poisson比仅与蜂窝夹芯几何参数有关,而与材料常数无关等。最后通过与文献[11]铝质蜂窝夹芯的压缩实验结果比较,证实了本文所使用方法的有效性和部分公式的正确性。     

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.     

Nonlinear bending analysis of a 3D braided composite cylindrical panel subjected to transverse loads in thermal environments

The aim of this study is to investigate nonlinear bending for a 3-Dimensional(3D)braided composite cylindrical panel which has transverse loads on its finite length. By refining a micro-macro-mechanical model, the 3D braided composite can be treated as a representative average cell system. The geometric structural properties of its components deeply depend on their positions in the section of the cylindrical panel. The embedded elastic medium of the panel can be described by a Pasternak elastic foundation. Via using the shell theory of the von Ka′rma′nDonnell type of kinematic nonlinearity, governing equations can be established to get higherorder shear deformation. The mixed Galerkin-perturbation method is applied to get the nonlinear bending behavior of the 3D braided cylindrical panel with a simply supported boundary condition.Based on the analysis of the braided composite cylindrical panel with variable initial stress, geometric parameter, fiber volume fraction, and elastic foundation, serial numerical illustrations are archived to represent the appropriate nonlinear bending responses.     

仿生负泊松比拉胀内凹蜂窝结构耐撞性

基于自然界微观生物结构的启发,设计了1种新型仿生负泊松比拉胀内凹蜂窝（ARH）,并对其耐撞性能进行数值模拟。结合竹子的梯度结构和椰子树的同心胞结构,提出了2种单向梯度和2种双向梯度同心ARH结构。梯度同心结构设计方法不仅可诱导结构渐进的冲击行为,而且因其较低的等效壁厚可改善其比吸能能力。与传统ARH结构相比,对仿生ARH结构的平台应力和吸能特性进行研究,并分析耦合压溃变形模式、收缩变形机理和负泊松比效应等来揭示结构的增强机理。结果表明：预测的耐撞响应和压溃变形模式与参考结果相似;相对传统的ARH,梯度同心ARH有更高的平台应力和比吸能,且平台应力的上升和压溃变形模式均呈梯度变化;梯度方向对压溃变形模式和各层变形顺序影响较大;双向梯度同心ARH比单向梯度同心ARH因耦合变形具有更高的吸能能力;同心胞数对蜂窝各层的收缩变形有较大影响。     

钛蜂窝体制备及压缩性能研究

采用融熔沉积快速成形法制备钛金属蜂窝结构材料,对粉浆制备、钛金属蜂窝结构蜡坯固化、脱蜡等工艺以及所制备的钛蜂窝体的压缩性能进行了研究.结果表明,采用融熔沉积快速成形可以制备钛金属蜂窝结构,工艺简单、尺寸可控,钛蜂窝结构的相对密度在9%～12.6%范围内,屈服强度和弹性模量的增加不大;相对密度超过12.6%后,屈服强度显著增加,但弹性模量增加的幅度不大.通过改变蜂窝体正六边形的边长或改变蜂窝体的壁厚均达到相同的相对密度条件下,蜂窝体的压缩强度差别不大,但对蜂窝体的弹性模量却有显著影响.     

固体推进剂药柱泊松比随机粘弹性有限元分析

为了研究泊松比的分布对固体推进剂药柱结构分析的影响，发展了一种地不可压缩材料的粘弹增量有限元方法，进行了泊松比随机粘弹性有限元的研究，要用局部平均方法对随机场进行离散，给出了二阶摄动有限 元变异方程。算例表明，对药桩进行随机模拟，计算效率和精度较高。     

蜂窝夹层结构中胶粘剂的模拟和研究

提出了一套定量研究蜂窝夹层板中胶粘剂作用的方法。从建立蜂窝芯、胶粘剂和面板的板单元有限元模型出发,用有限元软件计算了在线弹性范围内有胶粘剂和无胶粘剂蜂窝夹层板模型在受均布载荷情况下的变形,并作了对比分析,指出了胶粘剂对夹层板的加强作用,为定量研究胶粘剂在夹层结构中作用的模拟开辟道路。同时对胶粘剂的剥离性能进行了研究,总结了影响胶粘性能的因素。     

Analysis of nonlinear deformation and stability of oval cylindrical shells under combined loading by bending and torsion moments

A problem of geometrically nonlinear deformation and stability of cylindrical shells with noncircular cross-section contour is solved by the finite element method. The nonlinear system of algebraic equations to determine the nodal unknowns of finite elements is obtained with the use of the variational Lagrange principle. The system is solved by the method of successive loadings with the use of the Newton-Kantorovich method of linearization, the method of solving linear Craut’s equations and Sylvestor’s stability criterion. The nonlinear deformation and stability of shells with the oval and elliptical cross-sections under combined loading by bending and torsion moments are analyzed. The critical loads and buckling modes of shells are determined. The influence of deformation nonlinearity, shell ovality and ellipticity on the critical loads is clarified.     

弱界面粘结对复合材料有效性能的影响

采用非线性弹簧元模拟界面,用细观力学有限元法计算分析了不同界面特性下弱界面粘结的纤维增强金属基复合材料的宏细观性能。并考虑了3种不同的界面模型。结果表明弱界面粘结的存在使复合材料宏观性能下降。在常响应界面情况下,复合材料横向拉伸应力-应变曲线存在明显的转折点,对应于界面分离的起始点,转折点的位置取决于界面粘结强度。当存在渐进适应界面时,复合材料横向拉伸应力-应变曲线存在3个阶段。      

考虑阻尼性能的复合结构多尺度拓扑优化设计

最优阻尼复合结构应该是阻尼材料自身的材料性能和阻尼材料在板壳结构上的分布形态均是最优的。针对板壳阻尼复合结构的多尺度设计问题,建立了基于非比例阻尼模型的复合结构多尺度拓扑优化方法,实现了阻尼材料在宏微观两尺度上的协同设计,同时获得最优的阻尼材料宏观分布形态和微观构型。以结构模态阻尼比为目标,分别研究了复合结构的单目标和多目标多尺度设计问题。结果表明,在单目标设计中,当最大化结构的某一阶模态阻尼比时,优化后结构的该阶模态阻尼比最大,同时结构在该阶处的频率响应最小;在多目标设计中,以结构前3阶模态阻尼比之和为目标,虽然在每一阶处的性能劣于单目标设计结果,但是结构前3阶模态阻尼比的总体性能更优。同时,从微结构的构型可得,最优的微结构构型中低刚度高阻尼材料的分布相互连接,其损失模量（微结构复弹性矩阵的虚部）和阻尼因子（微结构复弹性矩阵的虚部与实部之比）都相对较高,且呈现负泊松比现象。优化后复合结构的动力学性能显著提高。     

航空发动机承力系统抗变形能力评估

针对航空发动机承力系统的结构和力学特征,基于安全性设计要求,建立了整机承力系统抗变形能力的评估方法,分别从结构固有抗变形能力、稳态载荷下的抗变形能力以及瞬态冲击载荷下的抗变形能力3方面提出了当量刚度、间隙匹配系数、冲击放大系数3个评估参数.以典型高涵道比涡扇发动机承力系统为对象进行了抗变形能力评估.结果表明:以截面的等效刚度和承力系统最大等效刚度的比值作为结构当量刚度,以稳态载荷下整机系统各个截面的最小间隙与 最大间隙的比值作为间隙匹配系数和以瞬态冲击载荷与各个支点及安装节上支反力的最大峰值载荷的比值作为冲击放大系数,这3个参数均能较好地反映出整机承力结构的危险位置和极限载荷下的响应特征.最终的评估结果可以为承力系统结构方案设计和优化提供参考.      

各向异性Kelvin开孔泡沫模型的弹性性能

在弹性小变形情况下,基于构造的各向异性Kelvin模型对开孔泡沫材料的变形进行了分析。综合考虑了胞体中斜支柱的轴向、弯曲和剪切变形以及水平支柱的轴向变形的影响,利用最小势能原理得到了材料的弹性性能与各向异性比及相对密度的关系。研究结果表明,各向异性比越大,沿胞体伸长方向的相对弹性模量和泊松比越大,而在垂直于胞体伸长方向上的相应值反而越小;两个方向上的相对弹性模量均随相对密度增加而增大,泊松比的变化趋势则正好相反。本文预测结果较好地符合了实验数据的变化趋势,且与已有的G-K模型比较接近,证明了该模型的有效性。