基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响,通过合理设计复合材料微观结构可以得到期望的宏观性能.均质化方法作为一种有效的设计方法,它从微观结构的角度出发,利用均匀化的概念,实现了对复合材料宏观力学性能的预测和设计.而当考虑非线性因素,均质化的实现就非常困难.本文利用双渐近展开方法,将位移按照宏观位移和微观位移展开,推导了非线性弹性均质化方程.通过直接迭代法,对非线性弹性均质化方程进行了求解,并给出了具体的迭代方法和实现步骤.本文基于迭代步骤和非线性弹性均质化方程编写MATLAB程序,对3种典型本构关系的周期性多孔材料平面问题进行了计算,对比细致模型的应变能、最大位移和等效泊松比,对程序及迭代方法的准确性进行了验证.之后对一种三元橡胶基复合材料进行多尺度均质化,将其分为芯丝尺度和层间尺度.用线弹性的均质化方法得到了芯丝尺度的等效弹性参数,并将其作为层间尺度的材料参数.在层间尺度应用非线性弹性均质化方法对结构进行计算,得到材料的宏观等效性能,并以实验结果为基准进行评价.     

基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响, 通过合理设计复合材料微观结构可以得到期望的宏观性能. 均质化方法作为一种有效的设计方法, 它从微观结构的角度出发, 利用均匀化的概念, 实现了对复合材料宏观力学性能的预测和设计. 而当考虑非线性因素, 均质化的实现就非常困难. 本文利用双渐近展开方法, 将位移按照宏观位移和微观位移展开, 推导了非线性弹性均质化方程. 通过直接迭代法, 对非线性弹性均质化方程进行了求解, 并给出了具体的迭代方法和实现步骤. 本文基于迭代步骤和非线性弹性均质化方程编写MATLAB 程序, 对3种典型本构关系的周期性多孔材料平面问题进行了计算, 对比细致模型的应变能、最大位移和等效泊松比, 对程序及迭代方法的准确性进行了验证. 之后对一种三元橡胶基复合材料进行多尺度均质化, 将其分为芯丝尺度和层间尺度. 用线弹性的均质化方法得到了芯丝尺度的等效弹性参数, 并将其作为层间尺度的材料参数. 在层间尺度应用非线性弹性均质化方法对结构进行计算, 得到材料的宏观等效性能, 并以实验结果为基准进行评价.      

周期性复合材料湿热力耦合问题的二阶渐近分析

渐近均匀化方法是一种很好的分析复合材料力学性能的方法。通过建立考虑材料湿热效应的双尺度渐近展开模型,研究了周期性复合材料在湿、热、力耦合作用下的结构响应。将带有小参数的位移渐近展开式代入湿热力耦合控制方程,利用等效积分"弱"变换推导出复合材料等效参数的单胞控制方程以及均匀化方程。为了提高计算精度,本文对均匀化解进行了一阶和二阶修正,利用FreeFem++软件进行了数值模拟。结果显示:双尺度二阶渐近分析能够高效、准确地计算出一系列多场耦合问题,为研究周期性复合材料的力学性能提供了新的方法。     

HT—7U超导托克马克纵场线圈等效模量的数值分析

HT－7U托克马克装置的纵场线圈是由多种材料组成的具有周期性分布的大型复杂结构，线圈可视为由超导线、支撑结构和绝缘材料组成的复合材料，结构极其复杂。整个线圈工作在液氦温区。在设计阶段对其宏观等效力学性能进行数值分析计算是十分必要的，但要对整个线圈直接进行有限元分析或实验是极其困难的，主要利用均匀化方法对其进行等效处理，从而分析计算其宏观等效模量，为线圈的设计和评估提供参考依据。另外本文对均匀化方法的边界条件进行了一些改进，提出了更加合理的三维边界条件。     

多相材料微结构布局及宏观结构拓扑并发优化

在传统双向渐进结构优化(BESO)方法基础上,充分考虑材料和结构的尺度关联性,基于均匀化理论将材料微结构胞元设计和宏观结构拓扑优化相结合,按照材料属性排序引入材料插值函数依次进行灵敏分析,建立周期性多相材料微结构布局及宏观结构拓扑并发优化设计方法。优化过程中,宏观结构受力的特性嵌入微观敏度生成过程,使得新型材料具备了特定宏观结构力学需求的更加轻型、高强的最佳力学性能;同时,微观材料胞元的等效材料属性又是宏观结构优化的基础材料,从而使得材料/结构具有尺度上的统一。相关算例说明该方法在解决多相材料微观分布优化和周期性多相材料微结构布局及宏观结构拓扑并发优化问题时具有边界清晰和收敛快等优点。     

多向编织复合材料的力学性能研究

综述并评价了关于二维和三维编织复合材料的有效弹性模量研究的代表性工作,并从材料设计的思想出发,宏观与微观相结合,材料科学与力学相结合,对多向编织复合材料的宏观力学性能与细观织物结构、组分性能的关系及编织复合材料非线性行为进行了详细的理论分析和研究     

考虑粒子分布特征的复合材料细观力学方法

研究了颗粒增强复合材料中颗粒增强体粒径分布对复合材料力学性能的影响,利用分形思想将增强粒子的概率分布特征考虑进来,对已有的复合材料细观力学等效夹杂方法进行修正,建立了一个考虑粒子统计分布的细观等效力方法.以混凝土为例,分析了颗粒增强体体积含量、夹杂与基体的模量比和分形结构的分辨率对复合材料力学性能的影响.结果表明,这种新方法能够适用于分析颗粒增强复合材料的细观结构对力学性能的影响.     

挠性航天器太阳翼全局模态动力学建模与实验研究

现代柔性航天器通常安装有大型太阳翼为其在轨运行提供所需动力. 航天器入轨后太阳翼展开并锁定成为铰链连接多板结构, 此类结构质量轻、跨度大、刚度低的特点使其低频振动和非线性振动问题越来越凸显. 分析和处理此类结构出现的复杂振动问题的关键在于建立系统精确的非线性动力学模型. 为此, 本文提出铰链连接多板结构解析全局模态的提取方法, 获取太阳翼的固有频率和解析函数表征的全局模态. 提出可变刚度的扭转弹簧等效模型, 考虑铰链非线性刚度及摩擦力矩等因素, 通过全局模态离散得到系统的低维高精度非线性动力学模型, 研究了太阳翼在周期激励作用下的非线性特性. 开展太阳翼地面振动实验研究, 采用锤击法获取系统模态, 利用振动台施加正弦扫频激励, 将物理实验结果与理论结果进行对比, 从而验证全局模态动力学建模方法的合理性与准确性. 结果表明, 铰链刚度等结构参数对系统固有特性的影响较大, 铰链的存在会使太阳翼的动态响应出现跳跃等非线性现象. 全局模态动力学建模方法能很好地解决多板结构在非经典边界下解析全局模态求解的困难, 系统全局模态反映的是系统各个部件弹性振动的真实模态, 所建立的动力学模型具有低维高精度的特点, 对于复杂组合结构非线性动力学建模具有重要的参考价值.      

MODELING OF NONLINEAR BEHAVIORS OF IMMERSION JOINT

沉管隧道柔性接头的力学性能是其抗震设计的关键准则. 用有限元方法模拟接头的非线性力学性能需要解决接头处材料非线性和接触非线性两个问题. 为简化分析计算,该文采用分段线性化的方法表征接头的材料非线性问题,引进调整因子改进接触算法中的判断条件,处理接头的边界非线性问题. 通过沉管隧道接头的三维精细化建模,研究了沉管隧道接头在拟静力载荷下的响应,获得了接头的轴向等效刚度曲线、抗弯刚度曲线和非线性耦合的剪切特性曲线,进而分析了不同轴向压力对接头剪切特性的影响.     

格栅结构力学性能研究进展

格栅复合材料是一种新型轻质高强材料. 综述了格栅复合材料的周期构型特征和格栅结构的制备工艺. 归纳了二维周期格栅材料的等效刚度矩阵计算方法, 比较了不同构型格栅的基本力学性能, 介绍了胞元材料的微极弹性理论和格栅的强度与屈服面计算方法. 探讨了格栅的缺陷及其力学响应, 包括格栅的尺度效应、夹杂缺陷以及裂纹扩展特征, 介绍了波在格栅材料中传播机理的最新研究成果. 根据格栅材料在工程中的应用形式, 分类介绍了格栅板壳结构、格栅加筋板壳结构和格栅夹层结构的结构特点和破坏方式、设计优化准则和实验研究成果. 还归纳了作者所在研究小组近期在碳纤维格栅复合材料的制备、实验研究和理论分析等方面的最新工作进展.      

流固耦合的周期加强板的振动及声辐射研究

研究了流体负载下的无穷大双周期加强板, 在周期谐振力作用下的振动响应和声辐射,并提出了一种基于有限元和空间波数法的半解析半数值方法. 首先利用有限元的方法对周期结构进行单元离散, 并将结构对薄板的作用力等效为节点力的作用. 然后通过周期结构的振动方程, 结合薄板与结构的位移边界条件, 建立了节点力与薄板节点位移的函数方程. 最后应用空间波数法和傅里叶变换, 并采用数值计算的方法求解出薄板的节点位移, 得到了周期加强板关于离散节点位移的振动和辐射声压方程. 在数值算例中, 对该方法的正确性进行了验证, 并且分析了周期结构对薄板的振动和声辐射的影响.     

含孔隙变厚度FG圆板的湿热力学响应

功能梯度材料(functionally graded materials, FGM)是组份含量按特定方向连续变化的非均匀复合材料,可有效解决传统复合材料组份之间结合能力弱和不同组份性能难以协调等问题,达到诸如缓和应力集中和优化应力分布等效果,使整体材料在保持细观结构完整性的同时充分发挥各组份材料的性能优势.由于制备技术等原因或出于特殊功能的需要,微孔或孔隙是各类型FGM中的常见缺陷.从细观结构上看,多孔FGM中的孔隙包含了单一组份内的材料孔隙和组份微粒间的结构间隙,这些孔隙将对FGM的力学性能,尤其是在湿热环境下的力学行为产生影响.本文考虑FGM中的两类细观孔隙(材料孔隙和结构孔隙),提出了令各类孔隙依赖于各自组份变化,再线性叠加得到的整体孔隙计算式.考虑组份材料和孔隙填充物(液相水和水蒸气)性质的温度相关性,建立了湿热相关FGM材料模型.针对厚度沿径向变化的旋转圆板结构,应用该FGM材料模型,推导了圆板的非线性稳态湿热控制方程及考虑湿热弹性本构的位移控制方程,采用微分求积法(differential quadrature method,DQM),获得了圆板的湿热场、位移场和应力分布.在数值算例中,利用退化模型的解析解对本文的数值计算方法进行了验证,继而通过改变各关键参数,讨论了两类孔隙率、梯度指数和圆板厚度变化对含孔隙FGM变厚度旋转圆板湿热力学响应的影响规律.      

Multi-scale modelling of strongly heterogeneous 3D composite structures using spatial Voronoi tessellation

3D composite materials are characterized by complex internal yarn architectures, leading to complex deformation and failure development mechanisms. Net-shaped preforms, which are originally periodic in nature, lose their periodicity when the fabric is draped, deformed on a tool, and consolidated to create geometrically complex composite components. As a result, the internal yarn architecture, which dominates the mechanical behaviour, becomes dependent on the structural geometry. Hence, predicting the mechanical behaviour of 3D composites requires an accurate representation of the yarn architecture within structural scale models. When applied to 3D composites, conventional finite element modelling techniques are limited to either homogenised properties at the structural scale, or the unit cell scale for a more detailed material property definition. Consequently, these models fail to capture the complex phenomena occurring across multiple length scales and their effects on a 3D composite’s mechanical response. Here a multi-scale modelling approach based on a 3D spatial Voronoi tessellation is proposed. The model creates an intermediate length scale suitable for homogenisation to deal with the non-periodic nature of the final material. Information is passed between the different length scales to allow for the effect of the structural geometry to be taken into account on the smaller scales. The stiffness and surface strain predictions from the proposed model have been found to be in good agreement with experimental results.The proposed modelling framework has been used to gain important insight into the behaviour of this category of materials. It has been observed that the strain and stress distributions are strongly dependent on the internal yarn architecture and consequently on the final component geometry. Even for simple coupon tests, the internal architecture and geometric effects dominate the mechanical response. Consequently, the behaviour of 3D woven composites should be considered to be a structure specific response rather than generic homogenised material properties.     

Multi-scale analysis in elasto-viscoplasticity coupled with damage

The purpose of this study is to present a micromechanical approach, based on the transformation field analysis (TFA), proposed by Dvorak, which has been generalized at Onera in order to analyze the nonlinear behavior of heterogeneous materials in elasto-viscoplasticity coupled with damage. In such analysis, the macroscopic constitutive equations are not purely phenomenological but are built up from multi-scale approaches starting from the knowledge of the properties of the constituents at the microscopic or mesoscopic scales. The model can take into account some local characteristics that can evolve during the thermo-mechanical applied loads or the manufacturing process, like the grain size for metallic alloys or the fiber volume fraction for composites.The determination of some specific tensors which are present in this formulation is closely linked to the microstructure morphology of heterogeneous materials constituting the macroscopic structure. For example, an Eshelby’s based approach is more appropriate to characterize polycrystalline materials with a random microstructure, while the homogenization of periodic media technique can be used for composite materials with a sufficiently regular microstructure. The proposed methodologies allowing to perform this nonlinear analysis across the scales are illustrated with examples based on the behavior of structures reinforced with a long fiber unidirectional metal matrix composite.     

Meshless method for nonlinear heat conduction analysis of nano-composites

Carbon nanotubes (CNTs) may become ideal reinforcing materials for high-performance nano-composites due their exceptional properties. Still, much work is needed to be done before the potentials of CNT based composites can be fully realized. The evaluation of effective material properties of nano-composites is one of many difficult tasks. Simulations using continuum mechanics approach can play a significant role in the analysis of these composites. In the present work, nonlinear heat conduction analysis of CNT based composites has been carried out using continuum mechanics approach. Element free Galerkin method has been applied as a numerical tool. Thermal conductivities of nanotube and polymer matrix are assumed to vary quadratically with temperature. Picard and quasi-linearization schemes have been utilized to obtain the solution of a system of nonlinear equations. Cylindrical representative volume element has been used to evaluate the thermal properties of nano-composites. Present simulations show that the temperature dependent matrix thermal conductivity has a significant effect on the equivalent thermal conductivity of the composite, whereas temperature dependent nanotube thermal conductivity has a small effect on the equivalent thermal conductivity of the composite. The results obtained by Picard method have been found almost similar with those obtained by quasi-linearization approach.     

考虑微结构连接性的双尺度结构自然频率拓扑优化

多孔材料因具有轻量化、高孔隙率和减振/散热等优良多物理特性,在航空航天等领域具有广阔应用前景。采用拓扑优化方法对含多种多孔材料的结构进行结构与材料微结构构型一体化设计,有助于获得具有优良力学性能的结构设计。然而,传统逆均匀化微结构设计方法无法确保不同多孔材料微结构之间的连接性,设计结果不具备可制造性。本文面向含多种多孔材料的双尺度结构基频最大化设计问题,考虑不同微结构之间的连接性,协同设计多孔材料的微结构构型及其在宏观尺度下的布局。采用均匀化方法计算多孔材料的宏观等效力学性能,通过对不同多孔材料微结构单胞的边界区域采用相同的拓扑描述确保双尺度优化过程中任意空间排布下不同微结构的连接性,并通过优化算法确定微结构间的连接形式及微结构拓扑。在宏观尺度,提出结合离散材料插值模型和RAMP插值模型RAMP (Rational Approximation of Material Properties)的多孔材料各向异性宏观等效刚度及质量插值模型,获得清晰的多孔材料宏观尺度布局并减轻优化过程中伪振动模态的影响。建立以双尺度结构基频最大化为目标,以材料用量为约束的优化列式,推导灵敏度表达式,并基于梯度优化算法求解双尺度结构拓扑优化问题。数值算例表明,采用本文优化方法能够有效确保基频最大化双尺度结构设计中不同多孔材料微结构之间的连接性,增强优化设计结果的可制造性。     

Complicated nonlinear responses of a simply supported FGM rectangular plate under combined parametric and external excitations

In this paper, we use the asymptotic perturbation method based on the Fourier expansion and the temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported rectangular plate made of functionally graded materials (FGMs) subjected to a through-thickness temperature field together with parametric and external excitations. Material properties are assumed to be temperature-dependent. Based on the Reddy’s third-order plate theory, the governing equations of motion for the plate are derived using the Hamilton’s principle. The Galerkin procedure is employed to obtain a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms. The resonant case considered here is 1:2 internal resonance, principal parametric resonance-1/2 subharmonic resonance. Based on the averaged equation in polar coordinate form, the stability of steady state solutions is analyzed. The phase portrait, waveform and Poincaré map are used to analyze the periodic and chaotic motions of the FGM rectangular plate. It is found that the FGM rectangular plate exhibits the chaotic motions under certain circumstances. It is seen that the nonlinear dynamic responses of the FGM rectangular plate are more sensitive to transverse excitation. The excitation force can be used as a controlling factor which can change the response of the FGM rectangular plate from periodic motion to the chaotic motion.     

Consistently linearized constitutive equations of micromechanical models for fibre composites with evolving damage

The numerical analysis of engineering structures is usually based upon the assumptions of a homogeneous as well as a continuous medium. These simplifications are maintained also for structures made of fibre reinforced composite materials which possess by definition a heterogeneous finescale architecture. Furthermore in the course of the loading of such structures void nucleations might arise out of the debonding of the embedded fibres or the growth of microcracks inside the matrix phase. Hence, the assumption of a continuous and homogeneous medium is not valid from a microscopical point of view. Nevertheless, it is numerically advantageous to keep up these simplifying assumptions on the macrolevel. Therefore, the knowledge of the so called macroscopic or effective material behaviour is needed. The overall properties can be described in terms of volume averaged quantities that smear the heterogeneities of the microscopic structure and the influence of its defects. Since the evolution of damage within composite materials means a rather complex process, a purely phenomenological approach is hardly feasible. Hence, the average properties are to be obtained from a micromechanical analysis of the discontinuous and damaged finescale structure. The efficiently reformulated version of the micromechanically based Generalized Method of Cells (GMC) provides the macroscopic tangential constitutive tensor in closed-form. The numerical efficiency of the approach allows for the use of the GMC as the constitutive model for nonlinear finite element analyses. Two-scale simulations of macroscale composite structures considering process depending damage evolution on the microscale of heterogeneous media becomes feasible.     

基于代理模型的箭体连接结构极值响应分析与优化

螺栓法兰连接结构在航空航天等工程领域中广泛应用，其力学性能在不同工况和装配情况下十分复杂。由于拉压刚度差异，含连接结构的箭体动力学响应呈现明显的非线性特征。因此，考虑不同连接参数及工况下的连接非线性动力学响应，对结构优化设计有着重要意义。本文针对以双线性弹簧表征螺栓法兰连接非线性的箭体等效动力学模型，基于径向基函数(RBF)神经网络和响应面法分别建立其连接面处的极值响应代理模型，对比发现RBF神经网络模型在较高精度上可以实现对动响应极值的预测及分析；同时分析了不同载荷参数及刚度变化对连接结构动响应极值的影响；最后，利用RBF神经网络代理模型，开展了连接面加速度极值响应与螺栓弹簧力最小化为目标的连接结构参数优化。