有限杆中不可逆相边界的传播规律及其应用

 采用一种简单混合物相变本构模型,对不可逆相变材料有限杆中的宏观相边界传播规律进行了研究。结果表明,界面和加卸载条件对杆中相边界的传播有重要影响,不同界面条件下杆中新相体积含量的最终分布呈现出不同的形态。还解释了相变Taylor杆碰撞实验中发现的新现象,提出了利用冲击方法制备对称型梯度材料的可能性。     

α铁冲击相变的离散元方法

利用离散元方法结合基于无扩散相变的两相模型、热力学相容的自由能函数与有限速率相变动力学方程,模拟α铁的冲击相变过程.得到铁的相边界、冲击Hugoniot关系及自由面速度剖面,并对不同冲击压力下加卸载过程的波系传播和相互作用过程进行分析,获得了加卸载波速特征.     

微通道内冰晶生长过程的相场模拟

为研究微通道内冰晶生长的微观机理以便提出相应的防结冰措施，建立了微通道内结冰过程的相场模型，模型中引入了实际边界条件的影响(取为第三类边界条件),相场计算中采用随机方法生成晶核。基于有限差分法对相场模型进行了数值求解，对不同边界条件影响强度(以努塞尔数Nu表征)下冰晶生长过程进行了系统研究。研究结果表明：边界对微通道内的冰晶生长影响显著，Nu越大，微通道内冰晶生长第一阶段(冰晶未扩展到边界时)结晶速率越大，使得充分结晶(定义为结晶百分数达到80%)所需总时间越短；同时应在结冰初始阶段对其进行及时干预才能有效防止结冰。     

亚表面异质缺陷对功能梯度材料表面温度场的影响

基于双曲型热传导方程,采用镜像法和波函数展开法,求解了含亚表面异质圆柱缺陷的半无限功能梯度材料的表面温度场,给出了功能梯度材料中热波散射的一般解.分析了亚表面异质圆柱缺陷的几何参数(如埋藏深度)和热物理参数(如导热系数、热扩散长度、热扩散率及热弛豫时间等)对功能梯度材料表面温度场的影响.温度波由调制的超短脉冲激光在功能梯度材料表面激发,异质圆柱缺陷表面的边界条件为导热边界.研究结果可望为功能梯度材料的红外热波无损检测、导热反问题提供计算方法和参考数据.     

透明边界条件算法的比较研究及改进

研究了束传播算法(BPM)中简单透明边界条件(STBC)和完全透明边界条件(CTBC)两种边界处理算法对计算结果精度的影响.通过改进和综合两种边界条件算法,提出改进型透明边界算法(ITBC).该边界算法相对于STBC与CTBC降低了计算精度对于传播步长的依赖性,提高了计算精度,改善了透明边界条件算法在BPM中的稳定性.     

轴向载荷下功能梯度材料Timoshenko梁动力屈曲分析

假设功能梯度材料Timoshenko梁各项物性参数只沿厚度方向按幂函数进行连续变化,研究了功能梯度材料Timoshenko梁的动力屈曲。基于一阶剪切理论,采用Hamilton原理推导出轴向载荷作用下,功能梯度材料Timoshenko梁动力屈曲的控制方程。利用里兹法与棣莫弗公式相结合,获得了功能梯度材料Timoshenko梁在夹支-固支边界条件下动力屈曲临界载荷的解析表达式和屈曲解。应用MATLAB编程计算,讨论了功能梯度材料Timoshenko梁的几何尺寸、梯度指数、模态数、材料构成、泊松比以及弹性模量对临界载荷的影响。结果表明:功能梯度材料Timoshenko梁动力屈曲临界载荷随梁长度的增大而减小,随着梯度指数的增大而减小,随模态数的增大而增大,说明冲击载荷越大,高阶模态越容易被激发;随着泊松比和弹性模量的增大而增大,且泊松比的影响较小,而弹性模量的影响较大。由于剪切项的影响,临界载荷-临界长度的关系曲线在加载端变化趋势平缓。随着模态数的增大,梁的屈曲模态越为复杂。     

四边简支含多孔材料双层板隔声特性

有限大含多孔材料和空气层复合板结构隔声特性的研究尚不充分。该文旨在研究四边简支边界条件下复合板结构隔声特性。首先基于流体饱和多孔弹性介质的声传播理论计算了声波在多孔介质中的传播波数；继而采用四边简支边界条件下板结构的模态函数，利用模态叠加法和伽辽金法推导了复合板结构隔声系数理论模型，并数值求解复合板隔声量。将理论模型得到的四边简支复合板隔声量与实验结果对比，验证了理论模型的正确性。最后，详细讨论了边界条件、板结构尺寸和多孔材料厚度等主要参数对隔声特性的影响。结果表明：四边简支复合结构隔声特性曲线上“谷值”出现得较少，并且简支复合板隔声特性的第一个“吻合频率”比固支支撑复合板更靠近低频，当频率超过3000 Hz以后，简支和固支边界条件复合板结构隔声特性趋于一致。     

基底支撑刚度梯度变化对石墨烯层间摩擦力的影响

基于纳米摩擦能耗理论,利用分子动力学方法建立了公度接触下支撑刚度梯度变化的石墨烯层间摩擦力模型,分析了基底质心刚度和支撑刚度梯度变化对基底和薄片各接触区摩擦能耗的贡献.结果表明:软边界区始终贡献驱动力;硬边界区贡献的摩擦力最大,且随着支撑刚度的增大,硬边界区对总摩擦的贡献比也越高.各接触区的摩擦力是薄片和基底之间的褶皱势和接触区产生的法向变形差两部分的共同作用.前者是公度接触下阻碍滑移的界面势垒和刚度梯度方向上不同刚度支撑原子热振动引起的势梯度;后者是接触边界过渡区两侧原子的非对称变形和自由度约束突变引起的非平衡边界势垒相耦合的结果.本文对研究公度接触下刚度梯度支撑的纳米器件的相对运动规律有指导意义.     

用MEI方法研究脉冲线源辐射问题

 脉冲线电流源的辐射问题是研究高功率微波辐射、传播和散射问题的基础。用时域有限差分方法结合时域MEI吸收边界条件来对该问题进行求解，通过与不同种类边界条件配合得出的数值解的比较可以证明，利用时域MEI方法的一阶吸收边界条件对线源辐射问题进行处理时，可以使截断边界离源更近，从而减少了计算量，并达到提高计算精度的目的。     

铁冲击相变的分子动力学研究

用分子动力学方法模拟了单晶铁(Fe)在一定初始温度下冲击相变(α相→ε相)的微观过程，结果显示温度会导致冲击相变压力阈值降低.基于此微观过程，对加卸载波系的传播规律进行了相应计算和分析，结果表明在卸载过程中逆相变波(ε相→α相)相对于波前以当地纵波声速传播，而相对波后以亚声速传播，这可由卸载压力-密度曲线给出相应解释；计算了不同初态的卸载压力-密度状态曲线，并给出了逆相变带的分布，其分布规律显示了卸载过程逆相变的滞后现象. 关键词： 分子动力学 多体势 冲击波 相变     

Vibration response of stepped FGM beams with elastically end constraints using differential transformation method

In this paper, free vibration response of stepped beams made from functionally graded materials (FGMs) is investigated. The beams are supported by various types of elastically end constraints. The differential transformation method (DTM) is employed to solve the governing differential equations of such beams in order to obtain natural frequencies and mode shapes. The power law distribution is used and modified to describe material compositions across the thickness of the beams made of FGMs. Two main types of the stepped FGM beams in which their material compositions can be described by using the modified power law distribution are selected to investigate their vibration behaviour. The significant parametric studies such as step ratio, step location, boundary conditions, spring constants and material volume fraction are taken into investigation.     

利用Taylor展开法研究Lamb波在功能梯度材料中的传播特性

超声技术可用于对功能梯度材料(FGMs)的性质进行评估. 由于FGMs性质的非均匀性,采用分布函数来描述FGMs弹性常数和密度沿厚度方向的变化趋势,并提出利用Taylor展开的方法来解决分布函数为任意函数时的FGMs中Lamb波的传播问题. 利用本征函数展开法得到了铁基氧化铝FGMs中Lamb波的相速度色散曲线,讨论了材料性质分布对铁基氧化铝FGMs中Lamb波传播特性的影响. 为FGMs性质(沿板厚方向变化)的反演提供了理论依据. 关键词： 功能梯度材料 Lamb波 Legendre多项式 分布函数     

Modeling of thermomechanical fracture of functionally graded materials with respect to multiple crack interaction

Different aspects of thermomechanical fracture of functionally graded materials (FGMs) are considered. Among them are the crack interaction problems in a functionally graded coating on a homogeneous substrate (FGM/H). The interaction between systems of edge cracks is investigated, as well as, how this mutual interaction influences the fracture process and the formation of crack patterns. The problem is formulated with respect to singular integral equations which are referred to the boundary equation methods. The FGM properties are modeled by exponential functions. The main fracture characteristics are calculated, namely, the stress intensity factors, the angles of deviation of the cracks from their initial propagation direction and the critical stresses when the crack starts to propagate. The last two characteristics are calculated using an appropriate fracture criterion. The problem contains different parameters, such as the geometry (location and orientation of cracks, their lengths, and the width of the FGM layer) and material parameters, i.e. the inhomogeneity parameters of elastic and thermal coefficients of the functionally graded material. The influence of these parameters on the thermo-mechanical fracture of FGM/H is investigated. As examples the following real material combinations are discussed: TiC/SiC, Al₂O₃/MoSi₂, MoSi₂/SiC, ZrO₂/nickel and ZrO₂/steel.     

FGMs稳态热传导分析的重心Lagrange插值配点法

提出一种求解二维功能梯度材料（FGMs）稳态热传导问题的重心Lagrange插值配点法.基于Chebyshev节点构造二维重心Lagrange插值函数及其偏导数,然后基于配点法将其直接代入FGMs热传导问题的控制方程和边界条件,得到系统离散方程.重心Lagrange插值配点法是一种真正的无网格方法,很好地融合了重心Lagrange插值和配点格式的优势,具有高效、稳定、高精度和易于数值实现的优点.采用重心Lagrange插值配点法分别对指数型、二次型和三角型FGMs热传导问题进行数值模拟.结果表明：该方法具有较高的计算效率和计算精度,对材料梯度参数的变化不敏感.可以进一步拓展到FGMs瞬态问题和FGMs的热力耦合分析.     

FGM with REDx: chemically reactive dimensionality extension

We propose a new approach to improve the accuracy of flamelet-generated manifolds (FGMs) method by extending the manifolds with additional chemically reactive degrees of freedom. Following the ideas of intrinsic low-dimensional manifold, the dimensionality of the FGM is increased by performing a local time-scale analysis of the chemical source term. A few slow characteristic directions of the reaction kinetics are used to extend the FGM, while the remaining reaction groups, characterised by fast time-scales, are assumed in steady state. The introduced method for FGM REactive Dimensionality extension is abbreviated as FGM-REDx. It is tested in one-dimensional simulations reproducing an expansion of burnt gases in an aero-engine stator. This process is characterised by a rapid change of enthalpy and pressure, altering, among others, the chemistry of pollutants CO and NO. The primary focus was on the assessment of the FGM's capability to predict the pollutants emissions. The rates of physical/thermodynamic perturbations turned out to be severe enough for the chemical species composition to go off the flamelet. The FGM extended with one additional chemically reactive dimension has been generated and successfully applied to the test cases, yielding a high accuracy gain over the standard FGM.     

TRANSIENT RESPONSES IN A FUNCTIONALLY GRADED CYLINDRICAL SHELL TO A POINT LOAD

A numerical method is proposed for analyzing transient waves in cylindrical shells of a functionally graded material (FGM) excited by impact point loads. In the present method, the FGM shell is divided into layer elements with three nodal lines along the wall thickness. The material property within each element is assumed to vary linearly in the thickness direction, which represents the spatial variation of material property of FGM. This can further reduce the number of elements to obtain more accurate results effectively. The Hamilton principle is used to develop approximate dynamic equilibrium equations. The displacement response is determined by employing the Fourier transformation and the modal analysis. As examples, the displacement responses of FGM shells excited by point loads are calculated, and the characteristics of waves in FGM shells are discussed. The computations have shown the efficiency of the present method.     

方腔内相变材料固液相变传热研究

基于相变材料(PCM,phase change material)的相变储能设备具有储能密度高的特点。本文建立了基于相变储能元件伪焓模型的固液相变格子Boltzmann模型,研究了内部管道位置、方腔倾斜角度对PCM融化过程的影响规律。结果表明,在内管道靠近方腔上部时,由于上部界面(固液相变界面或上壁面)对自然对流阻碍作用,使PCM的融化速率减慢。但是,在此时使方腔发生倾斜,会改变管道热流体到上部界面的距离,强化PCM的热质传递过程,使融化加快。     

Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core

In this paper, the Ritz minimum energy method, based on the use of the Principle of Virtual Displacements (PVD), is combined with refined Equivalent Single Layer (ESL) and Zig Zag (ZZ) shell models hierarchically generated by exploiting the use of Carrera's Unified Formulation (CUF), in order to engender the Hierarchical Trigonometric Ritz Formulation (HTRF). The HTRF is then employed to carry out the free vibration analysis of doubly curved shallow and deep functionally graded material (FGM) shells. The PVD is further used in conjunction with the Gauss theorem to derive the governing differential equations and related natural boundary conditions. Donnell–Mushtari's shallow shell-type equations are given as a particular case. Doubly curved FGM shells and doubly curved sandwich shells made up of isotropic face sheets and FGM core are investigated. The proposed shell models are widely assessed by comparison with the literature results. Two benchmarks are provided and the effects of significant parameters such as stacking sequence, boundary conditions, length-to-thickness ratio, radius-to-length ratio and volume fraction index on the circular frequency parameters and modal displacements are discussed.     

A computational approach towards modelling dislocation transmission across phase boundaries

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with its specific material properties, separated by a fully coherent and non-damaging phase boundary. Each phase is modelled as a continuum enriched with a Peierls–Nabarro (PN) dislocation region, confining dislocation motion to a discrete plane, the glide plane. In this paper, a single glide plane perpendicular to and continuous across the phase boundary is considered. Along the glide plane bulk induced shear tractions are balanced by glide plane shear tractions based on the classical PN model. The model's ability to capture dislocation obstruction at phase boundaries, dislocation pile-ups and dislocation transmission is studied. Results show that the phase contrast in material properties (e.g. elastic stiffness, glide plane properties) alone creates a barrier to the motion of dislocations from a soft to a hard phase. The proposed model accounts for the interplay between dislocations, external boundaries and phase boundary and thus represents a suitable tool for studying edge dislocation–phase boundary interaction in two-phase microstructures.     

Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition

Linear thermal buckling and free vibration analysis are presented for functionally graded cylindrical shells with clamped-clamped boundary condition based on temperature-dependent material properties. The material properties of functionally graded materials (FGM) shell are assumed to vary smoothly and continuously across the thickness. With high-temperature specified on the inner surface of the FGM shell and outer surface at ambient temperature, 1D heat conduction equation along the thickness of the shell is applied to determine the temperature distribution; thereby, the material properties based on temperature distribution are made available for thermal buckling and free vibration analysis. First-order shear deformation theory along with Fourier series expansion of the displacement variables in the circumferential direction are used to model the FGM shell. Numerical studies involved the understanding of the influence of the power-law index, r/h and l/r ratios on the critical buckling temperature. Free vibration studies of FGM shells under elevated temperature show that the fall in natural frequency is very drastic for the mode corresponding to the lowest natural frequency when compared to the lowest buckling temperature mode.