固体非傅立叶温度场的时域间断Galerkin有限元法

运用时域间断Galerkin有限元法[1],对高频非傅立叶热波动问题[2-3]进行分析。其主要特点是:取温度及温度的时间导数为基本未知量,对其分别进行3次Hermite插值和线性插值。在保证节点温度自动保持连续的基础上,温度的时间导数在离散时域存在间断。数值结果表明所提出的方法能够滤掉虚假的数值震荡,能够良好地模拟固体中的非傅立叶热波动行为。     

热冲击作用下层合皮肤组织热传导过程数值模拟

在急剧温度变化等强间断温度冲击作用下的生物层合组织非傅里叶热传导分析中,经典时域连续有限元方法(如Newmark等方法)会在波阵面以后的和层合组织界面附近的区域表现出强烈的数值振荡。这类数值振荡会影响问题求解精度,并带来较大不确定性。针对这类现象,本文发展了改进时域间断Galerkin有限元方法,进一步开展了相关问题的数值模拟。其控制方程的基本未知数(温度)及其时间导数在指定时间间隔内假设存在间断且独立插值。在有限元离散列式中引入比例刚度阵人工阻尼,以成功消除波前位置的虚假数值振荡行为。通过算例对比分析,相比Newmark方法和传统间断Galerkin方法,所提出的改进时域间断Galerkin有限元方法较好消除了波前、波后以及组织界面处的数值振荡,有效捕捉了波阵面的间断行为,提高了计算的精度。     

非傅里叶热弹性的时域间断迦辽金有限元方法

基于Lord-Shulman非傅里叶热弹性模型,提出了采用修正的时域间断迦辽金有限元方法(time discontinuousGalerkin finite element method, DGFEM)求解方法. DGFEM对温度场、位移场基本未知向量及其时间导数向量在时域中分别插值;在最终的求解公式中,引入了人工阻尼. 数值结果显示所发展的DGFEM 较好地捕捉了波的间断并消除了热冲击作用下虚假的数值振荡,能够良好地模拟热弹性问题并具有较高的精度.     

基于非傅立叶热传导半无限大体热冲击力学分析

在微观尺度下,陶瓷的热传导机理与宏观尺度下的热传导机理有较大的差异,由此产生的热应力与宏观尺度下的不同,本文针对热冲击条件下的半无限大体,基于非傅立叶热传导模型分析了温度场、应力场和单边裂纹的应力强度因子,并与基于傅立叶热传导模型分析的结果进行了比较.研究表明在半无限大体表面附近或裂纹较短时,基于非傅立叶热传导模型得到的应力最大值或应力强度因子最大值比基于傅立叶热传导模型得到的结果大,而在半无限大体内部或裂纹较长时,结果相反.     

短脉冲激光加热分数阶导热及其热应力研究

短脉冲激光加热引起材料内部复杂的传热过程及热变形,现有的以Fourier定律或Cattaneo-Vernotte松弛方程结合弹性理论为框架建立起来热应力理论在刻画其热物理过程存在严重缺陷. 本文基于分数阶微积分理论, 以半空间为研究对象, 建立了分数阶Cattaneo热传导方程和相应的热应力方程, 给出了问题的初始条件和边界条件, 采用拉普拉斯变换方法, 给出了非高斯时间分布激光热源辐射下温度场和热应力场的解析解, 研究了短脉冲激光加热的温度场及热应力场的热物理行为. 数值计算中, 首先对理论解进行数值验证, 然后取分数阶变量$p=0.5$研究温度场和热应力场的变化特点及激光参数对温度和热应力的影响,最后数值计算分数阶参数对温度和热应力场的影响. 计算结果表明, 分数阶Cattaneo传热方程和热应力方程描述的温度和热应力任然具有波动特性,与经典的Fourier传热模型和标准的Cattaneo传热模型相比, 分数阶阶次越大, 热波波速越小, 热波波动性越明显; 反之, 则热波波速越大, 热扩散性越强.激光加热和冷却的速度越快, 温度上升和下降的速度越快, 压应力和拉应力交替变化越快, 温度变化幅值越小, 热应力幅值影响不明显.      

改进时域间断Galerkin有限元方法在弹塑性波传播数值模拟中的应用

对于高频、强脉动荷载作用下的结构动力学波传播分析,对比于传统的时域算法,时域间断Galerkin方法能捕捉到波阵面的间断,有效得避免了由于间断引起的数值振荡。但时域间断方法却带来了波前面的虚假数值振荡。本文针对上述波前数值振荡的现象进行研究,通过引入人工阻尼的方法对时域间断Galerkin有限元方法进行进一步改进。数值结果表明,所发展的方法能够有效的滤掉强动荷载产生的波前数值振荡现象,同时降低了时域间断Galerkin方法的网格依赖性。     

结构层热扩散系数对超薄涂层热力性能的影响

将非傅立叶热传导模型(用于超薄热涂层)与傅立叶热传导模型(用于结构层)相结合 求解温度场,运用有限元法求解热涂层热应力和裂纹驱动力,并分析结构层材料热扩散系数 的变化对热涂层的热力学性能(温度场、应力场和断裂性能)的影响. 研究表明,结构层材 料性能变化对温度场的影响主要表现在热冲击后期,对热应力和裂纹尖端驱动力后期的变化 也有一定的影响.     

基于纯声子辐射模型的超薄绝缘夹层结构

在复合材料结构中起绝热、增韧作用的绝缘夹层,其加工厚度现在已达到纳米量级,原有的傅立叶热传导定律已无法描述其热能的传递行为,需从分子动力学、量子力学从发,针对不同研究对象建立相应的热传导模型．针对超薄绝缘夹层结构,将纯声子辐射模型和傅立叶热传导模型相结合数值求解热冲击条件下的温度场,并作为热载荷,用于求解结构上表面应力和夹层裂纹驱动力,其结果与只采用傅立叶热传导模型计算的结果相比较, 分析了物理参数对温度、应力和裂纹驱动力的影响．结果表明：与只采用傅立叶热传导模型计算的结果相比,按EPRT计算的热传导明显变慢,其表面剥离应力偏大,而夹层裂纹驱动力偏小．同时随着松弛时间增大和声子速度的降低,热传导减缓,表面横向剥离应力增大,超薄绝缘夹层内裂纹尖端驱动力减小．     

球对称瞬态非傅里叶热传导分析

基于非傅里叶热传导理论,分别从频域和时域分析了球对称瞬态热传导问题。频域求解时,采用Laplace变换结合状态空间法以及层合近似模型,过程清晰统一。时域求解时采用了分离变量法和叠加法,能减小数值反变换所带来的误差。数值算例比较了两种方法的计算效果,结果表明时域法可清晰捕捉热波传播过程中的前沿波阵面。     

岩土介质非稳态热固结耦合问题的热源函数法

考虑耦合效应的饱和土体热固结问题控制方程,利用Fourier变换、Laplace变换给出其在变换域上的解,将初始温度场分布视为虚拟的热源或者将热源等价为特定的初始温度分布,利用热源函数法给出瞬时线热源非稳态温度场、应力场和位移场的解析求解方法,通过在时间域和空间域上进行积分,给出有初始温度场分布以及有分布内热源存在且热源强度随时间变化条件下的热固结问题计算方法。对一无限大物体内存在有平面矩形域热源情况下周围介质的温度、孔隙水压力以及位移等的变化特征进行分析。研究表明,热源函数法可有效地求解一系列复杂情况下的热固结问题。     

THERMAL SHOCK OF SEMI-INFINITE BODY WITH MULTI-PULSED INTENSE LASER RADIATION

In order to investigate the thermal shock and the heat conduction property of a target under multi-pulsed laser radiation, analytic expressions of both temperature and thermal stress fields in the target are deduced on the basis of the non-Fourier conduction law and the thermo-elastic theory. Taking a stainless steel target as an example, we can solve the analytic expressions under appropriate boundary conditions by using the finite difference method and MATLAB software, and then reveal the evolution law of both surplus temperaturt, and thermal stress in the target. The results indicate that the temperature curves in the target irradiated by a multi-pulsed laser take on a delayed character in different sections away from the boundary, which is only affected by its relaxation time. The front of the stress wave is very steep in the non-Fourier numerical solutions, which presents an obvious thermal shock, so it is necessary to consider the non-Fourier effect of semi-infinite body under the high energy laser radiation.     

Non-Fourier heat conduction in a finite hollow cylinder with periodic surface heat flux

Analytical solution of the non-Fourier axisymmetric temperature field within a finite hollow cylinder exposed to a periodic boundary heat flux is investigated. The problem studied considering the Cattaneo–Vernotte (CV) constitutive heat flux relation. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used for solving the problem with time-independent boundary conditions, and the Duhamel integral is used for applying the time dependency. The solution is applied for the special cases of harmonic uniform heat flux and an exponentially pulsed heat flux with Gaussian distribution in outer surface for modeling a laser pulse, and their respective non-Fourier thermal behavior is studied.     

Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time

A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate. The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length. The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic tim...     

Transient hyperbolic heat conduction in thick-walled FGM cylinders and spheres with exponentially-varying properties

This paper focuses on non-Fourier hyperbolic heat conduction analysis for heterogeneous hollow cylinders and spheres made of functionally graded material (FGM). All the material properties vary exponentially across the thickness, except for the thermal relaxation parameter which is taken to be constant. The cylinder and sphere are considered to be cylindrically and spherically symmetric, respectively, leading to one-dimensional heat conduction problems. The problems are solved analytically in the Laplace domain, and the results obtained are transformed to the real-time space using the modified Durbin’s numerical inversion method. The transient responses of temperature and heat flux are investigated for different inhomogeneity parameters and relative temperature change values. The comparisons of temperature distribution and heat flux between various time and material properties are presented in the form of graphs.     

非傅立叶导热的最新研究进展

对迄今为止有关非傅立叶导热的研究成果进行了全面的综述,其中包括作者在该领域的最新研究进展:空心球体介质双曲线非傅立叶导热模型的分析求解,室温条件下多孔材料内非傅立叶导热的实验结果及数值模拟,非傅立叶导热的“瞬时薄层”模型,非傅立叶导热和非费克质量传递的耦合分析,非傅立叶导热的分子动力学模拟等．文中还对下一步的研究工作进行了展望.      

Axisymmetric non-Fourier temperature field in a hollow sphere

The non-Fourier axisymmetric (2+1)-dimensional temperature field within a hollow sphere is analytically investigated by the solution of the well-known Cattaneo–Vernotte hyperbolic heat conduction equation. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The method of solution is the standard separation of variables method. General linear time-independent boundary conditions are considered. Ultimately, the presented solution is applied to a (1+1)—as well as a (2+1)—dimensional problem, and their respective non-Fourier thermal behavior is studied. The present solution can be reduced to special cases of interest by choosing appropriate boundary conditions parameters. Dedicated to Prof. Gholamali Atefi, with appreciation and admiration on the occasion of his 65th birthday.     

Analysis of non-Fourier heat conduction in a solid sphere under arbitrary surface temperature change

In this paper, the non-Fourier heat conduction in a solid sphere under arbitrary surface thermal disturbances is solved analytically. Four cases including sudden, simple harmonic periodic, triangular and pulse surface temperature changes are investigated step-by-step. The analytical solutions are obtained using the separation of variables method and Duhamel’s principle along with the Fourier series representation of an arbitrary periodic function and the Fourier integral representation of an arbitrary non-periodic function. Using these analytical solutions, the temperature profiles of the solid sphere are analyzed, and the differences in the temperature response between the “hyperbolic” and “parabolic” are discussed. These solutions can be applicable to all kinds of non-Fourier heat conduction analyses for arbitrary boundary conditions occurred in technology. And as application examples, particular attention is devoted to the cases of triangular surface temperature change and pulse surface temperature change. The examples presented in this paper can be used as benchmark problems for future numerical method validations.