基于时域间断有限元方法的生物组织非傅立叶热行为数值分析

在热传导分析中,当热流与温度梯度存在时间延迟时,需采用非傅立叶热传导模型进行分析。生物组织具有较强的热松弛时间系数,承受激光、微波及烧烫等作用时,其呈现出较强的非傅立叶行为。本文对脉冲热源作用下生物组织的非傅立叶热传导进行研究,针对强脉冲引起的温度场在空间域的高梯度变化、波阵面的间断行为以及通用传统时域数值方法会带来虚假数值振荡的特点,提出采用所发展的时域间断Galerkin有限元法（DG-FEM ）进行求解计算。对多种脉冲热源作用下的非傅立叶热传导过程进行数值模拟,通过考量强脉冲作用下温度场分布和热致生物组织损伤行为的影响,表明了本文所发展的DGFEM 能够有效、准确地描述温度场空间分布和热传导过程以及非傅立叶行为下的生物热损伤更为明显,在生物组织热行为分析中应该受到重视。     

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.     

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。     

土体颗粒物流动物质点法模拟的弹塑性和非牛顿流体本构模型比较研究

土体颗粒物流动是一种典型的大变形破坏,具有非牛顿流体的流动特征。准确模拟土体颗粒物的流动及冲击过程,对滑坡和泥石流等地质灾害的防治具有重要意义。物质点法是一种无网格粒子类方法,已在各类大变形问题中得到了广泛应用。以往土体颗粒物流动的模拟,通常采用弹塑性本构模型,但缺乏对非牛顿本构模型的模拟分析。本文引入非牛顿本构模型的模拟分析,旨在为土体颗粒物流动模拟提供一种新的方法与思路。非牛顿本构模型的模拟分析是将非牛顿广义Cross模型引入三维物质点法,通过人工阻尼力模拟颗粒间的摩擦力,对土体颗粒物的坍塌、沿斜面滑动以及冲击障碍物等问题进行了动态模拟,研究了其运动全过程,并与弹塑性本构模型的模拟结果进行了对比验证。结果表明,基于非牛顿流体本构模型的物质点法可以较好地模拟土体颗粒物加速、减速到再次稳定的流动全过程及其对障碍物的冲击效应。     

复杂荷载下疲劳的非比例硬化数值模拟

许多统计资料表明,在所有的力学破坏中,由交变载荷作用引起的疲劳断裂破坏,占50%～90%.复杂荷载下(多数为非比例荷载)引起的疲劳响应是当前疲劳实验、理论和数值分析所关注的问题之一,也相继出现了很多描述非比例硬化的实验、理论和模型.本文应用Jiang-Sehitoglu疲劳塑性模型,引用了一系列材料参数,考虑屈服面大小的变化,在非比例加载条件下考虑到材料的非比例硬化,对具有典型非比例硬化材料-304不锈钢的疲劳本构进行了数值模拟,得到的结果和试验结果比较,可以看出具有很好的吻合性.     

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.     

基于相位差谱的空间相关非平稳地震动场的模拟

地震动的非平稳特性主要是由其相位差谱决定的,相位差谱与相位导数之间存在线性倍数关系。根据相位导数的显式计算公式,从能量的角度解释了相位导数的均值大致决定了时程峰值的发生时刻,相位导数的方差决定了强震段的持续时间。在相关地震动场模拟方法中,首次将相位差谱的统计模型引入空间相关非平稳地震动场的模拟方法之中,利用快速傅立叶变换技术生成地震动场。表示地震动随机特性的随机相位谱利用相位差谱的统计模型生成,生成的地震动场不仅具有空间相关性,而且在时域、频域内均具有非平稳特性。     

炸药导热系数的非补偿微热量热法测定

建立了非补偿微热量热法测定圆筒体炸药试样导热系数的实验装置和方法,测定了聚四氟乙烯、有机玻璃、高密聚乙烯三种标准物质及ＪＨ－９１０５、ＪＯＢ－９００３、ＪＯ－９１５９、ＪＯ－９１８５、ＪＯＢ－９００６、ＪＢ－９００１等六种塑料粘结炸药在２９８．２Ｋ下的导热系数,对非补偿测定法与补偿测定法进行了对比。结果表明：非补偿法与补偿法测试准确度相当,但测试时间大大缩短。     

涡轮增压器离心压气机非稳态工况流场分析

利用商用 CFD 软件对一小型车用离心压气机建立了数值模型,并将模拟结果与实验结果进行了对比:稳态的设计转速最高压比相差不超过 0.5%,最高效率相差不超过1.5%;非稳态模拟和实验得到的失速频率均为 3000Hz,模拟结果真实可信.主要利用设计转速下小流量工况时的非稳态数值模拟结果对喘振发生前离心压气机各部件的非稳态流动特点进行了详尽阐述.研究结果表明:小流量工况时离心压气机各部件均出现非稳态流动现象,这种非稳态效应在各部件中表现出不同的特点,且随着流量的减小这种非稳态效应会不断加剧.     

加热炉内板坯粘塑性下桡变形的研究

在加热妒内，由于高温及重力作用，板坯两端的悬臂将产生下桡变形。悬臂越长，下桡将越大，导致悬臂下桡部分与出口端墙相碰，影响出料而造成事故。本文对加热炉内板坯的下桡变形进行了分析计算。首先，建立了板坯的二维非稳态导热模型并用有限差分法计算了炉内板坯随时间的温度变化；然后建立了板坯悬臂粘塑性变形模型，用有限元法计算了高温条件下由重力引起的悬臂的下桡变形。由此理论模型计算出的板坯抽出温度与悬臂端下桡量与实测结果吻合良好，说明该理论模型及模型计算方法是正确的，可用于对装钢生产进行指导。     

非傅里叶热传导研究进展

傅里叶定律能够精确描述大多数的热传导问题,但对于超短脉冲激光加热等热作用的周期时间极短的超急速、超常规热传导等问题,非傅里叶效应将会显得至关重要．对非傅里叶热传导的实质、模型、模型的求解及应用与实验等几个方面的研究进展做了一个较详尽的概括与评述,并指出了今后需要着重研究的方向．      

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.     

Rational design of thermoelastic damping in microresonators with phase-lagging heat conduction law

The design of thermoelastic damping (TED) affected by the phase-lagging non-Fourier heat conduction effects becomes significant but challenging for enlarging the quality factor of widely-used microresonators operating in extreme situations, including ultra-high excitation frequency and ultra-low working temperature. However, there does not exist a rational method for designing the TED in the framework of non-Fourier heat conduction law. This work, therefore, proposes a design framework to achieve low thermoelastic dissipation of microresonators governed by the phase-lagging heat conduction law. The equation of motion and the heat conduction equation for phase-lagging TED microresonators are derived first, and then the non-Fourier TED design problem is proposed. A topology optimization-based rational design method is used to resolve the design problem. What is more, a two-dimensional (2D) plain-strain-based finite element method (FEM) is developed as a solver for the topology optimization process. Based on the suggested rational design technique, numerical instances with various phase lags are investigated. The results show that the proposed design method can remarkably reduce the dissipation of microresonators by tailoring their substructures.     

Multiple spatial and temporal scales method for numerical simulation of non-classical heat conduction problems: one dimensional case

A multiple spatial and temporal scales method is studied to simulate numerically the phenomenon of non-Fourier heat conduction in periodic heterogeneous materials. The model developed is based on the higher-order homogenization theory with multiple spatial and temporal scales in one dimensional case. The amplified spatial scale and the reduced temporal scale are introduced respectively to account for the fluctuations of non-Fourier heat conduction due to material heterogeneity and non-local effect of the homogenized solution. By separating the governing equations into various scales, the different orders of homogenized non-Fourier heat conduction equations are obtained. The reduced time dependence is thus eliminated and the fourth-order governing differential equations are derived. To avoid the necessity of C¹ continuous finite element implementation, a C⁰ continuous mixed finite element approximation scheme is put forward. Numerical results are shown to demonstrate the efficiency and validity of the proposed method.     

Axisymmetric non-fourier temperatures in cylindrically bounded domains

Heat conduction solutions are presented for the case where the material obeys a non-Fourier conduction law. In contrast to the Fourier law which predicts an infinite speed of heat propagation, the non-Fourier theory implies that the speed of thermal signals are finite. Axisymmetric problems for regions interior and exterior to a circular cylinder are investigated by using methods of Laplace transformation and asymptotic analysis. Comparisons of the temperature profiles are made with Fourier theory for the case of step function temperature boundary conditions.     

Experimental evidence about the controversy concerning Fourier or non-Fourier heat conduction in materials with a nonhomogeneous inner structure

Distinct non-Fourier behavior in terms of finite propagation velocity and a hyperbolic wave like character of heat conduction has been reported for certain materials in several studies published recently. However, there is some doubt concerning these findings. The objective of this paper is to present experimental evidence for a perfectly Fourier-like behavior of heat conduction in those materials with nonhomogeneous inner structure that have been under investigation in the other studies. This controversy needs to be settled in order to understand the physics of heat conduction in these materials.     

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.     

HEAT TRANSFER CHARACTERISTICS OF CONDUCTIVE MATERIAL UNDER INNER NON-UNIFORM ELECTROMAGNETIC FIELDS

Electronic transport properties can be influenced by the applied electromagnetic fields in conductive materials. The change of the electron distribution function evoked by outfields obeys the Boltzmann equation. In this paper, a general law of heat conduction considering the non-uniform electromagnetic effect is developed from the Boltzmann equation. An analysis of the equation leads to the result that the electric field gradient and the magnetic gradient in the conductive material are responsible for the influences of electromagnetic fields on the heat conduction process. A physical model is established and finite element numerical simulation reveals that heat conduction can be increased or delayed by the different directions of the electric field gradient, and the existence of the magnetic gradient always hinders heat conduction.