激光辐照引起非Fourier热传导问题的理论分析与计算

发布时间：2018-01-17 18:01

本文关键词：激光辐照引起非Fourier热传导问题的理论分析与计算　出处：《北京科技大学》2017年博士论文　论文类型：学位论文

【摘要】：激光作为一种特殊的定向高能束,己被广泛应用于很多工程领域,特别是在材料表面加工处理、生物医学外科等方面.探讨由激光辐照材料表面受热而引起的材料内部温度场的变化以及瞬态热应力问题已成为力学研究的一个重要课题.由于解析解要比数值解更为准确和有效地直接反映出控制变量与时空坐标以及材料、几何等参数之间的关系,如何求出问题的解析解一直以来是研究者所面临的挑战性问题.然而,至今为止多限于在变换域上给出的解析解或者是一维空间问题的解析解,而对高维空间问题在原时空域上的解析解所见文献研究甚少.本文针对不同传热介质,建立了考虑热波效应的空间轴对称非Fourier热传导的数学模型,采用关于时空变量的积分变换方法,特别是以求出相关问题的逆Laplace变换解析式为突破点,获得了所论问题在原时空域内的解析解,并且分析了均匀和非均匀材料的温度场分布、估算了生物(皮肤)介质中的热损伤以及热冲击下考虑惯性力效应的瞬态热应力等问题,主要研究工作和成果如下：(1)研究了激光辐照在半无限大固体材料表面的问题,建立了突加温度和瞬时脉冲热流两种不同边界条件下的非Fourier热传导模型,利用Laplace-Hankel变换及其逆变换,关键的突破是构造出了相应的逆Laplace变换的解析表达式,从而求得了问题在原时空域上的单积分形式解析解；其解可准确算出热波前的位置,并清晰展现出材料内部的温度场.还用隐格式差分方法数值解验证了本文解析求解的正确性.(2)针对局部圆形区域的激光辐照半无限大固体表面的非Fourier热传导问题,利用积分变换法求得问题在原时空域的精确解析解,并比较分析了温度分布的云图、等温-流线图及随时间的演化规律.(3)分析了两种不同加热情形下激光辐照皮肤表面时非Fourier热传导问题.考虑了血流灌注速度的影响,利用积分变换的方法,技巧性的构造了相应的逆Laplace变换的解析表达式,从而求出了问题的解析解.进而估算了皮肤热损伤区域并与经典热传导理论造成的皮肤热损伤进行比较.(4)针对功能梯度材料的非均质性,研究了指数型功能梯度材料表面受到激光辐照的非Fourier热传导问题.成功地求出了变系数的控制方程的初-边值问题在原时空域上的解析解,给出了温度随时间演化的温度场云图,并讨论了非均匀参数对热波传播的影响.(5)研究了热弹性材料表面受到激光辐照热冲击时,非Fourier热传导下材料内部的瞬态热应力场的分布问题.考虑了动态惯性效应,分别采用应力解法和位移解法得到了均质及功能梯度材料内部的瞬态热应力解析解,并讨论了瞬态热应力随时间变化的规律以及材料非均匀性的影响.
[Abstract]:As a kind of special laser directed energy beam has been widely used in many engineering fields, especially in the processing of surface treatment materials, biomedical surgery. To investigate the changes of the heated surface laser irradiation caused by the material internal temperature field and transient thermal stress problem has become an important topic of mechanics. The analytical solution is more accurate than the numerical solution effectively and directly reflect the control variable and the space-time coordinates as well as materials, the relationship between geometric parameters, how to obtain the analytical solution of the problem has been a challenging problem faced by researchers. However, so far limited to give the analytical solutions in transform space or is the analytical solution of one dimensional space, and the high dimensional space to resolve the problem in the original space domain solution by literature research is little. According to the heat transfer medium is established considering The mathematical model of axial symmetric and non Fourier heat conduction of the heat wave effect of the space, by using the integral transform method on the temporal variables, especially in order to calculate the inverse Laplace transform formula related problems as the breakthrough point, and obtain the analytical theory of problem in the original time domain solution, and analyzes the temperature field distribution in homogeneous and heterogeneous materials the estimated biological (skin) problem of transient thermal inertia effect stress considering medium heat injury and heat shock, the main research work and results are as follows: (1) study on the laser irradiation in a semi infinite solid material surface, a non Fourier heat conduction model of sudden temperature and the instantaneous heat pulse under two different boundary conditions, using the Laplace-Hankel transform and its inverse transform, the key breakthrough is to construct the analytical expression of inverse Laplace transform to obtain the corresponding problems in the original. Single integral form of analytical space-time domain solution; the solution can accurately calculate the wave front position, and shows the temperature field inside the material. Using implicit difference method of numerical solutions are verified analytically. (2) according to the local laser irradiation circular area of semi infinite non thermal Fourier the large conduction solid surfaces, by using the integral transform method to obtain accurate analytical problems in the original time domain solution, and analyzed the temperature distribution nephogram, isothermal streamlines and evolution with time. (3) analysis of the Fourier heat conduction problem of non laser irradiation on skin surface of two different heating conditions. Considering the effect of blood perfusion rate, using the method of integral transform, construction techniques of analytical expression of inverse Laplace transform accordingly, so as to obtain analytic solutions of the problem. We have estimated the skin thermal damage zone and the The skin damage caused by thermal classical heat conduction theory are compared. (4) according to the heterogeneity of functionally graded materials, studied the surface index of functionally graded materials by non Fourier heat conduction problem of laser irradiation successfully. The analytic problem in the original time-space domain boundary value equation with variable coefficients of the initial control - the temperature field nephogram and the temperature evolution over time, and discussed the effect of non-uniform parameters on thermal wave propagation. (5) studied the thermal elastic material surface irradiated by the laser thermal shock, the transient thermal stress field distribution inside the material non Fourier heat conduction should be considered. The dynamic inertia effect. Using the stress method and the displacement method to get the transient heat inside homogeneous and functionally graded materials stress analytic solution, and discussed the transient thermal stress changing with time and the effect of material inhomogeneity.

【学位授予单位】：北京科技大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O551.3;TN249

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