基于增量微分求积单元法的功能梯度材料夹层板非线性瞬态传热分析  

Nonlinear transient heat transfer analysis of functionally graded material sandwich slabs by incremental differential quadrature element method

作　　者：张忠 许家婧 曹小建 王艳超 朱军 姚潞 ZHANG Zhong;XU Jiajing;CAO Xiaojian;WANG Yanchao;ZHU Jun;YAO Lu(School of Transportation and Civil Engineering,Nantong University,Nantong 226019,China;BOZHON Precision Industry Technology Co.,Ltd.,Suzhou 215200,China;School of Mechanics and Civil Engineering,China University of Mining and Technology,Xuzhou 221116,China;Nantong Taisheng Blue Island Offshore Co.,Ltd.,Qidong 226259,China)

机构地区：[1]南通大学交通与土木工程学院,南通226019 [2]博众精工科技股份有限公司,苏州215200 [3]中国矿业大学力学与土木工程学院,徐州221116 [4]南通泰胜蓝岛海洋工程有限公司,启东226259

出　　处：《复合材料学报》2024年第11期6284-6296,共13页Acta Materiae Compositae Sinica

基　　金：国家自然科学基金(11802145,52308260);江苏省高等学校基础科学(自然科学)研究项目(23KJB560021);南通市科技项目(JC12022058);南通市社会民生科技计划面上研究项目(MS22022103)。

摘　　要：作为首次尝试,采用增量微分求积单元法(IDQEM)开展了功能梯度材料(FGM)夹层板的一维非线性瞬态传热分析。夹层板组分材料的热工参数随空间位置变化,且具有温度依赖性。基于IDQEM,沿层界面将夹层板划分为3个空间子域,同时将整个受热过程划分为若干时间子域。采用微分求积技术对任一时间子域内的控制方程、初始条件、界面条件及边界条件进行离散处理。由于所获得的离散方程建立在不同区域的节点上,因此对方程进行修改并将其表示为矩阵形式,以便它们可以建立在同一区域中。采用Kronecker积将联立的矩阵方程转化为一系列代数方程组,并采用Newton-Raphson迭代法近似求解,即可获得单个时间子域内的温度解。由于每个时间子域的初始条件可由上一个时间子域最终时刻的温度分布决定,因此从第一个时间子域逐渐递推到最后一个子域,即可获得整个受热过程的温度分布。数值算例验证了本方法的快速收敛性,与已有文献的解析和数值结果的对比验证了本方法的正确性。最后,讨论了热工参数温度依赖性、体积分数指数及热边界条件对FGM夹层板温度分布的影响。As a first attempt,the incremental differential quadrature element method(IDQEM)was adopted to perform the one-dimensional nonlinear transient heat transfer analysis of functionally graded material(FGM)sandwich slabs.The thermophysical properties of the slab were considered to be position-and temperaturedependent.To implement the IDQEM,the sandwich slab was divided into three spatial sub-domains along the layer interfaces,and the entire heating process was also divided into several temporal sub-domains.For each temporal sub-domain,the governing equations as well as the initial condition,interfacial condition,and boundary condition were discretized by the differential quadrature technique.Because the obtained discrete equations were built in different regions of grid points,a modification of the equations was proposed which were then expressed in the matrix forms so that they can be built in the same regions.Using the Kronecker product,the simultaneous matrix equations were transformed into a set of nonlinear algebraic equations,which were then solved by the Newton-Raphson iteration method to obtain the temperature profile for each temporal sub-domain.Because the initial condition of each temporal sub-domain was defined by the temperature results at the end of the previous sub-domain,the temperature profile of the slab during the entire heating process can be obtained by repeating the calculation procedure from the first temporal sub-domain to the last one.Numerical examples were carried out to verify the fast convergence of the present method.The correctness of the present method was verified through comparison with the analytical and numerical results reported in previous works.The effects of temperaturedependent thermophysical properties,volume fraction index,and thermal boundary on the temperature profile of the slab were discussed.

关 键 词：功能梯度材料夹层板 温度依赖性 瞬态传热 增量微分求积单元法 Newton-Raphson迭代法 

分 类 号：TK124[动力工程及工程热物理—工程热物理] TB33[动力工程及工程热物理—热能工程]