功能梯度材料热传导问题的近场动力学模型

当材料中存在不连续性缺陷的时候，传统的基于连续介质理论的方法在研究热传导问题时存在诸多不便．我们基于近场动力学方法(Peridynamics)建立了功能梯度材料的热传导模型，并且研究了在温度荷载作用下功能梯度材料的温度场的变化表现．该文概述了PD方法应用于热传导问题时的详细理论基础,描述了其建模思路以及计算体系,给出了使用PD方法模拟结构承受温度荷载时的计算格式，讨论了不同梯度形式对功能梯度材料内热传导的影响．算例结果表明：通过PD模型所得到的温度场与解析解吻合较好，证明了PD方法在分析功能梯度材料热传导行为等问题时的可行性．

Transient Heat Conduction Model for Functionally Graded Materials Based on Peridynamics

In bodies with discontinuities, such as crack, the classical methods based on continuum theory for heat transfer are not well applicable. We introduce a Peridynamic model for functionally graded materials and study their heat transfer behavior. This paper provides an overview of the theoretical basis, modeling ideas and modeling system of the Peridynamic method applied to heat conduction problems. The structure under the impact of temperature is simulated by Peridynamic method. The effect of the gradient form on the thermal behavior of functionally graded materials is also studied. The numerical results show that the temperature field obtained by the PD model is in good agreement with the analytical results and has a good convergence. It is proved that the PD method is feasible in analyzing the thermal conduction problems of functionally graded materials.