近场动力学中内核参数对非均匀材料热传导数值解的影响研究

Effects of Kernel Parameters of Peridynamic Theory on Heat Conduction Numerical Solution for Non-Homogeneous Material

以近场动力学(peridynamic,简称PD)理论为基础,推导了非均匀材料的热传导方程,给出了PD非均匀物性值的计算方法,数值离散过程和数值计算控制方程。编写了FORTRAN程序,并把计算结果和解析法进行了对比分析,验证了PD法的正确性。重点研究了PD方法中内核参数(等效热导率比例系数、表面修正因子以及形状因子)对非均匀材料热传导数值解的影响。结果表明:等效热导率比例系数、表面修正因子对温度响应影响较大,形状因子的影响基本可以忽略。考虑表面效应且等效热导率取为近场范围内2个材料点上的平均值时,非均匀材料的温度响应与解析解最为接近。

Based on peridynamic theory （PD）, heat conduction PD formulas for non-homogeneous material have been presented and numerical method to calculate non-homogeneous material properties for PD is given. Discretiza- tion process of PD heat conduction numerical formula is illustrated and the numerical equations are presented. A FORTRAN program is coded to implement PD calculations. Accuracy of this PD program is validated by results of analytical method. Effects of kernel parameters （equivalent thermal conductivity proportion factor, surface correction factor and shape factor） on PD heat conduction numerical results for non-homogeneous material are pri- marily studied. It is shown that equivalent thermal conductivity proportion factor and surface correction factor can af- fect thermal response, but effect of shape factor can be negligible. When surface correction factor is taken into con- sider and the equivalent thermal conductivity is specified as average of two material points within a horizon, solution of temperature response of non-homogeneous material based on PD theory approaches analytical solution.