梯度复合材料热传导分析的梯度单元法

Graded element method for the heat conduction analysis of gradient composites

给出了一种适用于梯度复合材料热传导分析的梯度单元,采用细观力学方法描述材料变化的热物理属性,通过线性插值和高阶插值温度场分别给出了4节点和8节点梯度单元随空间位置变化的热传导刚度矩阵。推导了在温度梯度载荷和热流密度载荷作用下,矩形梯度板的稳态温度场和热通量场精确解。基于该精确解对比了连续梯度模型和传统的离散梯度模型的热传导有限元计算结果,验证了梯度单元的有效性,并讨论了相关参数对梯度单元的影响。结果表明,梯度单元和均匀单元得到的温度场基本一致;当热载荷垂直于材料梯度方向时,梯度单元能够给出更加精确的局部热通量场;当热载荷平行于材料梯度方向时,4节点梯度单元性能恶化,8节点梯度单元和均匀单元的计算结果与精确解吻合很好。

Graded finite elements were proposed for the heat conduction analysis of gradient composites whose thermal properties were described by micromechanics.The spatially varying stiffness matrices of four-node and eight-node graded elements were calculated through linear and high-order interpolations of temperature fields.Several exact steady-state temperature and flux fields of graded composite plates under temperature gradient and thermal flux loads were presented.With reference to the exact solutions,the heat conduction finite element results of continuous gradient models and conventional,step-wise models were compared to validate the graded elements.The effects of some parameters on the graded elements were also discussed.It shows that the temperature fields resulting from graded and homogeneous elements are nearly the same;the graded elements can give more accurate local flux fields than homogeneous elements do when thermal loads are perpendicular to the material gradation;when they are parallel,the eight-node quadrilateral and homogeneous elements are both excellent,nevertheless,the four-node quadrilateral elements are worse.