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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。
A gradient element suitable for the thermal conductivity analysis of gradient composites is presented. The thermophysical properties of material changes are described by meso-mechanics. The gradient elements of 4-node and 8-node are given respectively by linear interpolation and high-order interpolation temperature field Thermal conductivity stiffness matrix with spatial position change. The exact solutions of the steady-state temperature field and the heat flux field of the rectangular gradient plate under the load of temperature gradient and heat flux density are deduced. Based on the exact solution, the results of finite element calculation of heat conduction between the continuous gradient model and the traditional discrete gradient model are compared, the validity of the gradient element is verified, and the influence of the relevant parameters on the gradient element is discussed. The results show that the temperature field obtained by the gradient element and the uniform element are basically the same. When the thermal load is perpendicular to the material gradient direction, the gradient element can give a more accurate local heat flux field. When the thermal load is parallel to the material gradient direction, The performance of the node gradient unit is deteriorated, and the calculation results of the 8-node gradient unit and the uniform unit agree well with the exact solution.