功能梯度材料热传导问题的仿真

为研究热传导问题的精确解，假设材料的热导率和对流换热系数按相同型指数函数规律分布，基于二维固体导热微分方程，采用分离变量法，给出了2D功能梯度材料（functionally graded material，FGM）板在对流换热边界条件下稳态温度场的精确解，并用有限元法对其结果进行了验证.具体算例分析表明：通过改变热导率梯度变化参数、流体介质温度、对流换热系数和结构几何尺寸可以优化2D-FGM板的温度场分布.所求得的精确解可作为其他关于FGM板温度场分布近似解的参考标准.

Nonlinear response of a shear deformable S-FGM shallow spherical shell with ceramic-metal-ceramic layers resting on an elastic foundation in a thermal environment

To study the accurate solution to the heat conduction problem, the thermal conductivity and convective heat transfer coefficients of the material were assumed to follow the same exponential functions, based on the 2D differential equation of heat conduction in solids. The accurate solution to the steady temperature field of 2D-FGM plate was obtained with variable separation method under convective heat transfer. The outcome was verified by the FEM. The analysis shows that the temperature field of 2D-FGM plate can be optimized by changing parameters of thermal conductivity, fluid medium temperature, heat transfer coefficient and geometry dimensions of structure. The accurate solution can be used as a reference standard for the approximate solution of the temperature field of the FGM plate.