功能梯度板条的热弹性力学解

Thermoelastic Solutions for Functionally Graded Strips

本文利用推广后的Mian和Spencer功能梯度板理论,研究了功能梯度板条在非均布温度场作用下的热弹性问题.采用该理论中的位移展开公式,在板厚度方向上考虑热传导引起的稳态温度场,材料常数沿板厚方向可以任意连续变化,从而得到了基于弹性理论的功能梯度板条在温度场作用下的解析解.通过数值算例分析,验证了本文理论的正确性并讨论了边界条件和梯度变化程度对功能梯度板条热弹性响应的影响.

In this paper, the thermoelastic problem of functionally graded strip under non-uniform temperature field is studied by using the generalized Mian and Spencer plate theory. For this purpose, the displacement formulas is expanded, and material constants vary continuously along the plate thickness direction. The steady state temperature field caused by heat conduction is considered in the thickness direction of the plate. Finally, the analytical solution of functionally graded strip based on the elastic theory under the temperature field is obtained. Through comparison with the numerical example analysis, the validity of the theory in this paper is verified, and the influences of the boundary conditions and the degree of material gradient on the thermo-elastic responses of functionally graded strip are also discussed.