不同力学边界下梯度功能材料板稳态热应力

用有限元法研究了由ZrO2和Ti-6Al-4V组成的梯度功能材料板的稳态热应力问题，检验了研究方法的正确性，给出了不同力学边界条件下该材料板的稳态热应力场分布。结果表明：无限自由长板内的热应力最小；当无限长板只能伸长、不能弯曲时，板内稳态拉应力最大，比无限自由长板时板内最大拉应力增大6．1倍；当无限长板的伸长、弯曲受限时，板内的压应力最大，比无限自由长板时板内最大压应力增大12．0倍；此外，材料组分形状分布系数M、对流换热系数、环境介质温度和孔隙度的变化对不同力学边界条件下该材料板稳态热应力场的影响显著。此结果为该材料的设计和应用提供了准确的理论计算依据。

Steady Thermal Stress of Functional Gradient Material Plate Under Different Mechanical Boundary

The steady thermal stress in the plate of a functional gradient material (ZrO2 and Ti-6Al-4V) (FGM) is analyzed with finite element method. The accuracy of this method is examined. The stress distributions under different mechanical boundary conditions are obtained. The results show that the thermal stress in the infinitely long traction-free plate of FGMs is the smallest. When there is only elongation without bending in the plate, the tensile stress is maximum, the maximum tensile stress is 7.1 times as large as those in the infinitely long traction-free plate. When elongation and bending of the plate are limited, the compressive stress is maximum and the maximum compressive stress is 13.0 times as large as those in the infinitely long traction-free plate. In addition, the effects of the changes of the parameter M of the material composition, the temperature of the surrounding medium, the porosity and the convective heat transfer coefficient on the steady thermal stresses are obvious. The results provide the foundations of theoretical calculation for the design and application of the material.