Shahzamanian M M, Shahrjerdi A, Sahari B B, Wu P D
Department of Mechanical Engineering, McMaster University, Hamilton, ON L8S 4L7, Canada.
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA.
Materials (Basel). 2022 Aug 12;15(16):5548. doi: 10.3390/ma15165548.
A steady-state thermal analysis for a hollow and axisymmetric functionally graded (FG) rotating disk with a uniform thickness was performed in this study. In the studied FG disk, metal and ceramic materials were considered for the inner and outer surfaces, respectively, when the material properties varied along the radial direction but not through material thickness variations. A power law distribution was employed to represent the material properties. Three different methods were used to present the temperature distribution along the radial direction of the FG disk, namely (1) an in-house finite element (FE) program, (2) the ANSYS parametric design language (APDL), and (3) an analytical solution. Furthermore, the in-house FE program presented the thermal stress and thermal strain of the FG disk. The weighted residual method in the FEM was used to present the temperature distribution when the material properties along an element are varying in contrast with using a commercial finite element software when the material properties are constant within an element to simulate FGMs. The accuracy of the in-house FE program was tested, and it was shown that the temperature distributions obtained by using the abovementioned methods were exactly the same. A parametric material gradation study was performed to understand the effects on the temperature, thermal strain, and stress. The material gradation was found to have a significant effect in this regard. The in-house finite element program enables one to perform a post-processing analysis in a more efficient and convenient manner than that through simulations in a finite element software program such as ANSYS. Lastly, this in-house code can be used to perform an optimization analysis to minimize the thermal strain and stress while the stiffness of the plate is maintained when the material properties within an element vary.
本研究对厚度均匀的空心轴对称功能梯度（FG）旋转盘进行了稳态热分析。在所研究的FG盘中，当材料特性沿径向变化但不随材料厚度变化时，分别考虑内表面和外表面使用金属和陶瓷材料。采用幂律分布来表示材料特性。使用三种不同方法来呈现FG盘沿径向的温度分布，即（1）内部有限元（FE）程序，（2）ANSYS参数设计语言（APDL），以及（3）解析解。此外，内部FE程序还给出了FG盘的热应力和热应变。当单元内材料特性变化时，有限元法中的加权残值法用于呈现温度分布，这与单元内材料特性恒定时使用商业有限元软件模拟功能梯度材料形成对比。对内部FE程序的精度进行了测试，结果表明使用上述方法获得的温度分布完全相同。进行了参数化材料梯度研究以了解其对温度、热应变和应力的影响。结果发现材料梯度在这方面有显著影响。与通过诸如ANSYS等有限元软件程序进行模拟相比，内部有限元程序能使人们以更高效、更便捷的方式进行后处理分析。最后，当单元内材料特性变化时，此内部代码可用于进行优化分析，以在保持板的刚度的同时使热应变和应力最小化。
