Abstract The purpose of this study is to analyze a circular annulus made of a functionally graded material (FGM) subjected to thermomechanical loading. The governing nonlinear differential equation for heat transfer, comprising of all the modes of heat transfer, such as conduction, convection, radiation, and internal heat generation, was formulated and then solved using the homotopy perturbation method (HPM). The stress field in the circular annulus due to thermomechanical loading was obtained using a HPM based approximate closed-form solution for a steady-state nonhomogeneous temperature field coupled with the solution of the classical theory of elasticity. The present work considered both Dirichlet and Neumann boundary conditions. A rigorous study on the effect of various thermomechanical parameters and grading parameters on temperature as well as the stress field is presented. The present approximate closed-form solution was validated with the finite element method (FEM) based solution. The close agreement between HPM based solutions of this work with the results of the ANSYS based FEM confirms the effectiveness and the viability of the present solution method for a FGM rotating disk with multiple variable nonlinearities. The present closed-form solution is more rational and computationally efficient over FEM and other numerical solutions.

中文翻译：

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功能梯度旋转盘中的热应力：近似封闭形式的解决方案

摘要 本研究的目的是分析由承受热机械载荷的功能梯度材料 (FGM) 制成的圆形环。由所有传热模式（如传导、对流、辐射和内部发热）组成的传热控制非线性微分方程被公式化，然后使用同伦微扰法 (HPM) 求解。使用基于 HPM 的近似封闭形式求解稳态非均匀温度场，并结合经典弹性理论的求解，获得由于热机械载荷引起的圆形环中的应力场。目前的工作考虑了 Dirichlet 和 Neumann 边界条件。对各种热机械参数和分级参数对温度和应力场的影响进行了严格的研究。本近似封闭形式的解决方案通过基于有限元方法 (FEM) 的解决方案进行了验证。这项工作的基于 HPM 的解决方案与基于 ANSYS 的 FEM 的结果之间的密切一致性证实了本解决方案对于具有多变量非线性的 FGM 旋转盘的有效性和可行性。目前的封闭形式解决方案比 FEM 和其他数值解决方案更合理且计算效率更高。这项工作的基于 HPM 的解决方案与基于 ANSYS 的 FEM 的结果之间的密切一致性证实了本解决方案对于具有多变量非线性的 FGM 旋转盘的有效性和可行性。目前的封闭形式解决方案比 FEM 和其他数值解决方案更合理且计算效率更高。这项工作的基于 HPM 的解决方案与基于 ANSYS 的 FEM 的结果之间的密切一致性证实了本解决方案对于具有多变量非线性的 FGM 旋转盘的有效性和可行性。目前的封闭形式解决方案比 FEM 和其他数值解决方案更合理且计算效率更高。