基于Mori-Tanaka方法的功能梯度厚壁圆筒近似热弹性理论解

An Approximate Thermoelastic Theoretical Solution of Functional Graded Thick-Walled Tube Based on the Mori-Tanaka Method

【目的】功能梯度厚壁圆筒的热弹性问题存在不考虑组分材料微观结构影响,已有文献只给出了基于Mori-Tanaka方法功能梯度厚壁圆筒受力学和热学荷载的数值解,并且只考虑了球形夹杂这一单一夹杂形状的情形。【方法】基于Mori-Tanaka方法对功能梯度厚壁圆筒的热弹性问题进行分析,给出了一种近似热弹性理论解,该理论解不仅与数值解契合度高,而且可以考虑夹杂形状对物理量的影响,最后分析了不同边界条件下夹杂形状对径向位移和各向应力的影响。【结果】结果显示,在两种边界下,夹杂形状对径向位移都有较大的影响;但在温度边界下,夹杂形状对径向应力有较大影响,对轴向应力和周向应力影响较小;在应力边界下,夹杂形状对轴向应力影响较大,对周向应力和径向应力影响较小。

【Purposes】 There is a problem of not considering the microstructure influence of component materials when analyzing the thermoelastic problem of functionally graded thick-walled tubes at present. Evaluating the equivalent parameters of functionally graded materials based on micromechanics methods such as the Mori-Tanaka method can effectively solve the problem mentioned above. However, existing literatures only provide numerical solutions based on the Mori-Tanaka method for functionally graded thick-walled tubes under combined thermal and mechanical loads. And in their works, only the spherical inclusion is considered. 【Methods】 To address the aforementioned issues, the thermoelastic problem of functionally graded thick-walled tubes is analyzed on the basis of the Mori-Tanaka method, and provides an approximate thermoelastic theoretical solution is provided. This theoretical solution not only has a high degree of compatibility with the numerical solution, but also considers the influence of inclusion shape on its physical quantities. Finally, the effects of inclusion shape on radial displacement and stresses under different boundary conditions are analyzed. 【Finding】 The results show that under both boundary conditions, the shape of the inclusion has a significant impact on the radial displacement. However, under the temperature boundary condition, the shape of inclusion has a significant impact on radial stress, but has a relatively small impact on axial and circumferential stresses. Under the stress boundary condition, the shape of inclusion has a greater impact on axial stress, but a smaller impact on circumferential and radial stresses.