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

Abstract

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.

Keywords

• functional graded materials
• thick-walled tube
• the mori-tanaka method
• thermoelastic theoretical solution
• inclusion shape