Functionally graded thick-walled tubes analysis by numerical methods

Functionally graded materials are increasingly used in the practice of engineering design, as is the case with thick-walled tubes. The use of these constructive elements requires a calculation, which should be as accurate, as accessible and as fast as possible. The present work responds to these requirements. For the calculation of tubes with thick walls made of functionally graded materials, two new ways were used, based on the concepts of multilayer (material) wall and equivalent material. The multi-layered wall concept considers the tube wall made of several layers, as in the case of the well-known multilayer plates, and the equivalent material concept considers the thickwalled tube made of homogeneous and isotropic material, but with fictitious properties, equivalent in behavior to the functionally graded material. The influence of Poisson's ratio is illustrated by some comparative results. The development of the calculus, the validation of the models and the analysis of the results are based on the numerical calculus using the finite element method. The models used, the transverse plane model, the axial-symmetric plane model and the 3D longitudinal model, are made in several variants regarding the fineness of the mesh. The paper also analyzes the influence of the Poisson ratio variation, compared to adopting a constant value. The results of the study, the models and concepts used are useful to specialists and designers of structures of this type, they have a high degree of generality and present openings for the use of other calculation methods.