ANALYTICAL AND NUMERICAL COMPARATIVE STUDY OF PROBLEM IN 2D ELASTICITY OF A HOLLOW TUBE SUBJECT TO NORMAL AND SHEAR STRESSES IN THE INTERNAL CONTOUR
Thiago Arnaud Abreu de Oliveira1; Rodolfo de Azevedo Palhares1; Danilo Carvalho de Moura1; Luís Vinícius Pereira Silva1; Luciano Lins Vieira1; Gilberto Gomes1
1 UNB
doi:10.20906/CPS/CILAMCE2017-0787
Resumo
Structures with hollow circular cross-sections are often used in engineering. The necessity to study pipes is considerably important in the nuclear, aerospace and petrochemical industries. Since the problem of hollow pipes as structural components of great importance to explain the behavior of several practical situations of engineering, this study allows a better understanding of the structural behavior of this element. This paper presents a problem of Elasticity Theory that is not commonly found in the literature and it aims not only the solution, but also to evidence the theoretical concepts involved. The problem consists of a hollow tube subjected to internal pressure as well as internal shear, with boundary conditions of free radial displacement and tangential displacement restrained. The methodology of this paper consists of a linear static analysis through analytical formulations and numerical simulations using Finite Element Method (FEM). For the analysis of the results, an analytical formulation of the problem was developed based on the elasticity theory in polar coordinates, and its results were compared with those obtained numerically, using the software ANSYS. The results analyzed were longitudinal and radial displacement and the acting tensions. After the analysis, the results were very approximate, and this approach occurred due the level of refinement of the finite element mesh. For greater precision of the numerical results it would be required an increase in the number of elements of the mesh, although it would increase the processing time. However, for engineering purposes and the purpose of this paper, the numerical results obtained were valid.
Palavras-chave: Hollow Tube; Elasticity Theory; Tension Field; Displacement Field