Análise de tensões empregando a formulação em coordenadas polares da teoria de volumes finitos

Abstract

This work presents a formulation for stress analysis of axisymmetric structures, such as circular tubes, cylinders and rings, based on a polar coordinate version of the Finite-Volume Theory. This formulation is well suited for stress analysis in structures with curved contours, presenting geometry and mechanical fields expressed in term of polar coordinates, aiming to improve the performance of the method in such situations. Unlike previous versions using polar coordinates, this formulation is based on the assembly of the local stiffness matrix, which relates surface-averaged tractions and displacements acting on the faces of the subvolume, and the direct stiffness method for the assembling of the global stiffness matrix, based on the kinematic and static incidences of the structure, that is, in the conditions of kinematic and static compatibilities of the structure. Some examples were analyzed and the results compared with analytical solutions of the linear elasticity theory (Lamé problem, fixed curved beam and the Kirsch problem), showing the efficiency of the proposed formulation.