Análise da torção elastoplástica de sólidos de revolução pelo método dos elementos de contorno

Abstract

This work presents the direct formulation of the Boundary Element Method for the analysis of elastic and elastoplastic torsion of solids of revolution. The problem under consideration is tri-dimensional; however, due to its axisymetric nature, it may be treated as a bi-dimensional one, with the analysis being made in the r-z plane of the cylindrical coordinate system (r; θ; z). Furthermore, its equations are uncoupled from the others which appear when the general axisymmetric case is considered. The formulation employed uses an axisymmetric fundamental solution, i.e., the fundamental displacement is that produced by a unit ring source acting in an infinite elastic body. The problem unknowns (or prescribed boundary conditions) are the angular transverse displacement and the corresponding surface traction. Shear stresses are computed in the appropriate way; boundary stresses are calculated from surface tractions and derivatives of interpolated displacements and stresses at selected internal points are obtained by using the corresponding integral equation. The numerical discretization employs linear or quadratic boundary elements for the elastic analysis and for elastoplastic applications, linear boundary elements and linear triangular internal cells are used. The elastoplastic problem is solved by using an initial strain incremental iterative procedure, in conjuction with the von Mises yield criterion.