Nonlinear elastoplastic analysis of thin-walled rods
Yuri Teixeira1; Eduardo M. B. Campello1
1 Department of Structural and Geotechnical Engineering, University of São Paulo
doi:10.20906/CPS/CILAMCE2015-0521
Resumo
This work presents the formulation and finite element implementation of an elastoplastic constitutive equation for the geometrically exact thin-walled rod theories of Campello et al. (2000, 2001, 2003, 2014). The equations are derived following a multiplicative decomposition of the deformation gradient, with von Mises yield criterion and isotropic hardening. Given the hypotheses that there is no in-plane distortion of the cross section and that the transverse shear stresses are small when compared to the normal stresses, it is adequate to consider plastic flow only in the normal direction of the cross section. In accordance with the reference kinematical theories, the constitutive relations are formulated both with and without consideration of cross-sectional warping, the implementation of which being on finite elements with seven and six degrees of freedom respectively. To attain an accurate implementation and capture cross-sectional localized plastic effects, we use a numerical integration scheme over the cross section and include all higher-order strain terms on the constitutive equations, as developed in later works on these theories. The resulting scheme is validated with numerical examples considering both isolated rods and planar and spatial frames. This work is part of a wider research effort for the development of mathematically consistent and computationally efficient models for the analysis of steel frame structures with consideration of geometrical nonlinearities and material inelasticity. It allows us to harness additional resistance of the material in cases of partial yielding of the structural members, and thereby achieve greater efficiency on the structural design. References: CAMPELLO, E. M. B. Análise não-linear de perfis metálicos conformados a frio. Dissertação de Mestrado. Escola Politécnica da USP. São Paulo: 2000. PIMENTA, P. M.; CAMPELLO, E. M. B. Geometrically nonlinear analysis of thin-walled space frames. In: II ECCM, Cracóvia, 2001. PIMENTA, P. M.; CAMPELLO, E. M. B. A fully non
Palavras-chave: elastoplasticity; geometrically exact rod; thin-walled rod; finite element method