Navegando por Autor "Barbosa, Gustavo Botelho"

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    Comparison between recent implicit time integration methods with frequency dissipation for nonlinear structural applications.
    (2022) Fernandes, William Luiz; Barbosa, Gustavo Botelho; Greco, Marcelo; Silveira, Ricardo Azoubel da Mota
    The present paper aims to test recent (Truly self-starting two sub-step method and three-parameter singlestep implicit method) and classical (Generalized-α, HHT-α, and WBZ-α methods) time integration methods using the geometrically nonlinear Positional Finite Element Method (PFEM). The numerical formulation is based on the total Lagrangian approach and uses the Hessian matrix to obtain the response. The mixed hardening inelastic model applied to PFEM is also presented. Two examples validate the time integration algorithms and the inelastic model. In the first example, the mixed hardening inelastic model is compared with the the bilinear stress-strain model and the elastic-perfectly plastic hinge model, and aspects such as amplitude decay and period elongation are discussed. In the second example, the implemented algorithms are verified in a severe geometrically nonlinear example, considering the influence of numerical dissipation, time interval, and the number of elements in the response. Results show the relevance of numerical damping for numerical stabilization and the good performance of the Generalized-α algorithm.
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    Two-dimensional beams in rectangular coordinates using the radial point interpolation method.
    (2020) Fernandes, William Luiz; Barbosa, Gustavo Botelho; Rosa, Karine Dornela; Silva, Emanuel; Fernandes, Walliston dos Santos
    The three-dimensional Theory of Elasticity equations lead to a complex solution for most problems in engineering. Therefore, the solutions are typically developed for reduced systems, usually symmetrical or two-dimensional. In this context, compu- tational resources allow the reduction of these simplifications. The most recognized methods of algebraic approximation of the differential equations are the Finite Differ- ences Method and the Finite Element Method (FEM). However, they have limitations in mesh generation and/or adaptation. As follows, Meshless Methods appear as an al- ternative to these options. The present work uses the Radial Point Interpolation Meth- od (RPIM) to evaluate the stress in two-dimensional beams in regions close to loading (Saint Venant’s Principle). Formulations based on the Fourier Series Theory and the RPIM are presented. Multiquadrics Radial Basis Functions were used to obtain the stiffness matrix. Two numerical examples demonstrate the validity of the RPIM for the proposed theme. The results were obtained from the formulations cited and the Finite Element Method for comparison.