Análise de estruturas e mecanismos reticulados planos com ligações viscoelásticas pela formulação posicional do método dos elementos finitos

Abstract

The work deals with the application of the Positional Formulation of the Finite Element Method (PFFEM) for analysis of 2D framed structures and mechanisms with nonlinear viscoelastic connections. An alternative formulation for static analysis of structures is presented using the PFFEM and the classical aproach of the incremental-iterative method. In the positional formulation, the nodal positions are choosen as the unknown variables of the problem, rather than nodal displacements normally used. The equilibrium equations of the system are written through the principle of stationary total potential energy and the solution of the final nonlinear system of equations are obtain by the Newton-Raphson procedure. The temporal integration is performed by the Newmarks algorithm. The total lagrangian formulation, the kinematics of Bernoulli-Euler and the elastic linear model in the material is used. In the connections modeling, an strategy that is able to consider many reologic models is created, though only Kelvin-Voigts connections is addressed in this work. At the end, numerical examples are provided showing the applicability of formulation for pratical problems.