Formulação de um elemento finito de viga tridimensional para dinâmica de corpos flexíveis

Abstract

In the last decades, many efforts have been done to build models to simulate multiphysics analisys. For instance, in aeronautical projects, computational models coupling flight dynamics, structural mechanics, aerodynamics and control have been developed. When it comes to structural failure analysis, multiphysics models can be useful to estimate dynamic loads resulting from simulated flight conditions, without a physical prototype. In this perspective, the present work aims at formulating a three-dimensional beam element in the context of flexible body dynamics. The approach addresses large displacements and rotations (associated with rigid body motion) and small strains. Following these assumptions, the equations of motion are obtained using the D’Alembert Principle. Then, considering a three-dimensional beam element, the equations corresponding to each element are developed. In order to reduce the problem order using modal transformation, as well as to verify the implementation of mass and stiffness matrices, free vibration analyzes of canonical problems are performed. Numerically obtained natural frequencies are compared to reference solutions by means of convergence analyzes. Then, free vibration analyzes are performed for a glider. Likewise, after mesh convergence (considering the 20th vibration mode), both the vibration modes and corresponding natural frequencies are outlined