Formulação de um elemento de viga de seção arbitrária com aplicação em dinâmica de corpos flexíveis

Abstract

In this work, the formulation of an arbitrary cross-section beam element with application in flexible body dynamics will be presented. The equations of motion are derived based on D’Alembert’s principle. Using the Finite Element Method, a composite arbitrary cross-section element with asymmetric bending, uniform torsion and axial extension is formulated. The area and inertia properties of the cross-section involved in the formulations are numerically obtained through Gaussian quadrature by discretizing its geometry. The torsion constant is calculated by solving the cross-sectional warping problem using 2D Finite Element analysis. The Newmark method is employed for solving the equation of motion. Finally, comparative test results are presented to verify the structural model against analytical models.