Análise experimental e numérica de uma viga sujeita a flexão

Abstract

The purpose of this work is to study the Finite Elements method of a beam subjected to bending, and compare different experimental measuring methods of displacement with numerical. For the measurement of the displacement three tools were used, a traditional measurement with graph paper, the non-contact measurement with the aid of a high-speed camera. For numerical, the measures were estimated by linear finite elements Euler-Bernoulli theory and Cosserat theory for non-linear finite element to evaluate the transition from linear to nonlinear regime. The last theory implies that the deformed shape of the beam is described by the displacement vector of the curve of centroids, and a mobile base, which is attached to the cross section of the beam , related to an inertial referential. The main advantage of using this method is that it is geometrically accurate and assists in the discretization of the motion equations. Since the Euler-Bernoulli theory considers only the pure bending of a beam and for structures with no shear deformation and for displacements smaller than 1% of the beam total length (.vertical displacement field), the method provides a quick and accurate resolution. For the measurement with the camera, it was applied an already developed algorithm whose main idea is convert the image array coordinates, which are in pixels, into measurement scales, in this case mm. To calculate the both methods, it was implemented algorithms in Matlab® platform. It is noticed at the end of the study the viability of both methods, yet computational methods are more precise and viable only with a higher acquisition cost.