Analytical and Numerical Analysis of Euler-Bernoulli Beams: Telescopic Beam Deflection

• Autor(a) principal: Bombas, Duarte André
• Data de Publicação: 2021
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.6/11679
• topic: Deflexão e Método de Elementos Finitos; Euler-Bernoulli; Rotação; Viga Telescópica

Aircraft morphology adaptation is a subject that is becoming increasingly more important in order to significantly improve its adaptation to the mission to perform. Variable wingspan aircraft have been studied for a while now and its benefits in terms of efficiency and performance are well known. However, they have a type of geometry that is structurally complex and difficult to analyze. This study appears with the purpose of simplifying said geometry and analyze the displacements that occur on a telescopic beam subjected to a certain load distributed along its span and in what way different types of supports between its constituent segments and certain structural differences can influence significantly, or not, such displacements. In this dissertation it is assumed a theoretical analysis of Euler-Bernoulli beams, whose primary characteristic is to neglect the shear strains along the beam’s length, admitting that plane cross-sections are perpendicular to the axis before and after the deformation. This theory is used due to the fact that this study only deals with small deflections and assuming that the beam does not decrease its dimensions on the longitudinal axis after the displacements. To test the three different cases of telescopic beam mechanisms, it is important to know what characteristics are necessary for a correct study of the displacements. Firstly, the two different segments have different flexural rigidities. Secondly, the types of supports used between the segments are different, being for Case 1 a cantilever beam support; for Case 2 a simply supported overhanging telescopic mechanism; and for Case 3 an overhanging telescopic support with a continuous contact. For both the analytical and numerical analysis, the parameters used are the total length of the beam (L), each segment’s length (L0, L1 and L2), the ratios between those lengths and the total length of the beam (KL0 and KL2 ) and the ratio between the flexural rigidity of the tip and root segments (KEI ). These parameters are used in order to obtain non-dimensionalized results. The analytical analysis is carried out and the equations that describe the deformation behavior of the beams are obtained. Posteriorly, the numerical analysis of the same cases is performed with the aid of finite element analysis computational tools, in order to compare those results with the former ones. With this, it is intended to understand how these types of support mechanisms and segment size alterations influence the deformations and what is the veracity and acuity of the equations that describe them. It is also proposed the hypothesis that an ideal margin of length of the telescopic segment exists where the beam’s tip deflection decreases, before it reaches its maximum value.