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Analytical Calculation of Static Deflection of Biperiodic Stepped Euler–Bernoulli Beam

Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991, USA

Université de Bretagne Sud, University of South Brittany, CNRS UMR 6027, IRDL, Centre de Recherche, Rue de Saint Maudé, BP 92116, 56321 Lorient Cedex, France

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Isaac Elishakoff

Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991, USA

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Noël Challamel

Université de Bretagne Sud, University of South Brittany, CNRS UMR 6027, IRDL, Centre de Recherche, Rue de Saint Maudé, BP 92116, 56321 Lorient Cedex, France

E-mail Address: noel.challamel@univ-ubs.fr

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https://doi.org/10.1142/S0219455423400096Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue on Structural Engineering Dedicated to the 70th Birthday of Professor Y. B. Yang
Guest Editors: Weiyong Wang, C. W. Lim and Jie Yang

Abstract

In this paper, we investigate the lateral deflection of a simply supported periodic stepped beam under uniform load by using an analytical method. This study considers each element of the biperiodic stepped beam as a Euler–Bernoulli beam. By using the local coordinates alongside with the boundary and continuity conditions, the different coefficients for each element caused by the jump of the bending rigidity are calculated. The continuous deflection problem of the multi-stepped repetitive beam is formulated as a linear first-order difference equation with second member. With these coefficients, the deflection at mid-span of the biperiodic beam is analytically found in exact form. This deflection is satisfactory compared to the results of a finite element model based on beam discretization techniques using Hermitian cubic shape functions. The normalized deflection at mid span converges non-monotonically towards the homogenization beam model based on equivalent homogenized stiffness.

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