Article
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Numerical Analysis of Cracked Double-Beam Systems
Version 1
: Received: 21 August 2023 / Approved: 22 August 2023 / Online: 23 August 2023 (07:36:23 CEST)
A peer-reviewed article of this Preprint also exists.
Rosa, M.A.D.; Lippiello, M. Numerical Analysis of Cracked Double-Beam Systems. Appl. Mech. 2023, 4, 1015-1037. Rosa, M.A.D.; Lippiello, M. Numerical Analysis of Cracked Double-Beam Systems. Appl. Mech. 2023, 4, 1015-1037.
Abstract
Based on the elasticity theory, this paper deals with the static analysis of a cracked double beam system in presence of a Winkler medium. The double-beam system is also supposed to be constrained at both ends by elastically flexible springs, with transverse and rotational stiffness. Using a variational formulation, the static governing equations are derived and solved by using analytical and numerical approaches. In the first approach, the closed-form solutions for the displacements functions are obtained based on the Euler-Bernoulli beam theory. In the second approach, the Cell-Discretization Method (CDM) is performed, according to which the two beams are reduced to a set of rigid bars linked together by means of elastic constraints, where the bending stiffness of the bars is concentrated. The resulting stiffness matrix is easily deduced, and the governing equations of the static problem can be immediately solved. A comparative analysis is performed in order to verify the accuracy and validity of the proposed method. This study focuses on the effect of various parameters including the crack depth and position, boundary conditions, elastic medium and slenderness. The validity of the proposed analysis is confirmed by comparing the present results with those obtained from the other approach. In particular, the results obtained by closed-form solution and Cell-discretization method (CDM) are compared by Finite element method (FEM). Accuracy of the results has been evaluated by making comparisons with the results in literature and reported in bibliography. It is demonstrated that the proposed algorithm provides a simple and powerful tool in dealing with the static analysis of a double-beam system. Finally, some concluding remarks are made.
Keywords
n/a; double-beam system, static analysis, crack, closed-form solution, CDM, FEM.
Subject
Engineering, Civil Engineering
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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