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A superconvergent elastically coupled double beam element for analysis of adhesively bonded lap joints

Paunikar, S and Gopalakrishnan, S (2021) A superconvergent elastically coupled double beam element for analysis of adhesively bonded lap joints. In: International Journal for Computational Methods in Engineering Science and Mechanics, 23 (4). pp. 307-333.

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Official URL: https://doi.org/10.1080/15502287.2021.1964637


A novel elastically coupled double beam (ECDB) finite element with superconvergent properties is developed to primarily study wave propagation in the bonded region of an adhesively bonded single lap joint. An ECDB element consists of two axial-flexural-shear coupled beams coupled with continuously distributed linear elastic springs. A general formulation applicable to both metals and composites is proposed. An exact solution to the static part of six-coupled governing equations of motion is obtained, which is then used to formulate exact stiffness and mass matrices. Consequently, the ECDB element thus formulated has superconvergent properties and is inherently free of shear locking. It is shown that merely a single ECDB element is sufficient to accurately capture the tip deflections of a cantilever double beam type geometry subjected to static loading, following which eigenvalue analysis is performed, and comparisons are made with the commercial finite element software—Abaqus. Further, wave propagation studies are carried out to demonstrate the efficiency of the element in evaluating ultrasonic wave responses across various metallic and composite ECDBs, and comparisons are made with Abaqus and frequency-domain spectral finite element (SFEM) model described in Paunikar and Goapalakrishnan (“Wave propagation in adhesively bonded metallic and composite lap joints modelled through spectrally formulated elastically coupled double beam element,” Compos. Struct., under review). Following this, wave propagation in symmetric metallic, geometrically asymmetric metallic, and symmetric laminated composite lap joints with strong and weak bonding is studied by employing two-noded Lagrangian frame elements to mesh the adherends and superconvergent elastically coupled double beam (SECDB) elements to mesh the bonded region. The results obtained from the superconvergent finite element (SCFE) simulations are compared with those given by Abaqus and SFEM. Lastly, the SCFE models for the cases of perfectly bonded aluminium and symmetric ply laminated composite are experimentally validated. We have shown that the SECDB element developed in this work may be used to efficiently carry out static and dynamic analysis in any symmetric or asymmetric bonded joint comprising of only metals or composites or a combination of the two. It is also demonstrated that various levels of adhesion in a bonded joint can be simulated by varying the coupling spring stiffness value. Additionally, the SECDB element may also be used to study other double beam like coupled structures, for instance, space platforms or dynamic vibration absorbers.

Item Type: Journal Article
Publication: International Journal for Computational Methods in Engineering Science and Mechanics
Publisher: Taylor and Francis Ltd.
Additional Information: The copyright for this article belongs to the Taylor and Francis Ltd.
Keywords: ABAQUS; Adhesive joints; Adhesives; Eigenvalues and eigenfunctions; Equations of motion; Frequency domain analysis; Laminating; Mesh generation; Metal analysis; Metals; Space platforms; Springs (components); Stiffness; Wave propagation, Adhesively bonded lap joint; Adhesively bonded single lap joints; Dynamic vibration absorber; Eigenvalue analysis; Finite element software; Governing equations of motion; Spectral finite elements; Static and dynamic analysis, Laminated composites
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 03 Dec 2021 07:52
Last Modified: 11 Jul 2022 05:46
URI: https://eprints.iisc.ac.in/id/eprint/70166

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