Calculation of three-layer plates by methods of vibration theory

Authors

  • Iaroslav Lavrenko Chair of Machine Dynamics and Strength of Materials, National Technical University of Ukraine «Igor Sikorsky Kyiv Politechnic Institute», Kyiv, Ukraine https://orcid.org/0000-0002-4384-4866
  • Olena Chaikovska Department of Theory, Practice and Translation of German, National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», Kyiv, Ukraine https://orcid.org/0000-0001-9945-4296
  • Sofiia Yakovlieva Structural engineer at FAM GmbH, Magdeburg, Germany

DOI:

https://doi.org/10.46299/j.isjea.20220104.03

Keywords:

solar panel, anti-sandwich, Kirchhoff theory, Reisner-Mindlin theory, natural frequencies, finite element method, ABAQUS

Abstract

A three-layer plate with thick hard outer layers and a thin soft inner layer was studied. A model is considered on the example of an anti-sandwich panel to describe the mechanical behavior of a plate on the example of a solar panel. A review of the scientific literature was conducted, in which models of both analytical and numerical methods for calculating three-layer plates are displayed. The scientific work uses the method of finite element analysis using a spatial shell element, as well as the theory of single- and multi-layer plates. These elements combine the topology of volumetric elements and the kinematic and structural equations of a classical shell element. Shell elements based on continuum mechanics were used for numerical simulation. The study was carried out under static load under different conditions, and also the self-oscillations of the anti-sandwich were analyzed using the theories of Kirchhoff and Reisner-Mindlin. As part of the scientific work, a study of the mechanical model of a thin solar panel was carried out using finite element analysis taking into account different temperature conditions and comparing the results with existing studies

References

Lopez, A., Roberts, B., Heimiller, D., Blair, N., Porro, G. (2012). U.S. Renewable Energy Technical Potentials: A GIS-Based Analysis. National Renewable Energy Laboratory Document 7, 1-40, ISBN: NREL/TP-6A20-51946. DOI: NREL/TP-6A20-51946.

Naumenko, K. und Eremeyev, V. A. (2014). A layer-wise theory for laminated glass and photovoltaic panels. Composite Structures 112(1), 283–291. ISSN: 02638223. DOI: 10 .1016/j.compstruct.2014.02.009.

Schulze, S.-H., Pander, M., Naumenko, K. und Altenbach, H. (2012). Analysis of laminated glass beams for photovoltaic applications. International Journal of Solids and Structures 49(15-16), 2027–2036. ISSN: 0020-7683. DOI: 10.1016/j.ijsolstr.2012.03.028. URL: http://dx.doi.org/10.1016/j.ijsolstr.2012.03.028.

Abaqus User’s Manual. Version 6.14. (2014).Dassault Systèmes Simulia Corp. Providence, RI, USA. URL: http://www-archive.ccee.iastate.edu/abaqus/Documentation/docs/v6.14/.

Quora. What is shear locking in FEA. Available at: https://www.quora.com/What-is-shear-locking-in-FEA

Backwoodssolar. Solar panels. Available at: http://www.backwoodssolar.com/products/solar-panels

Assmus, M., Naumenko, K. und Altenbach, H. (2016). A multiscale projection approach for the coupled global-local structural analysis of photovoltaic modules. Composite Structures 158, 340–358. ISSN: 02638223. DOI: 10.1016/j.compstruct.2016.09.036. URL: http://dx.doi.org/10.1016/j.compstruct.2016.09.036.

Eisenträger, J., Naumenko, K., Altenbach, H. und Köppe, H. (2015). Application of the first-order shear deformation theory to the analysis of laminated glasses and photovoltaic panels. International Journal of Mechanical Sciences 96-97, 163–171. ISSN: 00207403. DOI: 10.1016/j.ijmecsci.2015.03.012. URL: http://dx.doi.org/10.1016/j.ijmecsci.2015.03.012.

Eisenträger, J., Naumenko, K., Altenbach, H. und Meenen, J. (2015). A user-defined finite element for laminated glass panels and photovoltaic modules based on a layer-wise theory. Composite Structures 133(December), 265–277. ISSN: 02638223. DOI: 10.1016/j.compstruct.2015.07.049.

Naumenko, K. und Eremeyev, V. A. (2014). A layer-wise theory for laminated glass and photovoltaic panels. Composite Structures 112(1), 283–291. ISSN: 02638223. DOI: 10 .1016/j.compstruct.2014.02.009.

Weps, M., Naumenko, K., Altenbach, H. (2013). Unsymmetric three-layer laminate with soft core for photovoltaic modules. Composite Structures 105, 332-339. ISSN: 02638223. DOI: 10.1016/j.compstruct.2013.05.029.

Klinkel, S., Gruttmann, F., Wagner, W. (1999). A Continuum Based 3D – Shell Element for Laminated Structures. Continuum 71, 43-62. DOI: 10.1.1.727.6818.

Juhre D. (2015). Finite-Elemente-Methode. Available at: https://kipdf.com/finite-element-methode-jun-prof-dr-ing-daniel-juhre-institut-fr-mechanik-fakultt_5ab55e3a 1723dd389ca4c88b .html

Wierzbicki, T. (2013). MIT Course: Plates and Shells. Available at: https://ocw.mit.edu/courses/2-081j-plates-and-shells-spring-2007/

Altenbach, H., Altenbach, J und Naumenko, K. (2004). Ebene Flächentragwerke, 1–210. ISBN: 9783642058417. DOI: 10.1007/978-3-662-06431-3

Hosseini, S., Remmers, J., Verhoosel, C., de Borst, R. (2014). An isogeometric continuum shell element for non-linear analysis. Computer Methods in Applied Mechanics and Engineering 271, 1-22. ISSN: 00457825. ISBN: 978-1-4577-0079-8. DOI: 10.1016/j.cma.2013.11.023. URL: http://dx.doi.org/10.1016/j.cma.2013.11.023

Andelfinger, U., Ramm, E. (1993). EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements. International Journal for Numerical Methods in Engineering 36 (8), 1311-1337. ISSN: 10970207. DOI: 10.1002/nme.1620360805.

Yamashita, H., Valkeapää, A., Jayakumar, P., Sugiyama, H. (2015). Continuum Mechanics Based Bilinear Shear Deformable Shell Element Using Absolute Nodal Coordinate Formulation. Journal of Computational and Nonlinear Dynamics 10 (5). ISSN: 1555-1415. DOI: 10.1115/1.4028657.

Flores, F., Nallim, L., Oller, S. (2017). Formulation of solid-shell finite elements with large displacements considering different transverse shear strains approximations. Finite Elements in Analysis and Design 130, 39-52. ISSN: 0168874X. DOI: 10.1016/j.finel.2017.03.001. URL: http://linkinghub.elsevier.com/retrieve/pii/S0168874X16304528

Naceur, H., Shiri, S., Coutellier, D., Batoz, J. L. (2013). On the modeling and design of composite multilayered structures using solid-shell finite element model. Finite Elements in Analysis and Design 70-71, 1-14. ISSN: 0168874X. DOI: 10.1016/j.finel.2013.02.004. URL: http://dx.doi.org/10.1016/j.finel.2013.02.004

Dvorkin, E., Bathe, K.-J. (1984). A continuum mechanics based four‐node shell element for general non‐linear analysis. Engineering Computations 1 (1), 77-88. ISSN: 0264-4401. ISBN: 02644401. DOI: 10.1108/eb023562. URL: http://www.emeraldinsight.com/doi/10.1108/eb023562

Bischoff, M., Ramm, E. (1997). Shear deformable shell elements for large strains and rotations. International Journal for Numerical Methods in Engineering 40 (23), 4427-4449. DOI: 10.1002/(SICI)1097-0207(19971215)40:23<4427::AID-NME268>3.0.CO;2-9. Available at: http://doi.wiley.com/10.1002/%28SICI%291097-0207%2819971215%2940%3A23%3C4427%3A%3AAID-NME268%3E3.0.CO%3B2-9

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Published

2022-10-01

How to Cite

Lavrenko, I., Chaikovska, O., & Yakovlieva, S. (2022). Calculation of three-layer plates by methods of vibration theory. International Science Journal of Engineering & Agriculture, 1(4), 27–42. https://doi.org/10.46299/j.isjea.20220104.03