10.24423/EngTrans.2238.20221125
Bending of a Stepped Sandwich Beam: The Shear Effect
Joanna KUSTOSZ
0000-0002-9408-2099
Łukasiewicz Research Network – Poznan Institute of Technology, Center of Rail Vehicles
Poland
Krzysztof MAGNUCKI
0000-0003-2251-4697
Łukasiewicz Research Network – Poznan Institute of Technology, Center of Rail Vehicles
Poland
This paper is devoted to the stepped sandwich beam with clamped ends subjected to a uniformly distributed load. The bending problem of the beam is formulated and solved with consideration of the classical sandwich beam of constant face thickness. Two differential equations of equilibrium based on the principle of the stationary potential energy of the classical beam are obtained and analytically solved. Moreover, numerical-FEM models of the beams are developed. Deflections for an exemplary beam family with the use of two methods are calculated. The results of the study are presented in figures and tables.
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).
References
Birman V., Kardomateas G.A., Review of current trends in research and applications of sandwich structures, Composites Part B, 142: 221–240, 2018, doi: 10.1016/j.compositesb.2018.01.027
Carrera E., Brischetto S., A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates, Applied Mechanics Reviews, 62(1): 010803, 2009, doi: 10.1115/1.3013824
Chinh T.H., Tu T.M., Duc D.M., Hung T.Q., Static flexural analysis of sandwich beam with functionally graded face sheets and porous core via point interpolation meshfree method based on polynomial basic function, Archive of Applied Mechanics, 91(3): 933–947, 2021, doi: 10.1007/s00419-020-01797-x
Draiche K., Bousahla A.A., Tounsi A., Hussain M., An integral shear and normal deformation theory for bending analysis of functionally graded sandwich curved beams, Archive of Applied Mechanics, 91(12): 4669–4691, 2021, doi: 10.1007/s00419-021-02005-0
Icardi U., Applications of zig-zag theories to sandwich beams, Mechanics of Advanced Materials and Structures, 10(1): 77–97, 2003, doi: 10.1080/15376490306737
Kreja I., A literature review on computational models for laminated composite and sandwich panels, Central European Journal of Engineering, 1(1): 59–80, 2011, doi: 10.2478/s13531-011-0005-x
Magnucka-Blandzi E., Magnucki K., Effective design of a sandwich beam with a metal foam core, Thin-Walled Structures, 45(4): 432–438, 2007, doi: 10.1016/j.tws.2007.03.005
Magnucka-Blandzi E., Bending and buckling of a metal seven-layer beam with crosswise corrugated main core – Comparative analysis with sandwich beam, Composite Structures, 183: 35–41, 2018, doi: 10.1016/j.compstruct.2016.11.089
Magnucki K., Jasion P., Szyc W., Smyczynski M., Strength and buckling of a sandwich beam with thin binding layers between faces and a metal foam core, Steel and Composite Structures, 16(3): 325–337, 2014, doi: 10.12989/scs.2014.16.3.325
Magnucki K., Magnucka-Blandzi E., Lewiński J., Milecki S., Analytical and numerical studies of an unsymmetrical sandwich beam – bending, buckling and free vibration, Engineering Transactions, 67(4): 491–512, 2019, doi: 10.24423/EngTrans.1015.20190725
Magnucki K., Bending of symmetrically sandwich beams and I-beams – Analytical study, International Journal of Mechanical Sciences, 150: 411–419, 2019, doi: 10.1016/j.ijmecsci.2018.10.020
Magnucki K., Magnucka-Blandzi E., Generalization of a sandwich structure model: Analytical studies of bending and buckling problems of rectangular plates, Composite Structures, 255: 112944, 2021, doi: 10.1016/j.compstruct.2020.112944
Magnucki K., Magnucka-Blandzi E., Wittenbeck L., Three models of a sandwich beam: Bending, buckling and free vibration, Engineering Transactions, 70(2): 97–122, 2022, doi: 10.24423/EngTrans.1416.20220331
Nguyen C.H., Chandrashekhara K., Birman V., Enhanced static response of sandwich panel with honeycomb cores through the use of stepped facings, Journal of Sandwich Structures and Materials, 13(2): 237–260, 2011, doi: 10.1177/1099636210369615
Noor A.K, Burton W.S., Bert C.W., Computational models for sandwich panels and shells, Applied Mechanics Reviews, 49(3): 155–199, 1996, doi: 10.1115/1.3101923
Phan C.N., Frostig Y., Kardomateas G.A., Analysis of sandwich beams with a compliant core and with in-plane rigidity–extended high-order sandwich panel theory versus elasticity, ASME: Journal of Applied Mechanics, 79(4): 041001-1–11, 2012, doi: 10.1115.1.4005550
Sayyad A.S., Ghugal Y.M., Bending, buckling and free vibration of laminated composite and sandwich beams: a critical review of literature, Composite Structures, 171: 486–504, 2017, doi: 10.1016/j.compstruct.2017.03.053
Sayyad A.S., Ghugal Y.M., Modeling and analysis of functionally graded sandwich beams: A review, Mechanics of Advanced Materials and Structures, 26(21): 1776–1795, 2019 doi: 10.1080/15376494.2018.1447178
Steeves C.A., Fleck N.A., Collapse mechanisms of sandwich beams with composite faces and a foam core, loaded in three-point bending. Part 1: Analytical models and minimum weight design, International Journal of Mechanical Sciences, 46(4): 561–583, 2004, doi: 10.1016/j.ijmecsci.2004.04.003
Vinson J.R., Sandwich structures, Applied Mechanics Reviews, 54(3): 201–214, 2001, doi: 10.1115/1.3097295
Wang Z.D., Li Z.F., Theoretical analysis of the deformation of SMP sandwich beam in flexure, Archive of Applied Mechanics, 81(11): 1667–1678, 2011, doi: 10.1007/s00419-011-0510-7
Xiaohui R., Wanji C., Zhen W., A new zig-zag theory and C0 plate bending element for composite and sandwich plates, Archive of Applied Mechanics, 81(2): 185–197, 2011, doi: 10.1007/s00419-009-0404-0
Yang M., Qiao P., Higher-order impact modeling of sandwich structures with flexible core, International Journal of Solids and Structures, 42(20): 5460–5490, 2005, doi.org/10.1016/j.ijsolstr.2005.02.037
DOI: 10.24423/EngTrans.2238.20221125