Engineering Transactions, 70, 4, pp. 373–390, 2022
10.24423/EngTrans.2238.20221125

Bending of a Stepped Sandwich Beam: The Shear Effect

Joanna KUSTOSZ
ORCID ID 0000-0002-9408-2099
Łukasiewicz Research Network – Poznan Institute of Technology, Center of Rail Vehicles
Poland

Krzysztof MAGNUCKI
ORCID ID 0000-0003-2251-4697
Łukasiewicz Research Network – Poznan Institute of Technology, Center of Rail Vehicles
Poland

Damian GOLIWĄS
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.

Keywords: stepped sandwich beam; clamped ends; shear effect; bending
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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