Abstract
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, bendingReferences
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2. 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, https://doi.org/10.1115/1.3013824.
3. 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, https://doi.org/10.1007/s00419-020-01797-x.
4. 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, https://doi.org/10.1007/s00419-021-02005-0.
5. Icardi U., Applications of zig-zag theories to sandwich beams, Mechanics of Advanced Materials and Structures, 10(1): 77–97, 2003, https://doi.org/10.1080/15376490306737.
6. Kreja I., A literature review on computational models for laminated composite and sandwich panels, Central European Journal of Engineering, 1(1): 59–80, 2011, https://doi.org/10.2478/s13531-011-0005-x.
7. Magnucka-Blandzi E., Magnucki K., Effective design of a sandwich beam with a metal foam core, Thin-Walled Structures, 45(4): 432–438, 2007, https://doi.org/10.1016/j.tws.2007.03.005.
8. 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, https://doi.org/10.1016/j.compstruct.2016.11.089.
9. 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, https://doi.org/10.12989/scs.2014.16.3.325.
10. 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, https://doi.org/10.24423/EngTrans.1015.20190725.
11. Magnucki K., Bending of symmetrically sandwich beams and I-beams – Analytical study, International Journal of Mechanical Sciences, 150: 411–419, 2019, https://doi.org/10.1016/j.ijmecsci.2018.10.020.
12. 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, https://doi.org/10.1016/j.compstruct.2020.112944.
13. 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, https://doi.org/10.24423/EngTrans.1416.20220331.
14. 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, https://doi.org/10.1177/1099636210369615.
15. Noor A.K, Burton W.S., Bert C.W., Computational models for sandwich panels and shells, Applied Mechanics Reviews, 49(3): 155–199, 1996, https://doi.org/10.1115/1.3101923.
16. 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
17. 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, https://doi.org/10.1016/j.compstruct.2017.03.053.
18. 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 https://doi.org/10.1080/15376494.2018.1447178.
19. 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, https://doi.org/10.1016/j.ijmecsci.2004.04.003.
20. Vinson J.R., Sandwich structures, Applied Mechanics Reviews, 54(3): 201–214, 2001, https://doi.org/10.1115/1.3097295.
21. 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, https://doi.org/10.1007/s00419-011-0510-7.
22. 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, https://doi.org/10.1007/s00419-009-0404-0.
23. 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
