Browse > Article
http://dx.doi.org/10.12989/scs.2018.28.6.671

Stability of five layer sandwich beams - a nonlinear hypothesis  

Smyczynski, Mikolaj J. (Institute of Applied Mechanics, Poznan University of Technology)
Magnucka-Blandzi, Ewa (Institute of Mathematics, Poznan University of Technology)
Publication Information
Steel and Composite Structures / v.28, no.6, 2018 , pp. 671-679 More about this Journal
Abstract
The paper is devoted to the stability analysis of a simply supported five layer sandwich beam. The beam consists of five layers: two metal faces, the metal foam core and two binding layers between faces and the core. The main goal is to elaborate a mathematical and numerical model of this beam. The beam is subjected to an axial compression. The nonlinear hypothesis of deformation of the cross section of the beam is formulated. Based on the Hamilton's principle the system of four stability equations is obtained. This system is approximately solved. Applying the Bubnov-Galerkin's method gives an ordinary differential equation of motion. The equation is then numerically processed. The equilibrium paths for a static and dynamic load are derived and the influence of the binding layers is considered. The main goal of the paper is an analytical description including the influence of binding layers on stability, especially on critical load, static and dynamic paths. Analytical solutions, in particular mathematical model are verified numerically and the results are compared with those obtained in experiments.
Keywords
five layer beam; binding layers; shear effect; equilibrium paths; critical load;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Smyczynski, M.J. and Magnucka-Blandzi, E. (2015), "Static and dynamic stability of an axially compressed five-layer sandwich beam", Thin-Wall. Struct., 90, 23-30.   DOI
2 Smyczynski, M.J. and Magnucka-Blandzi, E. (2016), "Strength of the three layer beam with two binding layers", Arch. Civil Eng., 62(3), 189-206.   DOI
3 Smyczynski, M.J. and Magnucka-Blandzi, E. (2018), "The threepoint bending of a sandwich beam with two binding layers -Comparison of two nonlinear hypotheses", Compos. Struct., 183, 96-102.   DOI
4 Thai, H.-T. and Choi, D.-H. (2013), "A simple first-order shear deformation theory for laminated composite plates", Compos. Struct., 106, 754-763.   DOI
5 Yang, J., Chen, D., Ning, M., Yang, W. and Li, Q. (2012), "Analysis of dynamic stability for composite laminated beam with delamination", Progress Ind. Civil Eng., Pts. 1-5. 204-208, 3074-3077.
6 Yu, J., Wang, X., Wei, Z. and Wang, E. (2003), "Deformation and failure mechanism of dynamically loaded sandwich beams with aluminum-foam core", Int. J. Impact Eng., 28(3), 331-347.   DOI
7 Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2 - Buckling and free vibration", Int. J. Solids Struct., 42(18-19), 5243-5258.   DOI
8 Altenbach, H., Eremeyev, V.A. and Naumenko, K. (2015), "On the use of the first order shear deformation plate theory for the analysis of three-layer plates with thin soft core layer", ZAMM -J. Appl. Math. Mech. / Zeitschrift fur Angewandte Mathematik und Mechanik, 95(10), 1004-1011.   DOI
9 Allen, H.G. (1969), Analysis and Design of Structural Sandwich Panels, Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig.
10 Altenbach, H. and Eremeyev, V. (2011), Thin-walled Structures Made of Foams.
11 Ashby, M.F., Evans, A.G., Fleck, N.A., Gibson, L.J. and Hutchinson, J.W. (2000), Metal Foams: A Design Guide, Butterworth Heinemann, Boston, MA, USA.
12 Banhart, J. (2001), "Manufacture, characterisation and application of cellular metals and metal foams", Prog. Mater. Sci., 46(6), 559-632.   DOI
13 Belica, T., Malinowski, M. and Magnucki, K. (2011), "Dynamic stability of an isotropic metal foam cylindrical shell subjected to external pressure and axial compression", J. Appl. Mech.-Trans. ASME, 78(4), 8-20.
14 Jasion, P. and Magnucki, K. (2012), "Face wrinkling of sandwich beams under pure bending", J. Theor. Appl. Mech., 50(4), 933-941.
15 Carrera, E. and Brischetto, S. (2009), "A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates", Appl. Mech. Rev., 62(1), 17.
16 Farkas, J. and Jarmai, K. (1998), "Minimum material cost design of five-layer sandwich beams", Struct. Optimiz., 15(3-4), 215-220.   DOI
17 Grygorowicz, M., Magnucki, K. and Malinowski, M. (2015), "Elastic buckling of a sandwich beam with variable mechanical properties of the core", Thin-Wall. Struct., 87, 127-132.   DOI
18 Jasion, P. and Magnucki, K. (2013), "Global buckling of a sandwich column with metal foam core", Journal of Sandwich Structures & Materials. 15(6), 718-732.   DOI
19 Jasion, P., Magnucka-Blandzi, E., Szyc, W. and Magnucki, K. (2012), "Global and local buckling of sandwich circular and beam-rectangular plates with metal foam core", Thin-Wall. Struct., 61, 154-161.   DOI
20 Kim, N., Jeon, C. and Lee, J. (2013), "Dynamic stability analysis of shear-flexible composite beams", Arch. Appl. Mech., 83(5), 685-707.   DOI
21 Lee, L.J. and Fan, Y.J. (1996), "Bending and vibration analysis of composite sandwich plates", Comput. Struct., 60(1), 103-112.   DOI
22 Magnucka-Blandzi, E. (2009), "Dynamic stability of a metal foam circular plate", J. Theor. Appl. Mech., 47(2), 421-433.
23 Magnucka-Blandzi, E. (2011), "Dynamic stability and static stress state of a sandwich beam with a metal foam core using three modified Timoshenko hypotheses", Mech. Adv. Mater. Struct., 18(2), 147-158.   DOI
24 Magnucki, K., Smyczynski, M. and Jasion, P. (2013), "Deflection and strength of a sandwich beam with thin binding layers between faces and a core", Arch. Mech., 65(4), 301-311.
25 Magnucka-Blandzi, E. and Magnucki, K. (2007), "Effective design of a sandwich beam with a metal foam core", Thin-Walled Struct., 45(4), 432-438.   DOI
26 Magnucki, K., Malinowski, M. and Kasprzak, J. (2006), "Bending and buckling of a rectangular porous plate", Steel Compos. Struct., Int. J., 6(4), 319-333.   DOI
27 Magnucki, K., Szyc, W. and (red) (2012), Wytrzymalosc i statecznosc belek i plyt trojwarstwowych z rdzeniem z pianki aluminiowej, Wydawnictwo Politechniki Poznanskiej, Poznan.
28 Magnucki, K., Jasion, P., Krus, M., Kuligowski, P. and Wittenbeck, L. (2013), "Strength and buckling of sandwich beams with corrugated core", J. Theor. Appl. Mech., 51(1), 15-24.
29 Magnucki, K., Jasion, P., Szyc, W. and Smyczynski, M.J. (2014), "Strength and buckling of a sandwich beam with thin binding layers between faces and a metal foam core", Steel Compos. Struct., Int. J., 16(3), 325-337.   DOI
30 Malachowski, J., Klasztorny, M., Dziewulski, P., Nycz, D. and Gotowicki, P. (2012), "Experimental investigations and modelling of Alporas aluminium foam", Model. Eng., 42, 97-112. [In Polish]
31 Mohanty, S., Dash, R. and Rout, T. (2012), "Static and dynamic stability analysis of a functionally graded Timoshenko beam", Int. J. Struct. Stab. Dyn., 12(4).
32 Pawlus, D. (2011), "Critical loads calculations of annular threelayered plates with soft elastic or viscoelastic core", Arch. Civil Mech. Eng., 11(4), 993-1009.   DOI
33 Paczos, P., Wasilewicz, P. and Magnucka-Blandzi, E. (2016), "Experimental and numerical investigations of five-layered trapezoidal beams", Compos. Struct., 145, 129-141.   DOI
34 Pawlus, D. (2007), "Critical static loads calculations in finite element method of three-layered annular plates", Arch. Civil Mech. Eng., 7(1), 21-33.   DOI