Elastic buckling of a rectangular sandwich plate with an individual functionally graded core
More details
Hide details
Łukasiewicz Research Network – Poznan Institute of Technology, Poznan, Poland
Poznan University of Technology, Institute of Mathematics, Poznan, Poland
Poznan University of Technology, Institute of Applied Mechanics, Poznan, Poland
Submission date: 2023-09-15
Final revision date: 2023-11-13
Acceptance date: 2024-11-22
Online publication date: 2024-01-31
Publication date: 2024-01-31
Corresponding author
Krzysztof Sowiński   

Institute of Applied Mechanics, Poznan University of Technology, Jana Pawła II 24, 60-965, Poznan, Poland
Journal of Theoretical and Applied Mechanics 2024;62(1):171-185
This paper is devoted to a thin-walled sandwich plate with an individual functionally graded core. The nonlinear shear deformation theory of a straight normal line is applied. A system of three differential equations of equilibrium of this plate is obtained, based on the principle of stationary potential energy, which is reduced to two differential equations and solved analytically. The critical load of the rectangular sandwich plate is determined. A detailed analytical study is carried out for selected exemplary plates. Moreover, a numerical FEM model of this plate is developed. The results of these calculations are compared with each other.
Adhikari B., Dash P., Singh B.N., 2020, Buckling analysis of porous FGM sandwich plates under various types nonuniform edge compression based on higher order shear deformation theory, Composite Structures, 251, 112597.
Aguib S., Chikh N., Kobzili L., Djedid T., Nour A., Meloussi M., 2021, Analysis of buckling stability behavior of hybrid plate using Ritz approach and numerical simulation, Structures, 34, 3222-3237.
Berdichevsky V.L., 2010, An asymptotic theory of sandwich plates, International Journal of Engineering Science, 48, 3, 383-404.
Birman V., Kardomateas G.A., 2018, Review of current trends in research and applications of sandwich structures, Composites Part B: Engineering, 142, 221-240.
Bouazza M., Becheri T., Boucheta A., Benseddiq N., 2019, Bending behavior of laminated composite plates using the refined four-variable theory and the finite element method, Earthquakes and Structures, 17, 3, 257-270.
Bouazza M., Benseddiq N., 2015, Analytical modeling for the thermoelastic buckling behavior of functionally graded rectangular plates using hyperbolic shear deformation theory under thermal loadings, Multidiscipline Modeling in Materials and Structures, 11, 4, 558-578.
Bouazza M., Hammadi F., Khadir M., 2010, Bending analysis of symmetrically laminated plates, Leonardo Journal of Sciences, 16, 105-116.
Carrera E., Brischetto S., 2009, A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates, Applied Mechanics Review, 62, 1, 010803.
Dhuria M., Grover N., Goyal K., 2021, Influence of porosity distribution on static and buckling responses of porous functionally graded plates, Structures, 34, 1458-1474.
Ellali M., Amara K., Bouazza M., Bourada F., 2015, The buckling of piezoelectric plates on Pasternak elastic foundation using higher-order shear deformation plate theories, Smart Structures and Systems, 21, 1, 113-122.
Foroutan K., Carrera E., Pagani A., Ahmadi H., 2021, Post-buckling and large-deflection analysis of a sandwich FG plate with FG porous core using Carrera’s Unified Formulation, Composite Structures, 272, 114189.
Grover N., Maiti D.K., Singh B.N., 2013, A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates, Composite Structures, 95, 667-675.
Katili I., Batoz J.-L., Bouabdallah S., Maknun I.J., Katili A.M., 2023, Discrete shear projection method for mechanical buckling analysis of FGM sandwich plates, Composite Structures, 312, 116825.
Kołakowski Z., Mania R.J., 2015, Dynamic response of thin FG plates with a static unsymmetrical stable postbuckling path, Thin-Walled Structures, 86, 10-17.
Lopatin A.V., Morozov E.V., 2013, Buckling of a uniformly compressed rectangular SSCF composite sandwich plate, Composite Structures, 105, 108-115.
Magnucka-Blandzi E., Magnucki K., Stawecki W., 2021, Bending and buckling of a circular plate with symmetrically varying mechanical properties, Applied Mathematical Modelling, 89, 2, 1198-1205.
Magnucki K., 2022, An individual shear deformation theory of beams with consideration of the Zhuravsky shear stress formula, Current Perspectives and New Directions in Mechanics, Modelling and Design of Structural Systems, 682-689.
Magnucki K., Magnucka-Blandzi E., 2021, Generalization of a sandwich structure model: Analytical studies of bending and buckling problems of rectangular plates, Composite Structures, 255, 112944.
Magnucki K., Magnucka-Blandzi E., Wittenbeck L., 2023, Elastic buckling of a generalized cylindrical sandwich panel under axial compression, Bulletin of the Polish Academy of Sciences – Technical Sciences, 71, 2, 144623.
Magnucki K.,Witkowski D., Magnucka-Blandzi E., 2019, Buckling and free vibrations of rectangular plates with symmetrically varying mechanical properties – analytical and FEM studies, Composite Structures, 220, 355-361.
Mantari J.L., Monge J.C., 2016, Buckling, free vibration and bending analysis of functionally graded sandwich plates based on an optimized hyperbolic unified formulation, International Journal of Mechanical Sciences, 119, 170-186.
Mantari J.L., Oktem A.S., Soares C.G., 2012, A new higher order shear deformation theory for sandwich and composite laminated plates, Composites Part B: Engineering, 43, 3, 1489-1499.
Marczak J., Jędrysiak J., 2015, Tolerance modelling of vibrations of periodic three-layered plates with inert core, Composite Structures, 134, 854-861.
Meiche N.E., Tounsi A., Ziane N., Mechab I., Adda Bedia E.A., 2011, A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate, International Journal of Mechanical Sciences, 53, 4, 237-247.
Sahoo R., Singh B.N., 2013, A new shear deformation theory for the static analysis of laminated composite and sandwich plates, International Journal of Mechanical Sciences, 75, 324-336.
Sahoo R., Singh B.N., 2014, A new trigonometric zigzag theory for buckling and vibration analysis of laminated composite and sandwich plates, Composite Structures, 117, 316-332.
Sitli Y., Mhada K., Bourihane O., Rhanim H., 2021, Buckling and post-buckling analysis of a functionally graded material (FGM) plate by the Asymptotic Numerical Method, Structures, 31, 1031-1040.
Sobhy M., 2016, An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment, International Journal of Mechanical Sciences, 110, 62-77.
Yang M., Qiao P., 2005, Higher-order impact modeling of sandwich structures with flexible core, International Journal of Solids and Structures, 42, 20, 5460-5490.
Journals System - logo
Scroll to top