Mathematical modelling of a rectangular sandwich plate with a metal foam core

• Autorzy: Magnucka-Blandzi E.

Warianty tytułu

PL

Matematyczne modelowanie prostokątnej płyty trójwarstwowej z rdzeniem z pianki metalowej

• Języki publikacji: EN

Abstrakty

EN

The subject of the paper is a simply supported rectangular sandwich plate. The plate is compressed in plane. It is assumed that the plate under consideration is symmetrical in build and consists of two isotropic facings and a core. The middle plane of the plate is its symmetry plane. The core is made of a metal foam with properties varying across its thickness. The porouscellular metal as a core of the three layered plate is of continuous structure, while its mechanical properties are isotropic. Dimensionless coefficients are introduced to compensate for this. The field of displacements and geometric relationships are assumed. This non-linear hypothesis is generalization of the classical hypotheses, in particular, the broken-line hypothesis. The principle of stationarity of the total potential energy of the compressed sandwich plate is used and a system of differential equations is formulated. This system is approximately solved. The forms of unknown functions are assumed, which satisfy boundary conditions for supports of the plate. Critical loads for a family of sandwich plates are numerically determined. Results of the calculation are shown in figures.

PL

Przedmiotem pracy jest prostokątna płyta trójwarstwowa podparta przegubowo na czterech brzegach i ściskana w płaszczyźnie środkowej. Okładziny płyty są izotropowe i o takich samych właściwościach mechanicznych. Rdzeń wykonany z pianki metalowej jest również izotropowy, jego właściwości mechaniczne są zmienne na grubości. Płaszczyzna środkowa płyty jest jej płaszczyzną symetrii. Zdefiniowano pole przemieszczeń dla dowolnego punktu rdzenia oraz okładzin płyty. Sformułowano energię odkształcenia sprężystego płyty i pracę obciążenia. Następnie z zasady stacjonarności całkowitej energii potencjalnej otrzymano układ równań równowagi, który rozwiązano analitycznie w sposób przybliżony i wyznaczono obciążenie krytyczne płyty.

Słowa kluczowe

EN

sandwich plate; critical load; metal foam core

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2011
• Tom: Vol. 49 nr 2
• Strony: 439--455
• Opis fizyczny: Bibliogr. 29 poz., rys.

Twórcy

autor

Magnucka-Blandzi E.

• Poznań University of Technology, Institute of Mathematics, Poznań, Poland,

Bibliografia

• 1. Apetre N.A., Sankar V., Ambur D.R., 2008, Analytical modeling of sandwich beams with functionally graded core, Journal of Sandwich Structures and Materials, 10, 53-74
• 2. Banhart J., 2001, Manufacture, characterisation and application of cellular metals and metal foams, Progress in Materials Science, 46, 559-632
• 3. Bart-Smith H., Hutchinson J.W., Evans A.G., 2001, Measurement and analysis of the structural performance of cellular metal sandwich construction, Int. Journal of Mechanical Science, 43, 1945-1963
• 4. Carrera E., 2000, An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates, Composite Structures, 50, 183-198
• 5. Carrera E., 2001, Developments, ideas, and evaluations based upon Reissner’s mixed variational theorem in the modeling of multilayred plates and shells, Applied Mechanics Reviews, 54, 301-329
• 6. Carrera E., 2003, Historical review of Zig-Zag theories for multilayred plates and shells, Applied Mechanics Reviews, 56, 287-308
• 7. Carrera E., Brischetto S., Robaldo A., 2008, Variable kinematic model for analysis of functionally graded material plates, AIAA Journal, 46, 1, 194-203
• 8. Debowski D., Magnucki K., 2006, Dynamic stability of a porouse rectangular plate, PAMM, Proc. Appl. Math. Mech., 6, 215-216
• 9. Grigolyuk E.I., Chulkov P.P., 1973, Stability and Vibrations of Three Layers Shells, Mashinostroene, Moskow [in Russian]
• 10. Hohe J., Becker W., 2002, Effective stress-strain relations for two-dimensional cellular sandwich core: Homogenization, materials modes, and properties, Applied Mechanics Reviews, 55, 61-86
• 11. Kasprzak J., Ostwald M., 2006, A generalized approach to modeling displacements in plates made of non-homogeneous materials, XLV Sympozjon, Modelling in Mechanics, Wisla-Poland
• 12. Kotełko M., Mania R., 2005, Limitations of equivalent plate approach to the load-capacity estimation of honeycomb sandwich panels under compression, Fourth Int. Conf. Thin-Walled Structures, J. Loughlan (Edit.), Bristol & Philadelphia: IOP Publishing, 679-686
• 13. Magnucka-Blandzi E., 2008, Axi-symmetrical deflection and buckling of circular porous-cellular plate, Thin-Walled Structures, 46, 333-337
• 14. Magnucka-Blandzi E., 2009, Dynamic stability of a metal foam circular plate, Journal of Theoretical and Applied Mechanics, 47, 2, 421-433
• 15. Magnucka-Blandzi E., 2010, Dynamic stability and static stress state of a sandwich beam with a metal foam core using three modified Timoshenko hypotheses, Mechanics of Advanced Materials and Structures (in print)
• 16. Magnucka-Blandzi E., Magnucki K., 2007, Effective design of a sandwich beam with a metal foam core, Thin-Walled Structures, 45, 432-438
• 17. Magnucka-Blandzi E., Wasilewicz P., 2009, Strength of a rectangular sandwich plate with metal foam core, Proceedings of the International Symposium on Cellular Metals for Structural and Functional Applications, CELLMET 2008, G. Stephani, B. Kieback (Edit.), Fraunhofer IFAM Dresden, Germany, 283-298
• 18. Magnucki K., Magnucka-Blandzi E., 2006, Strength and stability of a sandwich beam with a porous-cellular core, 11-th Symposium Stability of Structures, K. Kowal-Michalska, R.J. Mania (Edit.), Zakopane, Chair of Strength of Materials and Structures, Lodz University of Technology, 259-266
• 19. Magnucki K., Malinowski M., Kasprzak J., 2006, Bending and buckling of a rectangular porous plate, Steel and Composite Structures, 6, 4, 319-333
• 20. Magnucki K., Ostwald M. (Edit.), 2001, Stability and Optimization of Sandwich Structures, Poznań, Zielona Gora, Wyd. Instytutu Technologii Eksploatacji w Radomiu [in Polish]
• 21. Magnucki K., Stasiewicz P., 2004a, Elastic bending of an isotropic porous beam, Int. Journal of Applied Mechanics and Engineering, 9, 2, 351-360
• 22. Magnucki K., Stasiewicz P., 2004b, Elastic buckling of a porous beam, Journal of Theoretical and Applied Mechanics, 42, 4, 859-868
• 23. Malinowski M., Magnucki K., 2005, Deflection of an isotropic porous cylindrical panel, Proc. of the 8th SSTA Conference, W. Pietraszkiewicz, C. Szymczak (Edit.), London, Leiden, New York, Philadelphia, Singapore: Taylor & Francis, 143-147
• 24. Noor A.K., Burton W.S., Bert C., 1996, Computational models for sandwich panels and shells, Appl. Mech. Rev., 49, 3, 155-199
• 25. Ohga M., Wijenayaka A.S., Croll J.G.A., 2005, Reduced stiffness buckling of sandwich cylindrical shells under uniform external pressure, ThinWalled Structures, 43, 1188-1201
• 26. Pandit M.K., Singh B.N., Sheikh A.H., 2008, Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory, Thin-Walled Structures, 46, 1183-1191
• 27. Plantema F.J., 1966, Sandwich Construction: The Bending and Buckling of Sandwich Beams, Plates and Shells, New York: John Wiley & Sons
• 28. Volmir A.S., 1967, Stability of Deformation Systems, Moscow: Nauka, Fizmatlit [in Russian]
• 29. Wang C.M., Reddy J.N., Lee K.H., 2000, Shear Deformable Beams and Plates, Elsevier, Amsterdam, Lousanne, New York, Oxford, Shannon, Singapore, Tokyo