Abstract
This paper is devoted to analytical and numerical studies of global buckling of a sandwich circular plate. The mechanical properties of the plate core vary along its thickness, remaining constant in the facings. The middle surface of the plate is its symmetrical plane. The mathematical model of the plate is presented. The field of displacements is formulated using the proposed nonlinear hypothesis that generalizes the classical hypotheses. The equations of equilibrium are formulated based on the principle of stationary total potential energy. The proposed mathematical model of the displacements considers the shear effect. The numerical model of the plate is also formulated with a view to verify the analytical one. Numerical calculations are carried out for the chosen family of plates. The values of the critical load obtained by the analytical and numerical methods are compared. The effects of the material properties of the core and the change of the plate radius on the critical load intensity are presented.
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Abbreviations
- R :
-
radius of the circular plate
- t c :
-
thickness of the core
- t f :
-
thickness of the facings
- E 0 :
-
Young’s modulus in the middle plane of the core
- E 1 :
-
Young’s modulus at the top and bottom surfaces of the core
- E f :
-
Young’s modulus of the facings
- ν c :
-
Poisson’s ratio of the core
- ν f :
-
Poisson’s ratio of the facings
- N R,cr :
-
static critical intensity of the load
- U ε :
-
elastic strain energy
- W :
-
work of the load
- w :
-
deflection
- u :
-
longitudinal displacement
- ψ0,ψ1:
-
dimensionless functions
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Citation: MAGNUCKA-BLANDZI, E., WISNIEWSKA-MLECZKO, K., SMYCZYNSKI, M. J., and KEDZIA, P. Buckling of a sandwich symmetrical circular plate with varying mechanical properties of the core. Applied Mathematics and Mechanics (English Edition), 39(7), 981–992 (2018) https://doi.org/10.1007/s10483-018-2347-8
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Magnucka-Blandzi, E., Wisniewska-Mleczko, K., Smyczynski, M.J. et al. Buckling of a sandwich symmetrical circular plate with varying mechanical properties of the core. Appl. Math. Mech.-Engl. Ed. 39, 981–992 (2018). https://doi.org/10.1007/s10483-018-2347-8
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DOI: https://doi.org/10.1007/s10483-018-2347-8