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Elastic stability of inhomogeneous thin plates on an elastic foundation
The elastic stability of infinite inhomogeneous thin plates on an elastic foundation under in-plane compression has been studied. The elastic stiffness constants depend on the coordinate variable in the thickness direction of the plate. The elastic foundation is represented as a Winkler-type model characterized by linear and nonlinear spring constants. First the Föppl-von Kärmän equations have been derived by taking variations of the elastic strain energy. Next the linear stability analysis of the plate under uniform in-plane compression has been developed and the critical loads and wave numbers for particular three cases have been derived. The effects of the material inhomogeneity, material orthotropy and loading orthotropy on the critical states are examined independently. Finally, a weakly nonlinear analysis of the plate at the onset of the buckling instability has been performed. With the multiple scales method, the amplitude equations for the unstable modes that provide insight into the mode type and its amplitude are derived and then the effect of the material inhomogeneity on buckling modes are evaluated qualitatively.
Elastic stability of inhomogeneous thin plates on an elastic foundation
The elastic stability of infinite inhomogeneous thin plates on an elastic foundation under in-plane compression has been studied. The elastic stiffness constants depend on the coordinate variable in the thickness direction of the plate. The elastic foundation is represented as a Winkler-type model characterized by linear and nonlinear spring constants. First the Föppl-von Kärmän equations have been derived by taking variations of the elastic strain energy. Next the linear stability analysis of the plate under uniform in-plane compression has been developed and the critical loads and wave numbers for particular three cases have been derived. The effects of the material inhomogeneity, material orthotropy and loading orthotropy on the critical states are examined independently. Finally, a weakly nonlinear analysis of the plate at the onset of the buckling instability has been performed. With the multiple scales method, the amplitude equations for the unstable modes that provide insight into the mode type and its amplitude are derived and then the effect of the material inhomogeneity on buckling modes are evaluated qualitatively.
Elastic stability of inhomogeneous thin plates on an elastic foundation
Elastische Stabilität von inhomogenen dünnen Platten auf einem elastischen Unterbau
Morimoto, Takuya (author) / Tanigawa, Yoshinobu (author)
Archive of Applied Mechanics ; 77 ; 653-674
2007
22 Seiten, 7 Bilder, 4 Tabellen, 21 Quellen
Article (Journal)
English
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