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The effect of different scalings in the modelling of nonlinearly elastic plates with rapidly varying thickness. (English) Zbl 0759.73032

Summary: We deal with the bending of a nonlinearly elastic plate with rapidly varying thickness, assuming it to obey a Saint-Venant-Kirchhoff’s constitutive law. Our analysis is centered on the case when the plate mean thickness and the periodic variation length scale are of different order. The associated limiting model is a fourth order system posed on the plate’s midplane, and with coefficients, determinated by the geometry of the plate, depending on the velocity of the mean thickness variation. The two-dimensional limiting problem generalizes nonlinear models already known in the literature for constant thickness plates. Finally, numerical results for plates with rib-like stiffeners are presented.

MSC:

74K20 Plates
74B20 Nonlinear elasticity
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
Full Text: DOI

References:

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