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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.

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
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