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Justification of the nonlinear Koiter’s shallow shell model by an asymptotic approach. (Justification du modèle non linéaire de coque faiblement courbée de W. T. Koiter par approche asymptotique.) (French) Zbl 0973.74047

Summary: We present a justification of the nonlinear Koiter’s shallow-shell model using an asymptotic approach. Our method needs no a priori assumptions. Transforming equilibrium equations into a nondimensional form, we introduce dimensionless numbers which characterize forces and shell geometry. In the case of a shallow shell subjected to moderate forces, we are able to derive the nonlinear Koiter’s shallow-shell model.

MSC:

74K25 Shells
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
74B20 Nonlinear elasticity
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