期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 17, 期 3, 页码 363-392出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202507001954
关键词
shells; membranes; polar materials; variational methods; size effects; Korn's inequality for shells; polyconvex shell
The existence of minimizers to a geometrically exact Cosserat planar shell model with microstructure is proven. The membrane energy is a quadratic, uniformly Legendre-Hadamard elliptic energy in contrast to traditional membrane energies. The bending contribution is augmented by a curvature term representing the interaction of the rotational microstructure in the Cosserat theory. The model includes non-classical size effects, transverse shear resistance, drilling degrees of freedom and accounts implicitly for thickness extension and asymmetric shift of the midsurface. Upon linearization with zero Cosserat couple modulus mu(c) = 0, one recovers the infinitesimal-displacement Reissner-Mindlin model. It is shown that the Cosserat shell formulation admits minimizers even for mu(c) = 0, in which case the drill-energy is absent. The midsurface deformation m is found in H-1(omega, R-3). Since the existence of energy minimizers rather than equilibrium solutions is established, the proposed analysis includes the large deformation/large rotation buckling behaviour of thin shells.
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