Elastic Plate Deformation with Transverse Variation of Microrotation, arXiv:0811.1534v1

Source: arXiv


The purpose of this paper is to present a new mathematical model for the deformation of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner plate theory, takes into account the transverse variation of microrotation of the plates. The model assumes polynomial approximations over the plate thickness of asymmet-ric stress, couple stress, displacement, and microrotation, which are con-sistent with the elastic equilibrium, boundary conditions and the consti-tutive relationships. Based on the generalized Hellinger-Prange -Reissner variational principle and strain-displacement relation we obtain the com-plete theory of Cosserat plate. We also proved the solution uniqueness for the plate boundary value problem.

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Available from: Lev Steinberg