Reyes-Carranza, Roberto C.

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    Comparison of elastic plate theories for micropolar materials
    (2010-05) Reyes-Carranza, Roberto C.; Steinberg, Lev; College of Arts and Sciences - Sciences; Bózga, Krzysztof; Romero, Juan; Department of Mathematics
    The purpose of this thesis is to develop a comparison between two theories of micropolar plates with moderate thickness. A comparison between the proposed and Eringen models is shown in the thesis. We used a special technique of the method of separation variables to obtain analytical solutions for the plate models. This special technique is general and can be used for any elliptic system of linear partial differential equations. The stress- strain polynomial approximations of the proposed model have been checked for consistency with the elastic equilibrium, boundary conditions and the constitutive relationships. The formulation of the variational principle for the proposed model is based on the generalized Hellinger-Prange-Reissner principle, which incorporates the proposed stress and strain-displacement approximations for the micro- polar plates. The proposed model produces a new theory of Cosserat plate, which includes a new form of constitutive relationships. The proposed and Eringen models are described by elliptic systems of partial differential equations. The differences in the systems are due to the different orders of polynomial approximations of asymmetric stress, couple stress, displacement, and micro-rotation over the plate thickness. The obtained analytical solutions for the micro- polar plate boundary value problem, have been used for numerical results and comparisons for a special case of syntactic foam plate.