Dr. Lev Steinberg – Abril 21-2022 – 10:30 am
Abstract
This talk will present the foundation and validation of the Cosserat Plate Theory, numerical experiments of deformation and vibration, and the unique properties of the Cosserat plates. This approach incorporares the high accuracy assumptions of the Cosserat plate deformation consistent with the Cosserat Elasticity equilibrium equations, constitutive formulas, strain-displacement, and torsion-microrotation relations. The Cosserat Plate Theory is parametric, where the “splitting parameter” minimizes the Cosserat plate energy. The validation of the theory is based on the comparison with the three-dimensional Cosserat Elastostatics and Elastodynamics. Some of the numerical results are obtanined using the Finite Element Method (FEM) specifically developed to solve the parametric system of equations will be also presented. The analysis of deformation of a variety of Cosserat plates shows the stress concentration reduction, higher stiffness of Cosserat plates, and the size-effect related to the microstructure. The analysis of vibration of Cosserat plates predicts size-related properties of the plate vibration, the existence of the additional so-called Cosserat plate resonances, and the dynamic anisotropy, related to the dependency of the resonances on the microelement’s shapes and orientation.