Boundary-value problems of the asymmetric theory of elasticity for thin plates

Abstract

Boundary-value problems of the three-dimensional asymmetric micropolar, moment theory of elasticity with free rotation are considered for thin plates. It is assumed that the total stress-strain state is the sum of the internal stress-strain state and the boundary layers, which are determined in an approximation using asymptotic analysis. Three different asymptotic forms are constructed for the three-dimensional boundary-value problem posed, depending on the values of dimensionless physical constants of the plate material. The initial approximation for the first asymptotic form leads to a theory of micropolar plates with free rotation, the initial approximation for the second asymptotic form leads to a theory of micropolar plates with constrained rotation, and the initial approximation for the third asymptotic form leads to a theory of micropolar plates with “small shear stiffness.” The corresponding micropolar boundary layers are constructed and studied. The regions of applicability of each of the theories of micropolar plates constructed are indicated.