Carrera unified formulation (CUF) for the micropolar beams: Analytical solutions

Abstract

New higher order models of micropolar beams, which is based on Carrera unified formulation have been developed here. The higher order theory is based on a variational principle of virtual power and the expansion of the 3D equations of the micropolar theory of elasticity into generalized series in terms of cross-section coordinates. The stress and strain tensors, as well as vectors of displacements and rotation, have been expanded into series in terms of cross-section coordinates. Thereby, all equations of the micropolar theory of elasticity (including generalized Hooke’s law) have been transformed to the corresponding equations for the coefficients of the series of cross-section coordinates. Then, in the same way, as in the classical theory of elasticity, a system of differential equations in terms of displacements and rotation with boundary conditions for the coefficients of the series of cross-section coordinates have been obtained. All equations for higher order theory of micropolar plates have been developed and presented here. The case of complete linear expansion has been considered in detail. The obtained equations can be used for calculating the stress–strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects.