Carrera unified formulation (CUF) for the micropolar plates and shells. II. Complete linear expansion case

New higher-order models of orthotropic micropolar plates and shells have been developed using Carrera Unified Formulation (CUF). Here, a complete linear expansion case (CLEC) has been considered in detail. The stress and strain tensors, as well as the vectors of displacements and rotation, have been presented as linear expansion in terms of the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the expansion on the shell thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the expansion of the shell thickness coordinates has been obtained. All equations for the case of CLEC theory of micropolar plates and shells have been developed and presented here. 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.

Automated summary

In this study, new higher-order models of orthotropic micropolar plates and shells were developed using the Carrera Unified Formulation (CUF). A complete linear expansion case (CLEC) was considered in detail. The stress and strain tensors, as well as the vectors of displacements and rotation, were presented as linear expansion in terms of the shell thickness coordinates. The equations of the micropolar theory of elasticity were transformed to the corresponding equations for the coefficients of the expansion, and a system of differential equations and natural boundary conditions were obtained. These developed equations can be used for calculating stress-strain and modeling thin-walled structures, considering micropolar couple stress and rotation effects.