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It is shown that the classical theories of micropolar plates and shells can be obtained using the Carrera Unified Formulation (CUF) approach as a special case of approximation. The theory of micropolar plates and shells based on the hypotheses of Timoshenko–Mindlin and Kirchhoff–Love is considered in detail. The stress and strain tensors, as well as the displacement and rotation vectors are presented as linear expansion along the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including the generalized Hooke's law) were transformed into the corresponding equations for the expansion coefficients in the coordinates of the shell thickness. All equations of the theory of micropolar plates and shells based on the hypotheses of Timoshenko–Mindlin and Kirchhoff–Love are presented here. Micropolar plates in Cartesian and polar coordinates, as well as micropolar shells of cylindrical, conical, spherical and shallow geometry are considered in detail. The equations obtained can be used to calculate the stress-strain state and simulate thin-walled structures at the macro, micro and nanoscale, taking into account the micropolar stresses and the effects of rotation. [ABSTRACT FROM AUTHOR]

Starting from the variational principle of virtual power for the three-dimensional equations of the micropolar theory of elasticity and using generalized series in terms of the plate thickness coordinates a new higher order models of orthotropic micropolar plates have been developed here for the first time. Following carrera unified formulation, the stress and strain tensors, as well as the vectors of displacements and rotation, have been expanded into series in terms of the plate 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 series expansion on the plate thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the series expansion of the plate thickness coordinates have been obtained in the same way as in the classical theory of elasticity. All equations for the higher order theory of micropolar plates have been developed and presented here. The case of complete linear expansion has been considered in detail and compared with the theories based on shear deformation and Kirchhoff hypothesis. 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Starting from the variational principle of virtual power for the 3-D equations of the micropolar theory of elasticity in orthogonal curvilinear coordinates and using generalized series in terms of the plate thickness coordinates a new higher order model of orthotropic micropolar plates and shells have been developed here. Following Carrera Unified Formulation (CUF), the stress and strain tensors, as well as the vectors of displacements and rotation, have been expanded into series 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 series expansion on the plate thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the series expansion of the shell thickness coordinates have been obtained in the same way as in the classical theory of elasticity. All equations for the higher order 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Navier's closed-form solution for the higher order theory of micropolar plates based on the CUF approach has been developed here. Obtained using a principle of virtual displacements the 2D system of the differential equations for the higher order theory of micropolar elastic plates is solved here for the case of simply supported plates using Navier's method of the variables separation. For the higher order theory of micropolar plates developed here, which is based on CUF, some numerical examples have been done and the influence the rotation field on the stress–strain fields has been analyzed. Methods of determination of the classical and micropolar elastic moduli of different materials have been analyzed, and available experimental data have been presented in Nowacki's notations. 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. [ABSTRACT FROM AUTHOR]

New higher order models of micropolar plates and shells have been developed here. The 3-D dynamic equations of the micropolar elasticity have been presented in an orthogonal system of coordinates using a generalized variational principle. For the creation of 2-D models of plates and shells the curvilinear system of coordinates related to the middle surface of the shell have been used along with a special hypothesis based on assumptions that take into account the fact that the rod is thin. Higher order theory is based on a generalized variational principle and the expansion of the 3-D equations of themicropolar theory of elasticity into Fourier series in terms of Legendre polynomials. The stress and strain tensors, as well as vectors of displacements and rotation have been expanded into Fourier series in terms of Legendre polynomials with respect to thickness. Thereby, all equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the Legendre polynomials coefficients. Then, in the same way as in the classical theory of elasticity, a system of differential equations in terms of displacements and rotation with initial and boundary conditions for the Legendre polynomials coefficients have been obtained. All equations for higher order theory of micropolar plates in Cartesian and polar coordinates as well as for cylindrical and spherical shells in coordinates related to the shells geometry have been developed and presented here in detail. The obtained equations can be used for calculating the stress-strain and for modelling thin walled structures in macro, micro and nano scale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]