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AbstractHere, natural frequencies and mode shapes for axisymmetric vibration of the composite laminate shells of revolution have been considered using the Unified Carrera Formulation (CUF) approach. For the first time, results of natural frequencies and mode shapes of complex geometry shells such as spherical, parabolic, elliptical, hyperbolic, catenoidal, toroidal and pseudospherical have been presented. Calculations have been done for the first, second, third, fourth and fifth order models and a comparison with the classical Timoshenko model. We consider thick, moderately thick, moderately thin and thin composite laminate shells. The higher-order layer-wise models of elastic composite multilayer shells of revolution are developed using the variational principle of virtual power for the 3-D linear anisotropic elastodynamics and generalized series in the thickness coordinates. The higher-order composite axisymmetric spherical, paraboloidal, elliptical, hyperbolic, catenoidal, toroidal and pseudo-spherical shell fixed at the ends are considered. Numerical calculations were performed using the computer algebra software Mathematica. The resulting equations have been used for theoretical analysis and calculation of the eigenvalues and eigenmodes of the higher-order shells of revolution used in science, engineering, and technology. The results of calculation can be used as benchmark examples for finite element analysis of the higher-order composite laminate shells. [ABSTRACT FROM AUTHOR]

Here, higher order models of elastic shells of revolution are developed using the variational principle of virtual power for 3-D equations of the linear theory of elasticity and generalized series in the coordinates of the shell thickness. Following the Carrera Unified Formulation (CUF), the stress and strain tensors, as well as the displacement vector, were expanded into series in terms of the coordinates of the shell thickness. As a result, all the equations of the theory of elasticity were transformed into the corresponding equations for the expansion coefficients in a series in terms of the coordinates of the shell thickness. All equations for shells of revolution of higher order are developed and presented here for cases whose middle surfaces can be represented analytically. The resulting equations can be used for theoretical analysis and calculation of the stress-strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. [ABSTRACT FROM AUTHOR]

Here, higher order models of elastic composite multilayer shells of revolution are developed using the variational principle of virtual power for the 3-D linear anisotropic theory of elasticity and generalized series in the shell thickness coordinates. Following the Unified Carrera Formula (CUF), the stress and strain tensors, as well as the displacement vector, were expanded into series in terms of the coordinates of the shell thickness. The higher-order cylindrical shell supported on the edges under axisymmetric loading, is considered and solved analytically using a Navier close form solution method. Also, composite axisymmetric circular plated as well as parabolic, hyperbolic and pseudo-spheric shell fixed ate the ends are considered. Numerical calculations were performed using the computer algebra software Mathematica. The resulting equations can be used for theoretical analysis and calculation of the stress-strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. The results of calculation can be used as benchmark examples for finite element analysis of the higher order elastic shells. [ABSTRACT FROM AUTHOR]

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]

An improved mathematical model of soft heart tissue has been developed here. Nonlinear material equations were derived from the fundamental principles of nonequilibrium thermodynamics. The passive and active phases of cardiac tissue deformation are considered using the nonlinear theory of hyperelasticity. Elastic potentials for both phases are presented in a simple form convenient for numerical calculations. To take into account muscle contraction in the active phase of deformation, coupled equations of mechanochemical kinetics are obtained. The proposed model can be used for computer modeling of the heart and circulatory system. [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]