Article
Materials Science, Multidisciplinary
E. Carrera, V. V. Zozulya
Summary: Based on the variational principle of virtual power and generalized series expansion, a new higher order model of orthotropic micropolar plates and shells in orthogonal curvilinear coordinates has been developed. The obtained equations can be used to calculate stress-strain and model thin-walled structures at different scales, taking into account micropolar couple stress and rotation effects.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Materials Science, Multidisciplinary
E. Carrera, V. V. Zozulya
Summary: A new higher order model of orthotropic micropolar plates was developed using the variational principle and generalized series expansion, transforming the equations of the micropolar theory of elasticity for coefficients of the series expansion. This theory can be used for stress-strain calculations and modeling of thin-walled structures at different scales, taking into account micropolar couple stress and rotation effects.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Mechanics
E. Carrera, V. V. Zozulya
Summary: Navier's closed-form solution for the higher order theory of micropolar plates based on the CUF approach has been developed. By using the principle of virtual displacements, the 2D system of differential equations for the higher order theory of micropolar elastic plates is solved. Numerical examples have been conducted to analyze the influence of rotation field on stress-strain fields.
ARCHIVE OF APPLIED MECHANICS
(2021)
Article
Materials Science, Multidisciplinary
E. Carrera, V. V. Zozulya
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.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Thermodynamics
E. Carrera, V. V. Zozulya
Summary: In this study, an analytical form Navier solution based on the CUF approach was developed for the higher-order micropolar theory of cylindrical shell. The cases of complete linear expansion and model based on Timoshenko-Mindlin shear deformation hypothesis were considered in detail. By solving the two-dimensional system of differential equations using the Navier variable separation method, the influence of the rotational field and micropolar couple stress on the stress-strain state was analyzed. The equations presented in this study can be used for stress-strain calculation and thin-walled structures modeling in macro-, micro-, and nanoscale, while considering the effects of micropolar couple stress and rotation.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2022)
Article
Materials Science, Multidisciplinary
V. V. Zozulya, E. Carrera
Summary: This study discusses the theory of micropolar plates and shells based on the hypotheses of Timoshenko-Mindlin and Kirchhoff-Love, and presents equations for calculating stress-strain states and simulating thin-walled structures, taking into account micropolar stresses and rotation effects.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Materials Science, Multidisciplinary
A. Czekanski, V. V. Zozulya
Summary: New higher-order models based on the linear theory of nonlocal elasticity are developed for plane rods and beams. These models are used to analyze tension-compression and transverse bending modes of nonlocal rod and beam vibration. By considering nonlocal effects, the proposed models can be applied to vibration analysis of rods and beams at macroscales, microscales, and nanoscales.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2021)
Article
Mechanics
Behnam Daraei, Saeed Shojaee, Saleh Hamzehei-Javaran
Summary: In this study, thermo-mechanical analysis of functionally graded material beams using micropolar theory is conducted based on the higher-order model in the framework of the Carrera unified formulation (CUF). The analysis considers the nonhomogeneous mechanical and thermal properties of the beams and takes into account the effect of the nonlinear temperature rise profile. Numerical examples demonstrate the influence of thermal loadings, power law indexes, orders of expansion and boundary conditions on the results. The equations can be applied to analyze beam structures in macro-, micro-, and nano-scale by considering micropolar couple stress and micro-rotation effects.
ARCHIVE OF APPLIED MECHANICS
(2023)
Article
Mechanics
E. Carrera, V. V. Zozulya
Summary: This paper develops higher order models of elastic shells of revolution using the variational principle of virtual power. By expanding the stress and strain tensors, as well as the displacement vector, in terms of the coordinates of the shell thickness, the equations of the linear theory of elasticity are transformed into corresponding equations for the expansion coefficients. These equations can be used for theoretical analysis and calculation of the stress-strain state, as well as for modeling thin-walled structures.
Article
Materials Science, Multidisciplinary
Xiangyang Xu, Nasim Fallahi, Hao Yang
Summary: This paper presents a refined finite element method based on the Carrera Unified Formula to analyze the free vibration of thin-walled beams with variable cross-section, length, and boundary. The one-dimensional CUF model is employed, and the geometry of the beams is discretized into one-dimensional elements along the axis, with the displacement field approximated using Lagrange polynomial expansion. Comparative studies show that the method is effective and capable for structural analysis of complex cross-section thin-walled beams.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Engineering, Civil
Van-Thien Tran, Trung-Kien Nguyen, Phong T. T. Nguyen, Thuc P. Vo
Summary: This paper proposes a unified higher-order shear deformation theory for stochastic vibration and buckling analysis of functionally graded microplates. The effects of different parameters on the critical buckling loads and natural frequencies of the microplates are investigated using the polynomial chaos expansion method and probability distribution. The results demonstrate the efficiency and accuracy of the proposed approach.
THIN-WALLED STRUCTURES
(2022)
Article
Engineering, Mechanical
Soomin Choi, Yoon Young Kim
Summary: This study proposes a new higher-order Vlasov torsion theory that includes desired torsion-related modes and provides explicit F-U and sigma-F relations consistent with Vlasov theory. By expressing the orthogonal sectional mode shapes relation, explicit relations for F-U and sigma-F are established, improving solution accuracy. This theory shows promise in interpreting physical significance of generalized forces and deriving explicit equilibrium conditions among generalized forces.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Engineering, Multidisciplinary
M. H. Nagaraj, J. Reiner, R. Vaziri, E. Carrera, M. Petrolo
Summary: This paper presents a refined progressive damage analysis method for fiber-reinforced laminated composites under compressive loads, utilizing higher-order structural theories and numerical assessments to verify its effectiveness.
COMPOSITES PART B-ENGINEERING
(2021)
Article
Engineering, Mechanical
Jaeyong Kim, Gang-Won Jang, Yoon Young Kim
Summary: In this study, a new method is proposed to address the issue of connection conditions for higher-order beam elements. The proposed method utilizes the vertices and intersection points of a joint section and imposes continuity conditions using Lagrange multipliers. Unlike previous studies, this method is applicable to beam frame structures with general section shapes without relying on geometric conditions.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2022)
Article
Materials Science, Multidisciplinary
Himanshu Sharma, Shuvajit Mukherjee, Ranjan Ganguli
Summary: In this work, a combination method called STSEM is proposed for computing the stochasticity of a higher-order sandwich composite beam with spatial variability in the material properties. The efficiency of both SSFEM and TSEM is utilized for uncertainty analysis of the sandwich beam, and sensitivity analysis of the material properties is performed.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Materials Science, Multidisciplinary
V. V. Zozulya
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2019)
Article
Materials Science, Multidisciplinary
A. Czekanski, V. V. Zozulya
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2020)
Article
Materials Science, Multidisciplinary
A. Czekanski, V. V. Zozulya
Summary: New higher-order models based on the linear theory of nonlocal elasticity are developed for plane rods and beams. These models are used to analyze tension-compression and transverse bending modes of nonlocal rod and beam vibration. By considering nonlocal effects, the proposed models can be applied to vibration analysis of rods and beams at macroscales, microscales, and nanoscales.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2021)
Article
Mechanics
A. Czekanski, V. V. Zozulya
ARCHIVE OF APPLIED MECHANICS
(2020)
Article
Materials Science, Multidisciplinary
E. Carrera, V. V. Zozulya
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.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Materials Science, Multidisciplinary
E. Carrera, V. V. Zozulya
Summary: Based on the variational principle of virtual power and generalized series expansion, a new higher order model of orthotropic micropolar plates and shells in orthogonal curvilinear coordinates has been developed. The obtained equations can be used to calculate stress-strain and model thin-walled structures at different scales, taking into account micropolar couple stress and rotation effects.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Mechanics
E. Carrera, V. V. Zozulya
Summary: Navier's closed-form solution for the higher order theory of micropolar plates based on the CUF approach has been developed. By using the principle of virtual displacements, the 2D system of differential equations for the higher order theory of micropolar elastic plates is solved. Numerical examples have been conducted to analyze the influence of rotation field on stress-strain fields.
ARCHIVE OF APPLIED MECHANICS
(2021)
Article
Materials Science, Multidisciplinary
E. Carrera, V. V. Zozulya
Summary: A new higher order model of orthotropic micropolar plates was developed using the variational principle and generalized series expansion, transforming the equations of the micropolar theory of elasticity for coefficients of the series expansion. This theory can be used for stress-strain calculations and modeling of thin-walled structures at different scales, taking into account micropolar couple stress and rotation effects.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Materials Science, Multidisciplinary
A. Martynenko, V. V. Zozulya
Summary: An improved mathematical model of soft heart tissue is presented, considering both passive and active phases of cardiac tissue deformation. Nonlinear material equations derived from nonequilibrium thermodynamics principles are used, along with coupled equations of mechanochemical kinetics to account for muscle contraction in the active phase. The proposed model is suitable for computer modeling of the heart and circulatory system.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2021)
Article
Materials Science, Multidisciplinary
V. V. Zozulya, E. Carrera
Summary: This study discusses the theory of micropolar plates and shells based on the hypotheses of Timoshenko-Mindlin and Kirchhoff-Love, and presents equations for calculating stress-strain states and simulating thin-walled structures, taking into account micropolar stresses and rotation effects.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Mechanics
E. Carrera, V. V. Zozulya
Summary: In this study, a Navier closed-form solution method for higher-order elastic shells of revolution developed using the CUF approach is presented. The method is applied to cylindrical shells supported on the edges and axisymmetric shells, as well as shallow spherical shells with rectangular planform. The resulting equations can be used for theoretical analysis, stress-strain state calculation, and thin-walled structure modeling and finite element analysis benchmarking.
Article
Mechanics
E. Carrera, V. V. Zozulya
Summary: This paper develops higher order models of elastic shells of revolution using the variational principle of virtual power. By expanding the stress and strain tensors, as well as the displacement vector, in terms of the coordinates of the shell thickness, the equations of the linear theory of elasticity are transformed into corresponding equations for the expansion coefficients. These equations can be used for theoretical analysis and calculation of the stress-strain state, as well as for modeling thin-walled structures.
Article
Thermodynamics
E. Carrera, V. V. Zozulya
Summary: In this study, an analytical form Navier solution based on the CUF approach was developed for the higher-order micropolar theory of cylindrical shell. The cases of complete linear expansion and model based on Timoshenko-Mindlin shear deformation hypothesis were considered in detail. By solving the two-dimensional system of differential equations using the Navier variable separation method, the influence of the rotational field and micropolar couple stress on the stress-strain state was analyzed. The equations presented in this study can be used for stress-strain calculation and thin-walled structures modeling in macro-, micro-, and nanoscale, while considering the effects of micropolar couple stress and rotation.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2022)
Article
Materials Science, Multidisciplinary
E. Carrera, V. V. Zozulya
Summary: In this study, higher order models for elastic shells of revolution were developed using the variational principle of virtual power and generalized series. These models can be used for analyzing and calculating the stress-strain state of elastic shells and for modeling thin-walled structures used in science, engineering, and technology.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)