A closed-form solution for asymmetric free vibration analysis of composite cylindrical shells with metamaterial honeycomb core layer based on shear deformation theory

Asymmetric free vibration analysis of composite cylindrical shells with a honeycomb core layer and adjustable Poisson’s ratio is performed analytically in this study. The equations of motion which are a system of coupled partial differential equations are extracted using Hamilton’s principle by employing the first-order shear deformation theory and they are solved analytically. To study the sensitivity of the results to the different parameters of the honeycomb structure, geometrical parameters, and boundary conditions, a parametric study is presented. It is concluded that for the auxetic composite shell with a negative Poisson’s ratio, by decreasing the Poisson ratio, the frequency decreases. Also, it is shown that by employing the composite shells the weight decreases significantly, while the asymmetric frequency will not change remarkably. By adjusting the Poisson ratio, the frequency variations are studied for a composite shell with a honeycomb core layer. The results are compared with the finite element method and some other references

Axisymmetric buckling of cylindrical shells with non - uniform thickness and initial imperfection

In this article, the axial buckling load of an axisymmetric cylindrical shell with nonuniform thickness is determined analytically with the initial imperfection by using the first order shear deformation theory. The imperfection is considered as an axisymmetric continuous radial displacement. The strain–displacement relations are defined using the nonlinear von-Karman formulas. The constitutive equations obey Hooke’s law. The equilibrium equations are nonlinear ordinary differential equations with variable coefficients. The stability equations are determined from them. The stability equations are a system of coupled linear ordinary differential equations with variable coefficients. The results are compared with the finite element method and some other references

An analytical procedure for buckling load determination of cylindrical shells with variable thickness using first order shear deformation theory

In this article, the buckling load of an axisymmetric cylindrical shell with a variable thickness is determined analytically by using the perturbation method. The loading is axial and the material properties are defined by the Hooke’s law. The displacement field is predicted by using the first order shear deformation theory and the nonlinear von-Karman relations are used for the kinematic description of the shell. The stability equations, which are the system of nonlinear differential equations with variable coefficients, are derived by the virtual work principle and are solved using the perturbation technique. Also, the buckling load is determined by using the finite element method and it is compared with the analytical solution results, the classical shell theory, and other references. The effects of linear and nonlinear shell profiles variation on the axial buckling load are investigated. Also, we studied the effects of geometric parameters on the buckling load results. The results show that the first order shear deformation theory is more useful for buckling load determination of thicker shells

Axisymmetric buckling of cylindrical shells with non - uniform thickness and initial imperfection

In this article, the axial buckling load of an axisymmetric cylindrical shell with nonuniform thickness is determined analytically with the initial imperfection by using the first order shear deformation theory. The imperfection is considered as an axisymmetric continuous radial displacement. The strain–displacement relations are defined using the nonlinear von-Karman formulas. The constitutive equations obey Hooke’s law. The equilibrium equations are nonlinear ordinary differential equations with variable coefficients. The stability equations are determined from them. The stability equations are a system of coupled linear ordinary differential equations with variable coefficients. The results are compared with the finite element method and some other references

Buckling analysis of super - light composite cylinders with auxetic core and isotropic facing sheets with variable thickness: an analytical approach

An analytical method is presented to determine the axial buckling load of composite cylindrical shells with honeycomb core layer and nonuniform thickness using the first-order shear deformation theory, the nonlinear von Karman theory, and the Hooke law relations. The composite shell consists of two isotropic inner and outer layers with non-uniform thicknesses and one honeycomb core with constant thicknesses and adjustable Poisson's ratio. The equilibrium equations are a system of nonlinear differential equations with variable coefficients, and they are derived by employing the virtual work principle. The equilibrium equations have been solved analytically using the matched asymptotic expansion method of the perturbation technique. The stability equations extracted using the adjacent criterion include a system of linear homogenous equations with variable coefficients. By solving these equations, the buckling load is obtained analytically. A parametric study investigates the effects of different geometrical and mechanical parameters such as the honeycomb structure on the buckling load. The metamaterial honeycomb core layer has an adjustable Poisson's ratio, and the effect of negative/positive Poisson's ratio has been studied on the buckling behavior. The accuracy of the presented method is studied by comparing the results with the finite element method and some other references in special cases

Axisymmetric analysis of auxetic composite cylindrical shells with honeycomb core layer and variable thickness subjected to combined axial and non-uniform radial pressures

An analytical method is proposed to determine the displacements of a composite cylindrical shell with auxetic honeycomb core layer and variable thickness under combined axial, internal, and external pressures. The thickness and pressure profiles can be arbitrary continuous functions. The displacements are defined in the framework of the first-order shear deformation theory. The composite shell consists of three layers, in which the inner and outer layers are isotropic and the core layer is made of an auxetic honeycomb material. The constitutive equations obey the Hooke law. The equilibrium equations which are a system of coupled differential equations with variable coefficients are extracted by employing the virtual work principle, and they are solved using the matched asymptotic expansion method of the perturbation technique. The effects of different parameters such as the geometry, honeycomb structure parameters, different load profiles, and the thicknesses on the results are studied. The results are compared with the finite element method and some other references

Geometrically nonlinear effect on forced vibrational behavior of superlight composite beams with auxetic core layer under harmonic excitation based on FSDT

The growing use of light composite materials in different industries such as automotive and aerospace has caused the need for more studies to analyze their behavior. In this study, an analytical solution for the nonlinear forced vibrational behavior of a multilayered superlight composite beam with a honeycomb core layer and adjustable Poisson’s ratio subjected to a harmonic excitation has been presented. The beam has two isotropic upper and lower layers with one honeycomb core layer. The Poisson’s ratio of the honeycomb core layer can be adjusted by changing the honeycomb cell parameters in a range of negative to positive values. The equations of motion have been extracted using the first-order shear deformation theory and nonlinear von Kármán relations. The equations are a system of coupled nonlinear partial differential equations that have been solved using the perturbation technique. To investigate the effect of different geometry and honeycomb cell parameters on the nonlinear response, a parametric study has been conducted. The effect of nonlinearity on the chaotic behavior and primary resonance is studied. The finite element method has been used to compare the results. It is observed that by adding a honeycomb layer, the total weight has been dropped by about 50% while the dynamic responses nearly remain the same

Analytical solution for buckling analysis of cylinders with varying thickness subjected to combined axial and radial loads

An analytical procedure has been proposed for buckling analysis of elastic cylindrical shells with varying thickness under combined axial and radial loads by considering the first-order shear deformation theory as the displacement filed. The kinematics of the problem is defined by the von-Karman relations, and the constitutive equation obeys Hooke's law. The equilibrium equations are a system of nonlinear coupled differential equations with variable coefficients and the corresponding stability equations which are a linear system with varying coefficients are solved to find the eigenvalues of the system. The results are compared with the finite element method and some other references

Analytical solution for buckling analysis of composite cylinders with honeycomb core layer

In this study, an analytical solution is presented to determine the buckling load of composite cylindrical shells with an auxetic honeycomb layer under a uniform axial load. The composite shell consists of three layers in which the core layer is made of the auxetic honeycomb structure with a negative Poisson’s ratio and the internal and external layers have been made of elastic and isotropic materials. The first-order shear deformation theory has been used as the displacement field. The equilibrium equations are determined by considering the von Kármán theory, and they are coupled nonlinear differential equations that are solved by employing the perturbation technique. The buckling load has been determined analytically by solving the stability equations, which are a system of coupled differential equations with variable coefficients. By conducting a parametric study, the effects of the honeycomb structure and the aspect ratios on the buckling load have been investigated. It is seen that by changing the geometrical parameters of the honeycomb structure, the Poisson ratio can be adjusted and the mechanical behavior of the composite shell has been modified. The results are compared with some other references and the finite element analysis

Nonlinear static analysis of composite cylinders with metamaterial core layer, adjustable Poisson’s ratio, and non - uniform thickness

In this article, an analytical procedure is presented for static analysis of composite cylinders with the geometrically nonlinear behavior, and non uniform thickness profiles under different loading conditions by considering moderately large deformation. The composite cylinder includes two inner and outer isotropic layers and one honeycomb core layer with adjustable Poisson’s ratio. The Mirsky Herman theory in conjunction with the von Karman nonlinear theory is employed to extract the governing equations which are a system of nonlinear differential equations with variable coefficients. The governing equations are solved analytically using the matched asymptotic expansion (MAE) method of the perturbation technique and the effects of moderately large deformations are studied. The presented method obtains the results with fast convergence and high accuracy even in the regions near the boundaries. Highlights: • An analytical procedure based on the matched asymptotic expansion method is proposed for the static nonlinear analysis of composite cylindrical shells with a honeycomb core layer and non-uniform thickness. • The effect of moderately large deformation has been considered in the kinematic relations by assuming the nonlinear von Karman theory. • By conducting a parametric study, the effect of the honeycomb structure on the results is studied. • By adjusting the Poisson ratio, the effect of auxetic behavior on the nonlinear results is investigated