Closed form solution for displacements of thick cylinders with varying thickness subjected to non-uniform internal pressure

Eipakchi, H.R.,Rahimi, G.H.,Esmaeilzadeh Khadem, S. Techno-Press 2003 Structural Engineering and Mechanics, An Int'l Jou Vol.16 No.6

In this paper a thick cylindrical shell with varying thickness which is subjected to static non-uniform internal pressure is analyzed. At first, equilibrium equations of the shell have been derived by the energy principle and by considering the first order theory of Mirsky-Herrmann which includes transverse shear deformation. Then the governing equations which are, a system of differential equations with varying coefficients have been solved analytically with the boundary layer technique of the perturbation theory. In spite of complexity of modeling the conditions near the boundaries, the method of this paper is very capable of providing a closed form solution even near the boundaries. Displacement predictions are in a good agreement with the calculated finite elements and other analytical results. The convergence of solution is very fast and the amount of calculations is less than the Frobenius method.

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

Hamidreza Eipakchi,Farid Mahboubi Nasrekani 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.43 No.2

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.

Response determination of a viscoelastic Timoshenko beam subjected to moving load using analytical and numerical methods

Tehrani, Mohammad,Eipakchi, H.R. Techno-Press 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.44 No.1

In this paper the dynamic behavior of a viscoelastic Timoshenko beam subjected to a concentrated moving load are studied analytically and numerically. The viscoelastic properties of the beam obey the linear standard model in shear and incompressible in bulk. The governing equation for Timoshenko beam theory is obtained in viscoelastic form using the correspondence principle. The analytical solution is based on the Fourier series and the numerical solution is performed with finite element method. The effects of the material properties and the load velocity are investigated on the responses by numerical and analytical methods. In addition, the results are compared with the Euler beam results.

Effect of different viscoelastic models on free vibrations of thick cylindrical shells through FSDT under various boundary conditions

Hossein Daemi,Hamidreza Eipakchi 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.73 No.3

This paper investigates the free vibrations of cylindrical shells made of time-dependent materials for different viscoelastic models under various boundary conditions. During the extraction of equations, the displacement field is estimated through the first-order shear deformation theory taking into account the transverse normal strain effect. The constitutive equations follow Hooke's Law, and the kinematic relations are linear. The assumption of axisymmetric is included in the problem. The governing equations of thick viscoelastic cylindrical shell are determined for Maxwell, Kelvin-Voigt and the first and second types of Zener’s models based on Hamilton’s principle. The motion equations involve four coupled partial differential equations and an analytical method based on the elementary theory of differential equations is used for its solution. Relying on the results, the natural frequencies and mode shapes of viscoelastic shells are identified. Conducting a parametric study, we examine the effects of geometric and mechanical properties and boundary conditions, as well as the effect of transverse normal strain on natural frequencies. The results in this paper are compared against the results obtained from the finite elements analysis. The results suggest that solutions achieved from the two methods are ideally consistent in a special range.

Response determination of a viscoelastic Timoshenko beam subjected to moving load using analytical and numerical methods

Mohammad Tehrani,H.R. Eipakchi 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.44 No.1

In this paper the dynamic behavior of a viscoelastic Timoshenko beam subjected to a concentrated moving load are studied analytically and numerically. The viscoelastic properties of the beam obey the linear standard model in shear and incompressible in bulk. The governing equation for Timoshenko beam theory is obtained in viscoelastic form using the correspondence principle. The analytical solution is based on the Fourier series and the numerical solution is performed with finite element method. The effects of the material properties and the load velocity are investigated on the responses by numerical and analytical methods. In addition, the results are compared with the Euler beam results.

Geometry and load effects on transient response of a VFGM annular plate: An analytical approach

Seyed Hashem Alavi,Hamidreza Eipakchi 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.70 No.2

In this article, the effect of different geometrical, materials and load parameters on the transient response of axisymmetric viscoelastic functionally graded annular plates with different boundary conditions are studied. The behavior of the plate is assumed the elastic in bulk and viscoelastic in shear with the standard linear solid model. Also, the graded properties vary through the thickness according to a power law function. Three types of mostly applied transient loading, i.e., step, impulse, and harmonic with different load distribution respect to radius coordinate are examined. The motion equations and the corresponding boundary conditions are extracted by applying the first order shear deformation theory which are three coupled partial differential equations with variable coefficients. The resulting motion equations are solved analytically using the perturbation technique and the generalized Fourier series. The sensitivity of the response to the graded indexes, different transverse loads, aspect ratios, boundary conditions and the material properties are investigated too. The results are compared with the finite element analysis.

Axisymmetric Buckling of Cylindrical Shells with Nonuniform Thickness and Initial Imperfection

Farid Mahboubi Nasrekani,Hamidreza Eipakchi 한국강구조학회 2019 International Journal of Steel Structures Vol.19 No.2

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 fi rst order shear deformation theory. The imperfection is considered as an axisymmetric continuous radial displacement. The strain–displacement relations are defi ned using the nonlinear von-Karman formulas. The constitutive equations obey Hook e ’s law. The equilibrium equations are nonlinear ordinary diff erential equations with variable coeffi cients. The stability equations are determined from them. The stability equations are a system of coupled linear ordinary diff erential equations with variable coeffi cients. The results are compared with the fi nite element method and some other references.

Free vibration behavior of viscoelastic annular plates using first order shear deformation theory

Saeed Khadem Moshir,Hamidreza Eipakchi,Fatemeh Sohani 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.62 No.5

In this paper, an analytical procedure based on the perturbation technique is presented to study the free vibrations of annular viscoelastic plates by considering the first order shear deformation theory as the displacement field. The viscoelastic properties obey the standard linear solid model. The equations of motion are extracted for small deflection assumption using the Hamilton’s principle. These equations which are a system of partial differential equations with variable coefficients are solved analytically with the perturbation technique. By using a new variable change, the governing equations are converted to equations with constant coefficients which have the analytical solution and they are appropriate especially to study the sensitivity analysis. Also the natural frequencies are calculated using the classical plate theory and finite elements method. A parametric study is performed and the effects of geometry, material and boundary conditions are investigated on the vibrational behavior of the plate. The results show that the first order shear deformation theory results is more closer than to the finite elements with respect to the classical plate theory for viscoelastic plate. The more results are summarized in conclusion section.