Circular Cylindrical Shell Panels Research Articles

Identification of the validity range of Donnell and Sanders shell theories using an exact vibration analysis of functionally graded thick cylindrical shell panel

Free vibration of Levy-type thick functionally graded (FG) circular cylindrical shell panels is investigated to identify the validity range of two common shell theories namely Donnell and Sanders theories. FG material properties change through the thickness direction according to a power law distribution. The state space approach is applied to solve the problem. The present results are compared with those of the literature and a 3D finite element model for isotropic and FG materials. The effects of various geometry and material parameters on the validity range of these theories are studied for different boundary conditions. The results show that unlike Sanders theory, Donnell one cannot accurately capture natural boundary conditions such as force and moment resultants.

Out-of-plane stresses in composite shell panels: layerwise and elasticity solutions

Boundary-layer effects in lengthy cross-ply laminated circular cylindrical shell panels under uniform axial extension are investigated by two analytical solutions. First, Reddy's layerwise theory with state-space approach is utilized to determine the local interlaminar stresses. In this method, the general displacement field is discretized through the shell thickness by a linear shape function. When the shell panel is subjected to an axial force, the axial strain is estimated by an equivalent single-layer theory. Second, the stress-function approach along with Fourier series expansion is applied to develop a novel elasticity solution. The elasticity solution, which is based on simply-support edge conditions, is presented to show the effectiveness of the first solution. The numerical results show good agreements. Interlaminar stresses within various symmetric and unsymmetric cross-ply composite shell panels are then calculated and discussed. It is shown that the normal out-of-plane stress can get high magnitudes along the physical interfaces.

Use of the differential quadrature method for the buckling analysis of cylindrical shell panels

Buckling loads are determined for thin isotropic circular cylindrical shell panels subject to radial pressure using the new differential quadrature method. The Budiansky stability theory serves as the basis of the analysis. For this problem involving four boundary lines a two-dimensional approach is used, and a detailed convergence study is carried out to determine the appropriate analysis parameters for the method. Numerical results are determined for a total of twelve cylindrical shell panel cases for a number of different boundary support conditions. The results are compared with analytical and finite element method results. Conclusions are drawn about the technical significance of the results and the solution process.

Static Analysis of Infinite Laminated Cylindrical Shell Panel

This paper presents an approximate three-dimensional elasticity solution for an infinitely long, cross-ply laminated circular cylindrical shell panel with simply supported boundary conditions, subjected to an arbitrary discontinuous transverse loading. The solution is based on the principal assumption that the ratio of the thickness of the lamina to its middle surface radius is negligible compared to unity. The validity of this assumption and the range of application of this approximate solution have been established through a comparison with an exact solution. Results of classical and first-order shear deformation shell theories have been compared with the results of the present solution to bring out the accuracy of these theories. It is also shown that for very shallow shell panels the definition of a thin shell should be based on the ratio of thickness to chord width rather than the ratio of thickness to mean radius.

Exact piezoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending

This work presents an exact piezoelastic solution of an infinitely long, simply-supported, orthotropic, piezoelectric, radially polarised, circular cylindrical shell panel in cylindrical bending under pressure and electrostatic excitation. The general solution of the governing differential equations is obtained by separation of variables. The displacements and electric potential are expanded in appropriate trigonometric Fourier series in the circumferential coordinate to satisfy the boundary conditions at the simply-supported longitudinal edges. The governing equations reduce to Euler Cauchy type of ordinary differential equations. Their general solution involves six constants for each Fourier component. These are solved from the algebraic equations obtained by satisfying the boundary conditions at the lateral surfaces. The solution of the inverse problem of inferring the applied pressure field from the given measured distribution of electrical potential difference between the lateral surfaces of the shell has also been presented. Numerical results are presented for typical pressure and electrostatic loadings for various values of radius to thickness ratio.

Exact piezothermoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending

This work presents an exact piezothermoelastic solution of infinitely long, simply supported, cylindrically orthotropic, piezoelectric, radially polarised, circular cylindrical shell panel in cylindrical bending under thermal and electrostatic excitation. The general solution of the governing differential equations is obtained by separation of variables. The displacements, electric potential and temperature are expanded in appropriate Fourier series in the circumferential coordinate to satisfy the boundary conditions at the simply-supported longitudinal edges. The governing equations reduce to Euler-Cauchy type of ordinary differential equations. Their general solution involves six constants for each Fourier component. These are solved from the algebraic equations obtained by satisfying the boundary conditions at the lateral surfaces. The solution of the inverse problem of inferring the applied temperature field from the given measured distribution of electrical potential difference between the lateral surfaces of the shell has also been presented. Numerical results are presented for typical thermal and electrostatic loadings for various values of radius to thickness ratio.

Analysis of a Long Thick Orthotropic Circular Cylindrical Shell Panel

An exact three-dimensional elasticity solution has been obtained for an infinitely long, thick transversely isotropic circular cylindrical shell panel, simply supported along the longitudinal edges and subjected to a radial patch load. Using a set of three displacement functions, the boundary value problem is reduced to Bessel's differential equation. Numerical results are presented for different thickness to mean radius ratios and semicentral angles of the shell panel. Classical and first-order shear deformation orthotropic shell theories have been examined in comparison with the present elasticity solution.

Assessment of shell theories for the static analysis of cross-ply laminated circular cylindrical shells

This paper examines the accuracy of classical shell theories (CST) according to Flugge, Sanders, Love and Donnell, with respect to the recently available three-dimensional elasticity solution, for cross-ply laminated circular cylindrical shells under static loads. Further, a study has also been made to examine to what extent incorporation of first order shear deformation (FSDT), in aforementioned shell theories, improves the results. In general, all the basic equations (for both CST and FSDT), of aforementioned shell theories, have been presented in a unified form using tracer coefficients. A Navier type solution has been used to analyse both a simply supported circular cylindrical shell of revolution and an all round simply supported circular cylindrical shell panel. A parametric study has been carried out keeping in view the lamination schemes and geometrical parameters of the shell. From the detailed comparisons of the results it has been shown that (i) Donnell's theory (CST and FSDT) could be in error for certain lamination schemes and geometrical parameters and (ii) improved results for stresses and displacements could be obtained by incorporating shear deformation on more accurate theory like Flugge (CST).

Thermally induced vibration of laminated circular cylindrical shell panels

This work is concerned with a two-dimensional finite element study of the transient response of laminated thin circular cylindrical shell panels subjected to thermal impact under the framework of linear coupled thermoelasticity. A nine-node isoparametric element is applied to the FEM formulation. Numerous examples are given, in which the shell panels are assumed to be thermally isolated at four edges and the bottom surfaces and a heat flux is then imposed suddenly on their top surfaces. The effects of boundary conditions, ply-angles and radii of curvature are discussed. In addition, the differences between uncoupled and coupled problems are especially addressed.

Supersonic flutter of laminated circular cylindrical shell panels

OMPOSITE materials are used in the construction of curved panels of aircraft and space vehicles. Only a few works1'3 are available on panel flutter analysis of shell panels. In this investigation, circular cylindrical shell panels of rectangular planform, with edges clamped laterally and free from in-plane stresses (movable edges), are considered. The panel is subjected to supersonic flow parallel to the generator on one side only. The aerodynamic forces are approximated by using two-dimensional quasisteady aerodynamic theory. The problem is solved by using the integral equation technique. Formulation A typical cross-ply laminated panel is shown in the inset of Fig. 1. Two fourth-order aeroelastic governing differential equations, based on DonnelPs shallow shell approximation, can be derived in terms of the transverse displacement w and stress function F.4 They are

Vibration and buckling characteristics of composite cylindrical panels incorporating the effects of a higher order shear theory

An analytical study is conducted to determine the fundamental frequencies and critical buckling loads for laminated anisotropic circular cylindrical shell panels, including the effects of transverse shear deformation and rotary inertia, by using the Galerkin technique. A linearized form of Sander's shell strain-displacement relations are derived, which include a parabolic distribution of transverse shear strains. The theory is valid for laminate thickness to radius ratios h/R of up to 1/5. Higher order constitutive relations are derived for the laminate. A set of five coupled partial differential equations of motion and boundary conditions are derived and then solved using the modified Galerkin technique. Simply supported and clamped boundary conditions are investigated. Comparisons are made with the Donnell shell solutions. The effects of transverse shear deformation and rotary inertia arc examined by comparing the results with classical solutions, where applicable. The radius of curvature is varied to determine the effects of membrane and bending coupling. The theory compares exactly with the Donnell solutions, which are valid up to 1/50. As expected, as length to thickness ratios are reduced, shear deformation effects significantly lower the natural frequencies and buckling loads. Analysis also shows that rotary inertia effects are very small. Finally, as h/R is varied from 0 (flat plate) to 1/5. (maximum limit), the frequencies and buckling loads increase due to membrane and bending coupling.