Theory Of Cylindrical Shells Research Articles

A Simple C0 quadrilateral thick/thin shell element based on the refined shell theory and the assumed strain fields

This is a companion paper of the authors' previous one. In this paper, a convenient form of the refined two-dimensional shell theory for the thick cylindrical shells proposed by the authors is given: and a simple and efficient C0 quadrilateral shell element is developed by the quasiconforming element technique. The element stiffness matrix presented here is given explicitly. This C0 thick/thin shell element satisfies the rigid body motion, passes the patch test and exhibits neither shear locking and membrane locking nor spurious kinematic modes. The numerical examples solved here demonstrate that the C0 quasi-conforming shell element gives very good results in the analysis of both thick and thin shells.

A refined dynamic theory for viscoelastic cylindrical shells and cylindrical laminated composites, Part 1: General theory

Through the use of a new technique, approximate theories are developed for the dynamic response of viscoelastic cylindrical shells and cylindrical laminated composites (CLC). The new technique eliminates the inconsistencies between the deformation shapes assumed over the thickness of the shell and the boundary or interface conditions to be satisfied on its lateral surfaces. Accordingly, the theory correctly predicts the dynamic behavior of shells or CLC without using any correction factors. Due to its length, the work is divided into two parts. The first part is devoted to the development of the approximate theories and the second part to the assessment. In this part, first the approximate equations of a single viscoelastic cylindrical shell are derived. Then, a discrete model (DM) is proposed for a composite made of viscoelastic laminae. In establishing DM, it is noted that the equations of a single shell hold also in each lamina of the composite. The equations of DM are completed by adding the interface continuity conditions to the above-mentioned equations. Finally, a continuum model (CM) is developed for a composite shell made of two alternating layers by using a smoothing operation. CM simplifies the determination of dynamic behavior of composite shells when the number of laminae is large.

A refined dynamic theory for viscoelastic cylindrical shells and cylindrical laminated composites, Part 2: An application

In this study, the general approximate theory developed in Part 1 for shells is assessed for axially symmetric elastic waves propagating in a closed circular cylindrical shell (hollow rod). The spectra predicted by zeroth and second order approximate theories are determined for various values of shell thicknesses and the Poisson ratios and they are compared with those of exact theory. It is found that the agreement between the two is good. Approximate and exact cut-off frequencies match almost exactly. The approximate theory is valid for thin as well as thick shells. These results, which are obtained without using correction factors, give an indication of the power of the general theories proposed in Part 1.

Formulation and Accuracy of the Circular Cylindrical Shell Theory Due to Higher Order Approximation

In this paper, the most general higher order equations of the three-dimensional static and dynamic theories for a circular cylindrical shell are derived by expanding the displacements into an infinite power series with respect to the radial coordinate of the shell. The present theory takes into account any higher order terms for both the static and dynamic problems. Several theories, which have been proposed, can be deduced by using the lower order terms of our theory. Three typical theories are the third-order theory, the Levinson theory and the Levinson-Voyiadjis-Baluch theory, which are redefined according to the present theory. Numerical results of natural frequencies for the simply supported cylindrical shell, as well as many other theories, are compared with the exact solutions.

Formulation and accuracy of a circular cylindrical shell theory due to a higher-order approximation.

Formulation and accuracy of a circular cylindrical shell theory due to a higher-order approximation.

Plane‐wave excitation of an infinite circular cylinder reinforced by a periodic set of rings

Analytical expressions are derived for the scattered field by an infinite fluid‐loaded cylindrical shell reinforced with the periodic set of rings and acoustically excited by an incident harmonic plane wave. Vibrations of the shell are treated using thin bending cylindrical shell theory by Kennard. The stiffeners interact with the cylindrical shell only through normal forces. Unknown quantities (i.e., scattered acoustic field, displacements of the shell) are expanded on the natural Bloch‐Floquet basis induced by the structure periodicity. Numerical simulations on a wide range frequency are reported, where the dimensionless product “ka” of the incident fluid wavenumber by the shell radius typically extends from 10−2 to 10−2, using a unique algorithm. Numerical predictions are compared with experimental data on different physical situations showing a good agreement. [Work supported by GERDSM.]

Dugdale model for circumferential through-cracks in pipes loaded by bending

The paper contains an analytical solution to the title problem by means of the semi-membrane theory of cylindrical shells. Results include the crack opening displacements as a function of circumferential angle, the fracture parameter J, and the effects of the crack on the compliance of the pipe.

Theory of cylindrical shells of anisotropic materials of different moduli

Theory of cylindrical shells of anisotropic materials of different moduli

Vibration Analysis of Rotating Cylindrical Shells Based on the Timoshenko Beam Theory

The basic equations for the beam-type vibration of rotating cylindrical shell are derived by the Timoshenko beam theory. The frequency analysis is presented for three kinds of boundary conditions and the validity of this model is examined by comparing the results with those based on the cylindrical shell theory. It is found that as for the natural frequencies of non-rotation, and rotation cylindrical shells and for the critical speeds reasonable results can be obtained by solving the problem on the basis of the Timoshenko beam theory.

Axisymmetrical impulsive responses of an infinite circular cylindrical shell filled with liquid.

In this paper, dynamic interaction phenomena on solid and liquid interfaces are discussed. Axisymmetrical responses of an infinite circular cylindrical shell perfectly filled with liquid are analyzed, based on Flugge's theory for a circular cylindrical shell and the potential theory for the ideal fluid under conditions of the impulsive external band pressure given on the outer surface of the shell. The deflection and the moment of the shell and the pressure in the fluid are evaluated by using the numerical inversion of the Laplace transformation method. The approximated solution for the shell with an equivalent mass on it is analyzed and is evaluated, abased on the solution for the solid and liquid interaction.

Characteristic roots of cylindrical shells based on an improved theory

This paper is concerned with the roots of the characteristic equation in the theory of circular cylindrical shells which contains the effect of shear deformation. An analytical method for finding the characteristic roots is first presented for the Mirsky-Herrmann type theory with five variables. A simplified improved theory with three variables similar to the classical theory is then derived by introducing approximations in the constitutive equations of the Mirsky-Herrmann theory. It is easily understood that the neglect of shear effect in the simplified theory leads to the well known classical Flugge theory. The roots of characteristic equations for the simplified and Flugge theory are compared with those of the Mirsky-Herrmann theory for the eigenfunctions in the longitudinal and circumferential directions.

Closure to “Discussion of ‘Theory of Orthotropic and Composite Cylindrical Shells, Accurate and Simple Fourth-Order Governing Equations’” (1985, ASME J. Appl. Mech., 52, p. 982)

Closure to “Discussion of ‘Theory of Orthotropic and Composite Cylindrical Shells, Accurate and Simple Fourth-Order Governing Equations’” (1985, ASME J. Appl. Mech., 52, p. 982)

Discussion: “Theory of Orthotropic and Composite Cylindrical Shells, Accurate and Simple Fourth-Order Governing Equations” (Cheng, S., and He, F. B., 1984, ASME J. Appl. Mech., 51, pp. 736–744)

Discussion: “Theory of Orthotropic and Composite Cylindrical Shells, Accurate and Simple Fourth-Order Governing Equations” (Cheng, S., and He, F. B., 1984, ASME J. Appl. Mech., 51, pp. 736–744)

Elasticity relations in the nonlinear theory of long cylindrical shells under a thermomechanic deformation

Elasticity relations in the nonlinear theory of long cylindrical shells under a thermomechanic deformation

Theory of Orthotropic and Composite Cylindrical Shells, Accurate and Simple Fourth-Order Governing Equations

A pair of complex conjugate fourth-order differential equations that govern the deformation of orthotropic circular cylindrical shells is presented. As shown in the paper, this pair of equations is as accurate as equations can be within the scope of the Kirchhoff assumptions. Also presented for the first time are several pairs of accurate and simple fourth-order equations which can be systematically and explicitly deduced from the previously mentioned pair of equations. Because of their accuracy and simplicity, these simple equations are of practical importance. The advantage in applying those fourth-order equations presented herein is that their solutions can be easily found in simple closed forms. This considerably simplifies calculations for solving problems of orthotropic and composite cylindrical shells as well as isotropic shells as a special case. Unlike other equations known in the literature, their general solutions remain unknown because of the algebraic complexities involved. The present method of deducing simple fourth-order equations improves upon the one used for isotropic shells in the first author’s previous paper entitled “Accurate Fourth-Order Equations for Circular Cylindrical Shells,” Journal of the Engineering Mechanics Division, ASCE, 1972.

Effect of shear deformation on thermal stresses in cylindrical shells

A theory of cylindrical shell including the shear deformation is developed and its effect on the thermal displacements and the thermal stresses are investigated. The theory presented in this work is a refined version of the Donnell type improved theory given earlier and a reduction method of the system of equation with five unknowns to one with three unknowns is proposed. In numerical examples for cylindrical shells under heat sources the thermal displacements and the thermal stresses in the present and the Donnell type theories are examined and are discussed together with those in the classical theories.

Analysis of Circular Cylindrical Shells

The paper is an account of the present state of the linear theory of circular cylindrical shells, problems of current interest, and in a broad sense the analytical methods that can be brought to bear on these problems.

Axisymmetric Vibrations of Conical Shells with Variable Thickness

In this paper, the axisymmetric free vibrations of truncated conical shells are analyzed by means of an improved shell theory. The equations of vibration and the boundary conditions are obtained from the stational condition of Lagrangian of the shells. The equations of vibration are solved exactly by a solution in series for a conical shell with linearly varied thickness along its axis and the effects of boundary conditions, thickness and semi-vertex angle on the natural frequencies are investigated. As a special case of the conical shell, we compare this theory with Mindlin's circular plate theory and with Mirsky's cylindrical shell theory.

Axisymmetric Vibrations of a Cylindrical Shell with Varying Thickness

In this paper, we analyze the axisymmetric vibrations of a cylindrical shell of which the thickness varies in the axial direction by using the thin cylindrical shell theory and an improved thick cylindrical shell theory. We solve the equations of vibration exactly by using a series solution. As numerical examples, we obtain the natural frequencies and the mode shapes of cylindrical shells with both ends clamped, simply supported and free and examine the variations of the natural frequencies and the mode shapes for the variations of the thickness. And also, we make clear the influences of the shear deformation and the rotatory inertia upon the natural frequencies and the mode shapes.

The Lowest Order Second-Approximation Theory of Circular Cylindrical Shells and a Simplified Equation

円筒かくの最低次の二次近似理論を構成し,三つの変位成分で表した微分方程式を導く.この理論は三次元効果を含んでおり,Love-Kirchhoffの仮定を前提として構成することはできない.次にこの理論を簡略化することにより,簡易方程式を導く.たわみ量の微分方程式の固有値の比較によれば,Morley-Koiterの式は,二次近似理論からみても,広い範囲で正確であること,上記簡易方程式も実用上かなりの精度が期待できること,が明らかになる.