Problem Of Cylindrical Shell Research Articles

Torsional, flexural, and torsional-flexural buckling modes of a cylindrical shell under combined loading

Stability problems for cylindrical shells under various loading modes were considered in numerous papers. A detailed analysis of such problems can be found, e.g., in the monograph [1]. We refer to the solutions presented in this monograph as classical. For long cylindrical shells in axial compression, one of the buckling modes is the purely beam flexural mode similar to the classical buckling mode of a straight rod. It is well known that it can be studied by using the nonlinear or linearized equations of the membrane theory of shells. In [2], it was shown that, on the basis of such equations constructed starting from the noncontradictory version of geometrically nonlinear elasticity relations in the quadratic approximation [3], under the separate action of the axial compression, external pressure, and torsion, there are also previously unknown nonclassical buckling modes, most of which are shear ones. In the present paper, we show that the use of the above equations for cylindrical shells under compression and external pressure with simultaneous pure torsion or bending permits revealing the earlier unknown torsional, beam flexural, and beam torsional-flexural buckling modes, which are nonclassical, just as those found in [2]. The second of these buckling modes is realized when axially compressing forces are formed in the shell with simultaneous torsion, and the third of them is realized under compression combined with pure bending. It was found that, earlier than the classical buckling modes, the torsional buckling modes can be realized for relatively short shells with small shear rigidity in the tangent plane, while the second and third buckling modes can be realized for relatively long shells.

Asymptotic method for analysis of a conical shell under local loading

Differential equations of the general theory describing the stress-strain state of conical shells are very complicated, and when computing the exact solution of the problem by analytic methods one encounters severe or even so far insurmountable difficulties. Therefore, in the present paper we develop an approach based on the method of asymptotic synthesis of the stressed state, which has already proved efficient when solving similar problems for cylindrical shells [1, 2]. We essentially use the fourth-order differential equations obtained by Kan [3], which describe the ground state and the boundary effect. Earlier, such equations have already been used to solve problems concerning force and thermal actions on weakly conical shells [4–6]. By applying the asymptotic synthesis method to these equations, we manage to obtain sufficiently accurate closed-form solutions.

Numerical and analytical study of severity of cracks in cylindrical and spherical shells

The present study deals with the severity of cracks in pressure equipments, where such defects are often involved. Our work is particularly concerned with the problem of cylindrical shells and also the little well-known problem of spherical shells, including all sorts of practical defects, namely axisymmetric or semi-elliptic, both internal and external cracks. The stress intensity factor in the linear elastic domain and the J integral in the elastoplastic range are performed using the finite element method and compared to the results provided by the application of the semi-analytical A16 or R6 simplified criteria, depending on a limit load calculation. The nocivity of the defects depends on the crack shape and size and other structural geometrical parameters. Use is made of a polynomial decomposition of the stress field in the vicinity of the crack in order to cover all industrial loadings. All the numerical results, for a wide range of shell and crack geometries, are depicted using appropriate tables and curves in order to check the fracture criteria more easily.

Nonconventional approaches to static problems for noncircular cylindrical shells in different formulations

Stress problems for noncircular cylindrical shells in classical, refined, and spatial statements are solved using nonconventional approaches based on discrete Fourier series and spline functions. Solutions for isotropic and orthotropic shells are presented as plots and tables

Stability of cylindrical shells made of a damageable physically nonlinear material

The bifurcation-instability problem for cylindrical shells made of physically nonlinear materials progressively damaged with increasing load is formulated and solved

On numerical solution of dynamic problems in the theory of reinforced shells

Dynamic problems for cylindrical shells reinforced with discrete ribs are examined. A numerical algorithm based on Richardson extrapolation is developed. Specific problems are solved, and the results are analyzed

Stress analysis of noncircular cylindrical shells with cross section in the form of connected convex half-corrugations

An approach is developed to solve the stress-strain problem for noncircular cylindrical shells with complex cross section in the form of connected convex half-corrugations. Numerical results are presented

Minimum Energy Characterizations for the Solution of Saint-Venant's Problem in the Theory of Shells

The linear theory of Cosserat surfaces is employed to study Saint-Venant's problem for cylindrical shells of arbitrary cross-section. We prove minimum energy characterizations for the solution of the relaxed Saint-Venant's problem previously obtained. Then, we determine the global measures of strain appropriate to extension, bending, torsion and flexure for certain classes of solutions to the relaxed problem.

Stability of Cylindrical Shells Made of Fibrous Composite with Damageable Matrix

The bifurcation stability problem for cylindrical shells made of fibrous composite with damageable matrix is formulated and solved

Application of Discrete Fourier Series in the Stress Analysis of Cylindrical Shells of Variable Thickness with Arbitrary End Conditions

An approach is proposed to solve boundary-value stress—strain problems for cylindrical shells with thickness varying in two coordinate directions. The approach employs discrete Fourier series to separate circumferential variables. This makes it possible to reduce the problem to a one-dimensional one, which can be solved by the stable discrete-orthogonalization method. Examples are given

Non-uniqueness in cylindrical shells optimization

Cylindrical shells are widely used in many structural designs, such as offshore structures, liquid storage tanks, submarine hulls, and airplane hulls. During the optimization process of cylindrical shells, one is faced with a set of very unique challenges. Unlike that of simpler structures such as beams or plates, the modal spectrum of cylindrical shell exhibits very unique characteristics. Mode crossing, uniqueness modal spectrum, and redundancy of modal constraints are just a few of the unique attributes faced during the optimization process. In cylindrical shells, the lowest natural frequency is not necessarily associated with the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index either. Solution of the vibration problem of cylindrical shells also indicates repeated natural frequencies. These modes are referred to as double peak frequencies. Mode shapes associated with each one of the natural frequencies are usually a combination of (i) radial (flexural), (ii) longitudinal (axial), and (iii) circumferential (torsional) modes. When a uniform shell is segmented longitudinally along its axis, the thickness optimization of the segment thicknesses will yield in a segmented shell with varying thickness segments. In this paper, the non-uniqueness in optimum design of cylindrical shells for vibration requirements is presented, and its implications are discussed. Related issues such as the new mode sequence, mode crossing, repeated natural frequencies and stationary modes are also discussed. The numerical results were compared with those obtained analytically. The analytical expressions for the equations of motion for segmented circular cylindrical shells are derived using Donnell–Mushtari. The eigenvalue problem of the analytical solution is then solved using a MATLAB program script to predict the natural frequencies and strain energy distribution for the various mode shapes in the modal spectrum.

Saint-Venant’s problem for Cosserat shells with voids

In this paper we investigate the mechanical behavior of Cosserat shells made from a material with voids. We formulate Saint-Venant’s problem for cylindrical shells and determine the solution of the relaxed problem. Then, we apply the theoretical results to study the deformation of circular cylindrical shells. We also compare the solution of Saint-Venant’s problem for Cosserat shells with corresponding results from the classical theory of shells.

Refined 15‐DOF triangular discrete degenerated shell element with high performances

AbstractA refined discrete degenerated 15‐DOF triangular shell element RDTS15 with high performances is proposed. For constructing the element displacement function, the exact displacement function of the Timoshenko's beam is used as the displacement on the element boundary, and the re‐constitute method for shear strain matrix is adopted. The proposed element can be used in the analysis of both moderate thick and thin plates/shells. Numerical examples presented show that the new model indeed possesses higher accuracy in the analysis of thin and thick plates/shells, and that it can pass the patch test required for the Kirchhoff thin plate elements, and also passed the inf–sup test for free cylindrical shell problems and satisfied both the bending‐ and membrane‐dominated test. Copyright © 2004 John Wiley Sons, Ltd.

Analysis of Stresses and Displacements in Orthotropic Noncircular Cylindrical Shells Under Centrifugal Loads

This paper addresses the class of stress–strain problems for thin orthotropic cylindrical shells of arbitrary cross section under centrifugal loads. Separating out the variables for a simply supported shell yields a system of ordinary differential equations for which the boundary-value problem is solved by a stable numerical method. Study is made of the distribution of displacements in shells of elliptical cross section versus the ratio of ellipse exes and the eccentricity of the axis of revolution relative to the geometrical axis of symmetry

Studying the Effect of the Spatial Frequency and Amplitude of Corrugation on the Stress–Strain State of Cylindrical Shells

An approach developed earlier to solve two-dimensional static problems for noncircular cylindrical shells is used to analyze the effect of the spatial frequency and amplitude of corrugation on the stress–strain state of shells. The results of the analysis are presented in the form of plots and tables

Uniform error estimates for a class of intermediate cylindrical shell problems

A uniform in thickness error estimate is obtained for a particular class of intermediate Koiter shell problems, solved with a classical conforming finite element method. The model problem is that of a cylinder under a class of irregular loads which, due to particular symmetries, allow a simplified reformulation on a one dimensional domain. The result is an almost hs error behavior in the H−1 dual norm, were s>0 depends on the load regularity. Such estimate is believable to be sharp (this additional claim is supported by some numerical tests).

Analysis of cracked plates and shells using “metis” finite element model

A special form finite element technique is presented for the calculation of displacement and stress field of cracked (or uncracked) plates and shells. The method based on a particular set of hybrid displacement finite element, namely “Metis elements”. Several numerical examples are considered to evaluate the performance of this model. For cracked plate in extension, the element HSM gives high accuracy in computation of stress intensity factors. For plate bending problem with or without crack, the element HSF presents also very good performance. The results are very close to the theoretical solutions of Timoshenko (without crack) and solutions of Chen, Sosa and Eischen (with crack). For the cylindrical shell problem, the present results are also in very good agreement with solutions proposed by Scordelis and Folias.

Efficient Higher-Order Shell Theory for Laminated Composites with Multiple Delaminations

A higher-order zigzag theory has been developed for laminated composite shells with multiple delaminations. General tensor-based formulation is developed for arbitrary curved shell with exact geometric description. A laminated shell theory with multiple delaminations for general lamination configurations is obtained by superposing a cubic varying displacement on a zigzag linearly varying displacement. The von Karman nonlinearity is included in the formulation for the potentialities of addressing problems requiring geometric nonlinearity such as large deflection and postbuckling problems. When top and bottom surface transverse shear stress free conditions and interface transverse shear continuity conditions including delamination interfaces are imposed the displacement of the minimal degrees of freedom is obtained. The proposed displacement field can systematically handle the number, shape, size, and locations of the delaminations. Through the variational principle, equilibrium equations and variationally consistent boundary conditions are obtained. To assess the accuracy and efficiency of the present theory, the linear buckling problem of cylindrical shell with multiple delaminations has been analyzed. The higher-order zigzag theory should work as an efficient tool for analyzing the behavior of composite laminated shells with multiple delaminations.

Analysis of Laminated Anisotropic Cylindrical Shell by Chebyshev Collocation Method

The governing equations of a laminated anisotropic cylindrical shell problem are a system of partial differential equations. The boundary conditions will complicate the problem. Thus, it is hard to handle the governing equations in the form of functions of independent variables. Herein, Chebyshev collocation method is proposed to achieve the exact solution theoretically of such a difficult problem. Finally, two examples with numerical results are presented. The preciseness and efficiency of the proposed Chebyshev collocation method for laminated anisotropic shell problem are highlighted.

AXISYMMETRIC VIBRATION OF CYLINDRICAL SHELLS WITH INTERMEDIATE RING SUPPORTS

This paper treats the axisymmetric vibration of thin circular cylindrical shells with intermediate ring supports based on the Goldenveizer–Novozhilov thin shell theory. An analytical method is proposed, and new exact solutions are presented to study the axisymmetric vibration characteristics of the ring supported cylindrical shells. In the proposed method, the state-space technique is employed to derive a homogenous differential equation system for a shell segment, and a domain decomposition approach is developed to cater for the continuity requirements between shell segments. Exact frequency parameters are presented for circular cylindrical shells that have multiple intermediate ring supports and various combinations of end support conditions. These exact vibration frequencies may serve as important benchmarks against which researchers can validate their numerical methods for such circular cylindrical shell problems.