Composite Circular Cylindrical Shells Research Articles

Free Vibration Analysis of Isotropic and Orthotropic Cylindrical Shells using Finite Element Method

The understanding of fundamental natural frequencies and mode shapes is crucial for assessing the resonant behavior of structures. Numerous scholars have investigated the free vibration properties of circular cylindrical shells. These cylindrical shell configurations find applications in diverse engineering fields such as aviation, rocketry, missiles, electric motors, and locomotive engines. Within this paper, an analytical solution is derived using the "first order shear deformation theory" to determine the frequency characteristics of free vibrations in symmetric laminated circular cylindrical composite shells. The outcomes are juxtaposed against classical and higher order theories. The central aim of this research is to scrutinize the influence of various parameters on the frequency traits of laminated composite shells. Furthermore, the analysis extends to laminated composite shells employing diverse stiffening methods, with their free vibration behavior explored through the utilization of FEA software ANSYS. Keywords: Cylindrical shell, free vibration, frequencies, mode shapes, laminated composites.

Analytical Approach for Large Size Reinforced Square Hole With Rounded Corners in Orthotropic Circular Cylindrical Shells

Full field tangential stress distribution in a uniaxially loaded composite circular cylindrical shell with various laminate sequences with reinforced square hole with rounded corners is achieved and good agreement is obtained with finite element results. Available solution for stress distribution in an infinite plate with square hole under axial load is suitably modified with unknown coefficients in the power series of hole shape parameter, ε and curvature parameter, β (orthotropic plate solution + trigonometric terms as a function of πβ2 /2). The reinforcement thickness for a desired target SCF value (preferably 50% reduction) and region of reinforcement over the shell surface w.r.t hole centre for any combination of hole size, shell thickness and radius are arrived at by an empirical relation based on numerical analysis. Solution for shell with reinforced square hole with β ≤ 0.25 is arrived at by an iterative technique and further expressed and validated for large size reinforced holes for β ≤ 2.0.

Computational model for the semi‐analytical assessment of the free‐edge effect in composite laminated shells

AbstractThe development of efficient computational models for the accurate prediction of the state variables in general composite laminated shells undergoing uniform edge loadings is a major challenge, especially when stress concentration phenomena such as the free‐edge effect have to be considered. This paper addresses this issue by introducing a higher‐order semi‐analytical approach for the assessment of the three‐dimensional stress field in circular cylindrical composite shells with arbitrary layups subjected to a uniform bending moment. The presented semi‐analytical approach combines a closed‐form analytical plane‐strain solution with a higher‐order layerwise approach, and the governing equations are derived by virtue of the principle of minimum elastic potential. The resulting system of coupled ordinary differential equations is then solved by means of the state‐space approach and the free constants are determined by evaluating the boundary conditions at the traction‐free edges. A comparison of the numerical results of the presented semi‐analytical method with finite element simulations for various composite laminates indicates that the developed method works with high accuracy, although being extremely efficient in terms of computational resources.

Optimal Sensor Placement in Composite Circular Cylindrical Shells for Structural Health Monitoring

This work presents an approach for optimal placement of strain sensors in composite circular cylindrical shells. The approach uses numerical strain values in longitudinal and transverse directions extracted from the top surface of the thin-walled composite cylindrical shell. Numerical model of composite cylindrical shell was modelled using the FE commercial solver ANSYS. The modal analysis was performed to determine the first 12 natural frequencies and corresponding mode shapes. Number of sensors and their locations were obtained taking into account physical constraints of strain sensors and optimization strategies. Finally, the optimal sensor placements were obtained. Maximal number of sensors in each direction equals 30.

Instability analysis of fluid-filled angle-ply laminated circular cylindrical shells subjected to harmonic axial loading

This paper presents the dynamic instability and nonlinear vibration analysis of fluid-filled laminated composite circular cylindrical shells subjected to harmonic axial loading. The shells are assumed to be simply supported and filled with still fluid. The mathematical model is prepared by using higher-order shear deformation theory (HSDT) which considers skew modes for accurate results in the analysis of angle-ply laminated composite cylindrical shells. The contained fluid is assumed to be non-viscous and incompressible. The nonlinear governing partial differential equations (PDEs) are obtained using Hamilton's principle, and these equations are discretised into ordinary differential equations (ODEs) by employing Galerkin's method. The pseudo-arclength continuation method along with the incremental harmonic balance (IHB) method is used in order to compute the nonlinear responses, which are plotted in the frequency domain. The regions of instability are determined by adopting Bolotin's method. The time history responses and phase portraits are also studied for empty and fluid-filled laminated cylindrical shells using the Newmark-beta method. A complete set of results that examine the effect of fluid filling, static load factor, dynamic load factor and lamination scheme are obtained.

Adhesively Bonded Tublar Single Lap Joint Effects on the Free Vibration Analysis of Laminated Composite Circular–Cylindrical Shells

Adhesively Bonded Tublar Single Lap Joint Effects on the Free Vibration Analysis of Laminated Composite Circular–Cylindrical Shells

A semi-analytical approach for instability analysis of composite cylindrical shells subjected to harmonic axial loading

In this article, nonlinear vibration and dynamic stability analyses of simply supported laminated composite circular cylindrical shells subjected to periodic edge loading are carried out. A third-order shear deformation shell theory that considers all the nonlinear terms in all five kinematic parameters and rotary inertia is used to develop the present mathematical model so that the model is also valid for thick cylindrical shells. Hamilton’s principle, an energy-based approach, is used to obtain the governing partial differential equations (PDEs) of motion of the cylindrical shell. Further, these equations are reduced into ordinary differential equations by employing Galerkin’s method. The incremental harmonic balance (IHB) method in conjunction with the pseudo-arc-length method is used to obtain the frequency-amplitude response of the system. For obtaining the zone of instability regions, Bolotin’s method is adopted. For more practical significance, analysis of results is also extended by considering damping into account for the composite cylindrical shells. Time history response and phase portrait are plotted by adopting Newmark-beta method. The effects of the static load factor, dynamic load factor, modal damping coefficient, and stacking sequence on nonlinear vibration, instability regions and time history responses are also examined.

Nonlinear forced vibration of functionally graded carbon nanotube reinforced composite circular cylindrical shells

The nonlinear forced vibration characteristics of functionally graded carbon nanotube reinforced composite (FG-CNTRC) circular cylindrical shells are investigated. On the basis of Reddy’s first-order shear deformation theory, von Karman geometric nonlinearity and Hamilton’s principle, the equations of motion are derived. The Galerkin technique is applied to discretize the partial differential equations into nonlinear ordinary differential equations, which are reduced by using Volmir’s assumption and the static condensation method. The incremental harmonic balance method is applied to analyze the dynamic response of FG-CNTRC cylindrical shells. A convergence study on the mode expansions is conducted by considering both axisymmetric and asymmetric modes. The natural frequencies and the resonance responses are compared with existing studies to examine the validity of this study. The effects of distribution and volume fraction of carbon nanotube, thickness-to-radius ratio, length-to-radius ratio, dimensionless radial excitation amplitude and damping ratio on the resonance responses of FG-CNTRC cylindrical shells are discussed. The results show that the reduced model of the system is reasonable. The frequency responses of FG-CNTRC cylindrical shells show both hardening and softening types of nonlinearities, and they are greatly influenced by the change of the fundamental vibrational mode.

Effects of carbon nanotubes distribution on the buckling of carbon nanotubes/fiber/polymer/metal hybrid laminates cylindrical shell

In this manuscript, buckling of carbon nanotubes reinforced circular cylindrical composite shell under hydrostatic presser with its ends closed by rigid disks is investigated, using Fourier decomposition and the Galerkin method. The accuracy of the utilized method is verified with previous research in buckling behavior of circular cylindrical shells. Both types of functionally graded and uniform distribution patterns of carbon nanotubes are studied. The novelty of this study is investigating the influence of carbon nanotubes distribution type and volume fraction on buckling resistance of carbon nanotubes reinforced circular cylindrical composite shell. Furthermore, the effect of material type and volume fraction of metal layers on fiber metal laminates is illustrated. The results show that buckling resistance of composite cylindrical shells increase about 10% by reinforcing with 5% carbon nanotubes. Also, it is shown that metal types Az91 and Ti6AlV have about same effect on buckling resistance of fiber metal laminates cylinders, and their effect are about 15% more than the effect of Al2024. With exploiting the executed analysis, pipes with optimum buckling resistance to weight ratio can be designed for hydrostatic loading.

Nonlinear free vibration analysis of delaminated composite circular cylindrical shells

This study aims to present an analysis of nonlinear free vibrations of simply supported laminated composite circular cylindrical shells with throughout circumference delamination. Governing equations of motion are derived by applying energy methods; using Galerkin’s method reduced the nonlinear partial differential equations to a system of coupled nonlinear ordinary differential equations, which are subsequently solved using a numerical method. This research examines the effects of delamination on the oscillatory motion of delaminated composite circular cylindrical shells and then the effects of increase in delamination length, shell middle surface radius, number of layers, and orthotropy as changes in material properties on the nonlinearity of these types of shells. The results show that delamination leads to a decrease in frequency of oscillations and displacement. An increase in delamination length, shell middle surface radius, and orthotropy of layers decreases nonlinearity and displacement, whereas an increase in the number of layers increases nonlinearity and displacement. It is also observed that an increase in the circumferential wave number can decrease the effect of delamination.

Modeling and nonlinear vibration characteristics analysis of symmetrically 3-layer composite thin circular cylindrical shells with arbitrary boundary conditions

Considering the large-deformation hypothesis, the modeling and nonlinear vibration characteristics of symmetrically 3-layer composite thin circular cylindrical shells with arbitrary boundary conditions are analyzed by applying four sets of artificial springs. Firstly, by employing a set of orthogonal polynomials and trigonometric functions, the energy equations of the shells are derived with Donnell's nonlinear thin-shell theory. Then, the arbitrary boundary conditions are simulated by imposing the equivalent elastic constraint to obtain the potential energy of the edges of the shell, which can be universally applicable to all classical boundary conditions. The vibration equation is obtained by using the Lagrange equation method. In order to obtain correct numerical results, several comparisons of linear and nonlinear results are carried out to validate the approach method in the present study; meanwhile, the calculation convergence is checked. At last, the influence of boundary conditions, geometric parameters, symmetrical lamination schemes and damping coefficients on the nonlinear amplitude-frequency characteristics of symmetrically 3-layer composite thin circular cylindrical shells are investigated. The numerical results indicate that the present method is powerful to calculate the nonlinear vibration response characteristics of symmetrically 3-layer composite circular cylindrical thin shells subjected to various boundary conditions.

Nonlinear dynamic response and vibration of FG CNTRC shear deformable circular cylindrical shell with temperature-dependent material properties and surrounded on elastic foundations

Based on Reddy’s first-order shear deformation theory, the nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube-reinforced composite (FG CNTRC) circular cylindrical shells subjected to an external dynamic load uniformly distributed on the surface of the shell and axial compression in thermal environment are presented. The circular cylindrical shells are surrounded on elastic foundations and reinforced by single-walled carbon nanotubes which vary according to the linear functions of the shell thickness. The shell’s effective material properties are assumed to depend on temperature and estimated through the rule of mixture. By applying the stress function, Galerkin method and fourth-order Runge–Kutta method, nonlinear dynamic response and natural frequencies for imperfect FG CNTRC circular cylindrical shells are determined. In numerical results, the influences of geometrical parameters, elastic foundations, initial imperfection, temperature increment, dynamic loads and nanotube volume fraction on the nonlinear vibration of FG CNTRC circular cylindrical shells are investigated. The obtained results are validated by comparing with those of other authors.

Non-linear vibration analysis of laminated composite circular cylindrical shells

The non-linear transverse dynamic response of laminated composite simply supported circular cylindrical shell subjected to periodic radial point loading and static axial partial loading is studied in this paper considering von Kármán type of non-linearity. The applied partial edge loading is represented by Fourier series and the exact prebuckling stress distribution within the cylindrical shell is computed by solving the in-plane elasticity problem. Donnell’s shell theory incorporating first order shear deformation, in-plane and rotary inertia is used to model the cylindrical shell. Galerkin’s method is used to reduce the governing partial differential equations to a set of non-linear ordinary differential equations. These equations are solved using Incremental Harmonic Balance (IHB) method to obtain frequency-amplitude responses for free and forced vibration. The numerical results illustrate the effects of number of layers, static partial preloading, and initial geometric imperfections on the non-linear forced vibration of laminated composite cylindrical shells.

Dynamic Stiffness Method for free vibration of composite cylindrical shells containing fluid

The present work deals with a theoretical investigation on free vibration of composite circular cylindrical shells containing fluid. A new precise analytical model using the Dynamic Stiffness Method (DSM) or Continuous Elements (CEM) based on the Reissner–Mindlin theory and non-viscous incompressible fluid equations has been proposed for the studied structures. Numerical examples are given for analyzing natural frequencies and harmonic responses of clamped-free cylindrical shells partially and completely filled with fluid. To compare with the theoretical results, some experimental results have been obtained on the free vibration of a clamped-free glass fiber/polyester cylindrical shells partially filled with water by using a multi-vibration measuring machine (DEWEBOOK-DASYLab 5.61.10). Results calculated by the proposed computational model for studied composite cylindrical shells are in good agreement with experiments.

Forced vibration analysis of composite cylindrical shells using spline finite strip method

In this study, forced vibration behavior of thin-walled composite circular cylindrical shells is investigated using the spline finite strip method (spline FSM). Spline FSM is one of the versions of finite element method (FEM) employing a special element called finite strip. The shells considered in this study are assumed to be thin; therefore, the classical bending theory of shells and Sanders–Koiter's strain–displacement relation are used in the theoretical formulation of developed method. Time-history response of shells concerning arbitrary type of forces, boundary conditions and damping effects are obtained using developed spline FSM. To check the validity of results a comparison has been performed with the results obtained by conventional finite element method using ANSYS software. As far as the time history response of cylindrical shells is available the natural frequencies are extracted using Fast Fourier Transform (FFT) approach. The evaluated natural frequencies of composite shells are then compared with those obtained from an eigenvalue analysis. The comparison of results revealed the fact that developed spline FSM is an accurate tool that can be used in transient and harmonic analyses of composite laminated cylindrical shells.

Dynamic stability of simply supported composite cylindrical shells under partial axial loading

The parametric vibration of a simply supported composite circular cylindrical shell under periodic partial edge loadings is discussed in this article. Donnell׳s nonlinear shallow shell theory considering first order shear deformation theory is used to model the shell. The applied partial edge loading is represented in terms of a Fourier series and stress distributions within the cylindrical shell are determined by prebuckling analysis. The governing equations of the dynamic instability of shells are derived in terms of displacements (u−v−w) and rotations(φx,φθ). Employing the Galerkin and Bolotin methods the dynamic instability regions are computed. Using the expression for the stress function derived in this paper, the pre-buckling stresses in the cylindrical shell due to partial loading can be calculated explicitly. Numerical results are presented to show the influence of radius-to-thickness ratio, different partial edge loading distributions and shear deformation on the dynamic instability regions. The linear and nonlinear responses in the stable and unstable regions are presented to bring out the characteristic features of the dynamic instability regions, such as the existence of beats, its dependence on forcing frequency and effect of nonlinearity on the response. The effect of dynamic load amplitude on the nonlinear response is also studied. It is found that for higher values of dynamic loading, the shell exhibits chaotic behavior.

A new third-order shear deformation theory with non-linearities in shear for static and dynamic analysis of laminated doubly curved shells

A geometrically nonlinear theory is developed for shells of generic shape allowing for third-order shear deformation and rotary inertia by using five parameters: in-plane and transverse displacements and the two rotations of the normal; geometric imperfections are also taken into account. The novelty is that geometrically nonlinear strain–displacement relationships are derived retaining full nonlinear terms in all the five parameters. These relationships are presented in curvilinear coordinates, ready to be implemented in computer codes. Higher order terms in the transverse coordinate are retained in the derivation so that the theory is suitable also for thick laminated shells. The theory is applied to laminated composite circular cylindrical shells complete around the circumference and simply supported at both ends. Initially static finite deformation and buckling due to lateral pressure is studied. Finally, large-amplitude forced vibrations under radial harmonic excitation are investigated by using the new theory and results are compared to another third-order shear deformation theory that neglects nonlinear terms in rotations of the normal.

BUCKLING ANALYSIS OF SHELLS SUBJECTED TO COMBINTED LOADS

A semi-analytical isoparametric finite element with three nodes per element and five degrees of freedom per node has been used for the solution. Moderately thick shell theory has been used for the analysis. Second order strains with the in plane and transverse non-linear terms are used for the derivation of geometric matrix. Full Fourier expansion is used in the circumferential direction to overcome the coupling that arises due to material anisotropy and torque prestress. Comparison of the results obtained due to finite element is made with simplified solutions using two thin shell theories with and without shear deformation. The effects of combined load (axial compression and external pressure) on pre-buckling characteristics of composite circular cylindrical and conical shells of various geometric properties have been presented.

Fundamental frequency of a cantilever composite cylindrical shell

Free vibrations of a cantilever composite circular cylindrical shell are considered in this paper. The edge of the shell is fully clamped at one end of the cylinder and is free at the open section of the other end. Variational equations of free vibrations are derived based on Hamilton’s principle and the problem is solved using the generalised Galerkin method. Analytical formulas enabling calculations of the fundamental frequency are obtained and verified by comparison with the results of a finite element modal analysis. The efficiency of the analytical solution is demonstrated using numerical examples including the design analysis of composite shells subject to constraints imposed on the fundamental frequency.

Combined influences of shear deformation, rotary inertia and heterogeneity on the frequencies of cross-ply laminated orthotropic cylindrical shells

The non-dimensional frequencies for symmetric and anti-symmetric cross-ply laminated heterogeneous composite circular cylindrical shells are analyzed by taking into account the effects of first-order deformations such as transverse shear deformations and rotary inertia. By using the Donnell-type shell theory, a set of fundamental dynamic equations of laminated circular cylindrical shells made of heterogeneous orthotropic materials is derived through Hamilton’s principle. The basic equations are reduced to the six-order algebraic equation. One of the lowest positive roots of the algebraic equation represents the fundamental frequency. Attention is focused on the case of cross-ply laminated heterogeneous orthotropic cylindrical shells, from which solution for homogenous and heterogeneous orthotropic monolayer cylindrical shells follows based on classical shell theory (CST) and shear deformation theory (SDT), as a special case. Moreover, further detailed numerical results dealing with non-dimensional frequencies and corresponding mode shapes of laminated heterogeneous cylindrical shells having symmetric or anti-symmetric cross-ply lay-up are discussed. Furthermore, some comparisons are made to show the reliability and accuracy of the study.