Thin Cylindrical Shell Research Articles

Study on buckling and post buckling behavior of cylinders under severe vibration

Buckling is one of the expected failure modes for fast reactor vessels under excessive seismic load. However, buckling occurrence condition under vibration load is not necessarily clear. Under BDBE(Beyond Design Basis Events), even if buckling occurs, as long as the coolant inside the main vessel is retained, the safety function is maintained. Therefore, in addition to buckling occurrence condition, it is important to investigate the post-buckling behavior. In order to investigate the buckling occurrence condition and post-buckling behavior of reactor vessels under excessive seismic load, vibration tests and FEM analyses applying vibration loads to two types of specimens were conducted. The specimens were columns which were basic structural member and thin cylindrical shells which were simplified and scaled down of fast reactor vessels. The results showed that buckling caused by vibration load is essentially different from buckling caused by static load. After buckling, the natural frequency was lower than the input frequency, which caused a phase delay, and the phase was opposite to the input, which prevented energy from being input, and the shape of the specimen was stable without excessive deformation. However, cracks could initiate on thin-walled cylinders. Identifying the likelihood and location of crack initiation and extension is a future issue.

Prediction of Nine Quasi-Isotropic Thin Steel Cylindrical Shells Axial Buckling Capacity Under Bending (Plasticity) and Axial Compression (Linear Elasticity)

Prediction of Nine Quasi-Isotropic Thin Steel Cylindrical Shells Axial Buckling Capacity Under Bending (Plasticity) and Axial Compression (Linear Elasticity)

Вимушена конвекція — дослідження регулярного теплового режиму в різних шарах по висоті рідини

The rate of cooling (heating) of experimental liquids was studied separately for five thermocouples located at different heights of the experimental probe. Research has been carried out on an experimental stand in the system “environment I — body II”, where “environment I” is water, and “body II” is the investigated liquid medium in a thin metal cylindrical shell under conditions of free convection. The regular mode of cooling (heating) of the object is characterized by a change in the temperature field over time, which is described by an exponential dependence, while the relative cooling rate t of all points of the body remains a constant value, independent of coordinates and time. The theory of a regular thermal regime has been widely used to solve many practical problems: to determine the rate of cooling (heating) of a body, to study the thermophysical properties of materials, heat transfer and radiation coefficients, thermal resistance, etc. The advantages of this method are that the design of the device and the technique of conducting the experiment are simple, the accuracy of the obtained results is quite high, and the time of the experiment is short. Non-stationary thermal conductivity corresponds to a thermal regime unstable in time, created by this or that thermal action on the body or environment. Non-stationary thermal conductivity is characterized by the fact that the temperature changes not only from point to point, but also over time. Non-stationary thermal conductivity occurs during heating or cooling of bodies, as well as when starting or stopping heat exchange devices, power units, etc. The experimental results are presented on the study of the rate of cooling (heating) of experimental liquids separately for five thermocouples located at different heights of the experimental probe under conditions of forced convection

Analytical solutions of hydroelastic interactions between waves and submerged open-net fish cage modeled as a porous cylindrical thin shell

In this paper, a new semi-analytical solution is proposed to describe the interactions between ocean waves and a flexible cylindrical net cage that is submerged at different depths below the mean water level. The flexible net is treated as a thin perforated shell, and its deformation is governed by the membrane vibration equation of cylindrical shells. The small-amplitude wave theory is adopted to simulate the wavefield, while the flow passing through the cage is described by the porous medium theory. The numerical results exhibit significant wave responses of the net cage, including the distribution properties of wave surfaces, dynamic pressure drops on the net interface, and net structure displacements. Furthermore, the influences of several important design parameters on the hydrodynamic action imposed on the net cage are revealed by parametric studies. The present studies conclude that the significant wave impact is mainly concentrated on the free water surface, and increasing the porosity and flexibility of the net can alleviate wave scattering and the hydrodynamic actions. In addition, at specific wave frequencies, the horizontal wave force acting on the cage will vanish. These findings should be useful to engineers who are designing offshore fish cage systems.

Effect of Hydrochloric Acid Corrosion and CFRP Coating on the Buckling Behavior of Cylindrical Shells Under External Pressure

Thin walled cylindrical shells are being widely used as silos, liquid tanks, marine structures, and industrial chemical plants. In such applications, the shells are mostly exposed to liquids. When shells filled with low-pH-liquids, corrosion occurs at the surface. Corroded material loss, causes the thickness of the shells to decrease, and it reduces the buckling capacity of shells. The purpose of this study is to investigate the effects of corrosion on the buckling capacity of thin walled cylindrical shells subjected to uniform external pressure. The model shells were half or full filled with 5% and 10% HCl (Hydrochloric Acid) solutions for corrosion. To tolerate the negative effects of corrosion, the cylinders were coated with varying sizes of CFRP sheet. Totally 12 models were investigated throughout this research, with the dimensions of 800x400x0.45 mm (with and without CFRP). The perfect non-corroded models were used to compare the behavior of all the models. Results show that corrosion causes a significant decrease on the buckling capacity of thin walled cylindrical shells. Acid ratio, filling rate and surface area coated with CFRP fabrics affects the buckling capacity of cylinders. Coating the cylinders with one layer of CFRP resulted with tolerating the buckling capacity loss.

Methodology for Design Process of Internal Supported Cylindrical Thin Shell Made by Additive Manufacturing

Abstract To improve specific stiffness and strength of cylinder type shell, it is essential to make use of free space inside the cylinder to generate internal supported structure for reinforcement. In this article, an available method is introduced to design this complex structure based on the advantages of additive manufacturing, which include the subprocess of design domain generation, topology optimization, reconstruction, and analysis. Firstly, the design domain inside cylinder is created by removing swept volume from cylindrical container space. The initial structure is obtained by topology optimization and reconstructed by considering the constraints of manufacturing. Then, mechanical properties of the refined structure are checked by finite element method to give a final model. A cylindrical thin shell with slider is chosen as an example to show the detailed work process of the proposed design method, and the designed structure is generated by selective laser melting technology finally. It is proved that the proposed method is suitable for designing additive manufacturing cylinder shell with internal support. Furthermore, a traditional cylindrical thin shell is selected as a benchmark to be compared with the designed model by mechanical properties. Through the comparisons, it is concluded that internal supported cylindrical thin shell has greater bearing capacity and less weight cost than the classical cylindrical structure.

Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells

The axially symmetric propagation of bending waves in a thin Timoshenko-type cylindrical shell, interacting with a nonlinear elastic Winkler medium, is herein studied. With the help of asymptotic integration, two analytically solvable models were obtained that have no physically realizable solitary wave solutions. The possibility for the real existence of exact solutions, in the form of traveling periodic waves of the nonlinear inhomogeneous Klein–Gordon equation, was established. Two cases were identified, which enabled the development of the modulation instability of periodic traveling waves: (1) a shell preliminarily compressed along a generatrix, surrounded by an elastic medium with hard nonlinearity, and (2) a preliminarily stretched shell interacting with an elastic medium with soft nonlinearity.

Axially compressed thin cylindrical shells: Asymptotic limits for a nonlinear basic state

The work presented here revisits the classical bifurcation problem for an axially compressed thin elastic circular cylinder when the nonlinear pre-buckling bending deformations are taken into account. Suitable scaling arguments and singular perturbation methods enable us to explore the link with the more widely studied classical cases in which the uniform membrane solution was used for describing the basic state. Our novel theoretical results are confirmed by direct numerical simulations of the full boundary-value problems corresponding to the relevant buckling scenarios.

A 2.5D coupled FEM–SBM methodology for soil–structure dynamic interaction problems

In this paper, a novel numerical methodology to deal with longitudinally invariant soil–structure interaction problems is proposed. The methodology uses the finite element method to model the structure and the singular boundary method to model the wave propagation in the soil, both formulated in the wavenumber–frequency domain. The versatility presented by the finite element method combined with the simplicity and computational efficiency of the singular boundary method results in a friendly, robust and accurate novel methodology to address the soil–structure interaction problems. The accuracy of the proposed method is assessed by comparing it against 2.5D FEM–MFS and 2.5D FEM–BEM approaches for two cases: a thin cylindrical shell and a star-like beam structure, both embedded in a full-space medium. Moreover, the computational efficiency of the proposed method is evaluated against 2.5D FEM–MFS and 2.5D FEM–BEM methods. In the final step, the applicability of the proposed method is studied through an example of a railway tunnel embedded in a layered half-space. The results presented in this work exhibit the advantages of the novel approach in modelling simplicity, numerical efficiency and robustness with respect to previous methodologies.

Analysis and Design of Reinforced Concrete Thin Cylindrical Shell

The need to come up with economical and efficient structural design led the engineers and researchers to focus more on shell structures. It is more durable, economical as it requires a minimum amount of material provides larger interior space and is aesthetic. A shell dominantly behaves as a membrane, though, at the edges, bending stresses get accumulated. Albeit several theories have been put forward, Schorer’s theory is eminent in the analysis of the long span thin cylindrical shells. This study is focused on the analysis of the stresses by utilizing the Fourier series and Schorer’s theory. Further, the shell is designed for the steel reinforcement as per the Concrete Reinforcing Steel Institute (CRSI) Design Handbook after calculating the final stress resultants and the detailing is also depicted.

Mathematical modelling of thermoelasticity problems for thin biperiodic cylindrical shells

The objects of consideration are thin linearly thermoelastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to formulate and discuss two new averaged mathematical models for the analysis of selected dynamic thermoelasticity problems for the shells under consideration: the non-asymptotictolerance and the consistent asymptotic models. The starting equations are the well-known governing equations of linear Kirchhoff-Love theory of thin elastic cylindrical shells combined with Duhamel–Neumann thermoelastic constitutive relations and coupled with the known linearized Fourier heat conduction equation in which the heat sources are neglected. For the microperiodic shells under consideration, the starting equations mentioned above have highly oscillating, non-continuous and periodic coefficients. The tolerance model is derived applying the tolerance averaging technique and a certain extension of the known stationary action principle. It has constant coefficients depending also on a cell size. Hence, this model makes it possible to study the effect of a microstructure size on the global shell thermoelasticity (the length-scale effect). The consistent asymptotic model is obtained using the consistent asymptotic approach. It has constant coefficients being independent of the period lengths. Moreover, the comparison between the tolerance model for biperiodic shells proposed here and the known tolerance model for cylindrical shells with a periodic structure in the circumferential direction only (uniperiodic shells) is presented.

Application of artificial neural network to predict buckling load of thin cylindrical shells under axial compression

The buckling of thin cylindrical shells under axial compression is long-standing problem due to significant difference between experimental and theoretical buckling load predicted by classical buckling theory. The knockdown factors predicted by present design recommendations are very conservative and predictions are less accurate. Artificial Neural Networks (ANN) are used in this study to accurately predict buckling load using experimental data from 38 previous studies. The buckling load was predicted using nine input parameters. The experimental data was divided into two sets having similar distributions of input parameters: training dataset (90%) and validation dataset (10%). The buckling loads predicted by ANN are in good agreement with experimental buckling loads and predictions are within ±10% with few exceptions. The specimens with parameters falling in the range of input parameters were predicted well by ANN, and accuracy of the prediction depends on number of similar parameters in a specific range used for training. The predictions by five design recommendations including NASA and EC-3 were compared with experimental buckling load, the percentage errors of predictions compared to experimental data for more than 50% specimens were within ±50%. The trained ANN models predict buckling loads with higher accuracy compared to design recommendations and can be used for practical designs.

Dynamic divergence of circular cylindrical shells conveying airflow

Experimental studies have shown that circular cylindrical shells, supported at both ends, conveying internal fluid flow can lose stability by dynamic divergence when the shell is highly pliable. This is an instability phenomenon starting as a divergence, with amplitude comparable to the shell radius, that largely constrains the flow. This results in pressure building up and reopening the shell, triggering a dynamic instability. The characteristics of dynamic divergence instability are studied in-depth in this paper for the first time to elucidate the nature and characteristics of this phenomenon. Experiments have been conducted on an elastomer (silicone rubber) thin circular cylindrical shell clamped at both ends and subjected to internal airflow. Bifurcation diagrams have been obtained by varying the flow velocity as the control parameter, exhibiting strong subcritical behaviour and large hysteresis in the flow velocity for the onset and cessation of dynamic instability. The possible existence of a chaotic component in the oscillations was firstly discerned by looking at high-resolution photos taken with a high-speed camera. The existence of chaos in the dynamic response following the initial divergence was then confirmed by means of several qualitative and quantitative measures and criteria for chaos, such as phase plane plots, Poincaré maps, power spectra, the largest Lyapunov exponent, autocorrelation, and probability density function. All these measures have shown that the chaotic nature of dynamic divergence may be intensified or weakened depending on the flow velocity. The results demonstrate that generally at higher flow velocities the oscillations display more complex nonlinear dynamics.

Computational simulation of critical speed and dynamic analysis of agglomerated CNTs/fiber/polymer/metal laminates rotating cylindrical shell

The main object of this research is to consider the effects of agglomeration on the free vibration and critical speed of rotating carbon nanotubes (CNTs)/fiber/polymer/metal laminates (CNTFPMLs) thin cylindrical shells. The strain–displacement relations are obtained using Love’s first approximation shell theory, and moduli of carbon nanotubes reinforced composites (CNTRCs) cylindrical shells are derived using Eshelby-Mori-Tanaka. Furthermore, fibers are reinforced by means of extended rule of mixture. There are four phases for generating CNTFPMLs cylindrical shell which are fiber, CNTs, polymer matrix and metal. In this work, the effects of several items on vibration of agglomerated CNTFPMLs rotating cylindrical shells are considered, namely, material properties of the fiber phase, lay-ups, volume fractions of metal and composite sections, rotational speed and agglomeration constants. The results demonstrated that the non-dimensional frequencies of symmetric agglomerated CNTs were greater than asymmetric for μ = 0 and μ = 1 , while they were smaller for μ = 0.5 . In addition, although the cylindrical shell reaches the critical speed for symmetric and asymmetric agglomerated CNTs with glass fiber (at μ = 0 and μ = 1 ), respectively, the non-dimensional frequencies of none of the cylindrical shells reach the critical speed and their forward directions are changed before reaching the critical speed for μ = 0.5 .

An Analytical Approach for the Nonlinear Free Vibration Analysis of Thin-Walled Circular Cylindrical Shells

This paper presents a new formulation combining the nonlinear theory of Novozhilov with the classical finite element method for the purpose of evaluating the vibratory characteristics of thin, closed and isotropic cylindrical shells. The theory developed in this paper is able to include the shell curvature effect in the circumferential direction of the orthogonal displacements and considers the impact of initial geometric imperfections on the dynamic response of the system. The formulation first takes a general form by expressing the shell displacements as an alliance between the generalized coordinates and spatial functions. Nonlinear kinematic relationships are inferred from Novozhilov’s theory. The equations of motion as well as the expressions of the mass, linear and nonlinear stiffness matrices are derived through the Lagrange method by considering the coupling between the different modes. An application of this model is illustrated in a further step, by adopting the displacement functions derived from exact solutions of linear Sanders’ theory equilibrium equations for thin cylindrical shells. The governing equations of motion are solved with the help of a direct iterative method. Linear and nonlinear frequencies are validated by comparison with the results in the literature. The relative nonlinear frequencies are determined as a function of vibration amplitudes and then compared with published results for several cases of shells. Excellent agreement is observed between the results derived from this theory and those found in the literature. The effect of different parameters including axial and circumferential wave number, length-to-radius ratio, thickness-to-radius ratio and various boundary conditions, on the nonlinear frequencies of cylindrical shells is investigated.

Applicability and Limitations of Simplified Elastic Shell Theories for Vibration Modelling of Double-Walled Carbon Nanotubes

The applicability and limitations of simplified models of thin elastic circular cylindrical shells for linear vibrations of double-walled carbon nanotubes (DWCNTs) are considered. The simplified models, which are based on the assumptions of membrane and moment approximate thin-shell theories, are compared with the extended Sanders–Koiter shell theory. Actual discrete DWCNTs are modelled by means of couples of concentric equivalent continuous thin, circular cylindrical shells. Van der Waals interaction forces between the layers are taken into account by adopting He’s model. Simply supported and free–free boundary conditions are applied. The Rayleigh–Ritz method is considered to obtain approximate natural frequencies and mode shapes. Different aspect and thickness ratios, and numbers of waves along longitudinal and circumferential directions, are analysed. In the cases of axisymmetric and beam-like modes, it is proven that membrane shell theory, differently from moment shell theory, provides results with excellent agreement with the extended Sanders–Koiter shell theory. On the other hand, in the case of shell-like modes, it is found that both membrane and moment shell theories provide results reporting acceptable agreement with the extended Sanders–Koiter shell theory only for very limited ranges of geometries and wavenumbers. Conversely, for shell-like modes it is found that a newly developed, simplified shell model, based on the combination of membrane and semi-moment theories, provides results in satisfactory agreement with the extended Sanders–Koiter shell theory in all ranges.

On the modelling of stability problems for thin cylindrical shells with two-directional micro-periodic structure

Thin linearly elastic Kirchhoff-Love-type circular cylindrical shells having a micro-periodic structure in circumferential and axial directions (biperiodic shells) are considered. The aim of this paper is to investigate the effect of a periodicity cell size on the stationary and dynamical stability of such shells. In order to take into account the length-scale effect in some special stability problems, an averaged non-asymptotic biperiodic shell model derived by means of the known tolerance modelling procedure is applied. Governing equations of this averaged model have constant coefficients depending also on a microstructure size, contrary to the starting exact shell equations with periodic, non-continuous and highly oscillating coefficients (the well-known governing equations of Kirchhoff-Love second-order theory of thin elastic shells). The effect of a cell size on critical forces and on frequency equation being a starting point in the analysis of parametric vibrations and dynamical stability is studied. It will be shown that the micro-periodic heterogeneity of the shells leads to the fourth-order ordinary differential frequency equation, which can be treated as a certain generalization of the known Mathieu second-order equation. It reduces to the Mathieu equation provided that the length-scale effect is neglected.

Localization and snaking in axially compressed and internally pressurized thin cylindrical shells

Abstract This paper uncovers new manifestations of the homoclinic snaking mechanism in the post-buckling regime of a pressurized thin cylindrical shell under axial load. These new forms tend to propagate either wholly or partially in a direction that is orthogonal to the direction of the applied load and so, unlike earlier forms in Woods & Champneys (1999, Heteroclinic tangles in the unfolding of a degenerate Hamiltonian Hopf bifurcation. Phys. D, 129, 147–170), are fundamentally 2D in nature. The main effect of internal pressurization on the snaking mechanism is firstly to transition the circumferential multiplication of buckles from a one-tier pattern to a three-tier pattern. Secondly, internal pressurization can induce oblique snaking, whereby the sequential multiplication of buckles occurs in a helical pattern across the cylinder domain. For low levels of internal pressure, the single dimple remains—as in the unpressurized case—the unstable edge state that forms the smallest energy barrier around the stable pre-buckling equilibrium. For greater levels of pressure, the edge state changes to a single dimple surrounded by four smaller dimples. By tracing the limit point that denotes the onset of these edge states in the parameter space of internal pressure and axial load, we justify and validate the empirically derived design guideline for buckling of pressurized cylinders proposed by Fung & Sechler (1957, Buckling of thin-walled circular cylinders under axial compression and internal pressure. J. Aeronaut. Sci., 24, 351–356).

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

Exact benchmark solutions of random vibration responses for thin-walled orthotropic cylindrical shells

The exact solutions of random vibration responses of orthotropic thin cylindrical shells are imperative for verifying numerical approaches. This study proposes the discrete analytical method (DAM) and achieves the exact benchmark responses of thin-walled orthotropic cylindrical shells under stationary and nonstationary random excitations for the first time. Firstly, by revisiting the governing motion equations of elastic orthotropic shells based on the Flügge shell theory, the closed-form modal shape functions of orthotropic cylindrical shell with shear diaphragm boundary condition are introduced into stationary and nonstationary random vibration analyses. The power spectral density functions and root mean squares (RMSs) for stochastic responses of thin shell subjected to various random excitations, including the point, surface, base acceleration and moving excitations, are analytically derived by using the pseudo excitation method. Moreover, DAM is proposed to enhance the computational efficiency by implementing the discretization of the modal coordinates, frequency and temporal domains. Finally, the exact benchmark solutions of stationary and nonstationary stochastic responses are achieved, and the results indicate high accuracy and efficiency of proposed DAM. The excitation bandwidth and spatial distribution have significantly different effects on various types of responses, and maximum response RMS declines with increasing of acceleration of moving load.