Thin-walled Cylindrical Shells Research Articles

Free vibration analysis of hybrid laminated thin-walled cylindrical shells containing multilayer FG-CNTRC plies

Free vibration analysis of hybrid laminated thin-walled cylindrical shells containing multilayer FG-CNTRC plies

A Comprehensive Synthesis on Analytical Algorithms for Assessing Elastic Buckling Loads of Thin-Walled Isotropic and Laminated Cylindrical Shells

A comprehensive review is presented on the main analytical methods used in the specialized literature to evaluate the buckling loads of thin-walled cylindrical shells (TWCS) subjected to different mechanical loads or load combinations. The analytical formulations are first presented for unstiffened TWCS, followed by stiffened TWCS in different configurations (stiffeners in the axial direction, circumferential direction or both axial and circumferential directions, placed on the external or internal surface of the shell). This research can serve as a helpful resource for researchers investigating this field, allowing the analytical methods to be used as a reference basis for numerical and experimental results regarding the behavior of structures in the category of TWCS.

Buckling Analysis of Variable Stiffness Composite Cylindrical Shells Under Axial Compression Considering Imperfection Sensitivity

Thin-walled composite cylindrical shells are nowadays widely used as primary structures in the aerospace industry. The so-called variable stiffness (VS) composite cylindrical shells with flexible stiffness tailoring characteristics have been made possible by existing AFP techniques. Considering the inherent imperfection sensitivity property of axially compressed thin-walled cylindrical shells, the buckling behaviors of the axially compressed VS composite cylindrical shells with initial geometric imperfections and delamination imperfections are investigated respectively in this paper. The design buckling loads of the axially compressed VS composite cylindrical shells are first determined by the probing method, which is verified by comparing with the existing test data and numerical simulation results. Additionally, a parametric study is conducted to investigate the effects of delamination imperfections on the buckling loads. The constraint delamination sizes of the VS composite cylindrical shells based on the design buckling load in this paper are given. Furthermore, the effects of continuously variable fiber angles on the buckling loads are investigated considering the imperfection sensitivity. The specific VS composite cylindrical shells with both high- buckling loads and low-imperfection sensitivity are obtained. Results indicate that the effects of imperfection sensitivity need to be carefully considered in buckling design of the axially compressed VS composite cylindrical shells.

Simulating the effects of geometric imperfections on the buckling of axially compressed cylindrical shells through reducing localized stiffness

Thin-walled cylindrical shells are prone to buckling under axial compression. The load-carrying capacity of the shells can thus be significantly reduced. It's well known that the buckling loads of axially compressed cylindrical shells are quite sensitive to the initial geometric imperfections. Even though the magnitudes of these imperfections are relatively small, the corresponding buckling loads can be significantly reduced compared to the perfect shells. In this paper, the effects of geometric imperfections on the buckling loads are equivalently simulated by reducing localized stiffness of the cylindrical shells. Firstly, the method for simulating the effects of geometric imperfections on the buckling loads of cylindrical shells is introduced in detail. Then, the proposed method is used to simulate the effects of single dimple imperfection and multiple dimple imperfections on the buckling loads of cylindrical shells. Results show that the buckling loads and load-displacement curves of the shells with single and multiple dimple imperfections can both be well simulated by the localized stiffness reduction method. Furthermore, the measured geometric imperfections from manufactured cylindrical shells are investigated. The numerical results simulated by the proposed method are also verified by the shell models with real measured geometric imperfections and the experimental results from the literature. The applicability and reliability of the proposed equivalent method in dealing with complex imperfection configurations can thus be validated. Results show that the proposed equivalent method is suitable for simulating various geometric imperfections of the cylindrical shells. It is promising to be applied as an efficient tool to quantify the imperfection sensitivity of buckling loads and provide a new solution for buckling analysis of cylindrical shells.

Broadband vibration isolation in cylindrical shells embedded with total reflection elastic meta-shells

In this research, we propose a pioneering conceptual design paradigm of elastic meta-shells for broadband elastic wave control in cylindrical shells. We theoretically reveal the mechanism for wave isolation in cylindrical shells, which arises from the closure of all transmission channels (i.e., total reflection) when 0th-order diffraction is the only remaining diffraction mode. In addition, to solve the dynamic coupling behavior between multi-order diffraction modes, we extend the acoustic mode-coupling theory to elastic waves in cylindrical shells. Based on the diffraction theory and multiple reflection effect, we construct a total reflection elastic meta-shell and numerically demonstrate efficient broadband elastic wave isolation in the frequency range of 5 k–7 kHz. Finally, the vibration isolation performance is experimentally verified by embedding a total reflection elastic meta-shell in a finite thin-walled cylindrical shell waveguide. Results confirm the feasibility of the elastic meta-shell design concept and its ability to achieve fully passive, high-efficiency, and broadband vibration isolation. Our vibration isolation strategy could broaden the applicable scope of elastic meta-structures and open new horizons for vibration isolation, mechanical energy filtering, and elastic wave signal processing in cylindrical shells.

A methodology for evaluating damage in thin-walled cylindrical shells using bounded ultrasonic beam scattering

This paper introduces an ultrasonic detection methodology specifically designed to assess damage in thin-walled cylindrical shells, which crucially relies on the interaction between a bounded ultrasonic beam and a thin-walled cylindrical shell immersed in fluid, considering both water-filled and air-filled cavities. Initially, we derive the scattered sound field expression for a bounded ultrasonic beam obliquely striking the shell. Subsequently, through finite element simulations and experimental verification, we observe that when the incident bounded beam is emitted at the critical angles defined in this study, early damage significantly enhances the received sound pressure amplitude detected by a symmetrically positioned receiver. Notably, a mere 5 % decrease in the shell's elastic modulus leads to a notable 233.69 % increase in the area under the amplitude-frequency curve of the received sound pressure for water-filled cavities and a remarkable 642.85 % surge in area for air-filled cavities. Experimental data further validates the sensitivity of this method towards varying corrosion damage states. This approach combines the reliability of linear ultrasonic methods with the enhanced sensitivity of nonlinear ultrasonic techniques, offering a significant advancement over traditional ultrasonic detection methods for inspecting cylindrical shells. The proposed assessment method holds immense potential in providing novel insights for inspecting cylindrical shells in practical applications.

Determining the mechanical behavior of thin-walled cylindrical shells of cement composite containing graphene oxide and glass fibers with the help of fuzzy logic model and artificial neural network

Determining the mechanical behavior of thin-walled cylindrical shells of cement composite containing graphene oxide and glass fibers with the help of fuzzy logic model and artificial neural network

Impact Experiment and Buckling Criterion Analysis of Thin-Walled Cylindrical Shells

The impact test of tubular components is usually carried out by way of drop hammer impact. In fact, in many ships’ equipment, the form of load is often carried out by way of drop impact test. In this paper, the drop impact test is used to study the buckling of tubular structure under impact load, so as to make it closer to the impact form of components in actual ship structure. Firstly, the stress, strain, acceleration at each moment and the buckling deformation mode of the tubular member after the impact are obtained through the drop impact experiment, and then the impact process is analyzed. Secondly, the finite element method is used for numerical simulation of the impact process, and the accuracy of the finite element analysis results is verified by comparing with it. Thirdly, the finite element method proved to be effective and was used to simulate single and multiple drop impacts under more working conditions, and a large amount of data was obtained. Finally, according to the existing impact criteria based on the results of drop weight impact, it is applied to the drop impact process, and the accuracy of each impact criterion is analyzed and compared. This method makes up for the deficiency of the traditional experimental method of using falling weight to simulate impact, and provides a reference for the critical buckling condition of similar thin-walled cylindrical shells under impact.

Improved Fourier Series-Ritz Method for Free Vibration Analysis of Hard Coating Damping Thin-Walled Cylindrical Shells with Thickness Variation Under Arbitrary Boundary Conditions

Improved Fourier Series-Ritz Method for Free Vibration Analysis of Hard Coating Damping Thin-Walled Cylindrical Shells with Thickness Variation Under Arbitrary Boundary Conditions

The influence of R/t-ratio on the imperfection sensitivity of the buckling load of thin-walled CFRP cylindrical shells

Thin-walled cylindrical shells under axial compression load are prone to buckling. The influencing factors leading to a reduction of the buckling load are a major design challenge. The sensitivity to imperfection increases with rising slenderness. In literature, cylinders with the same parameters and different slenderness are rarely tested in a larger number of samples. In this contribution, seven cylindrical shells, six of them nominally identical, are tested on two different test rigs and compared with twelve specimens with a smaller radius and same wall thickness from a previous series of tests. It is shown how the imperfection sensitivity is dependent on the R/t-ratio. Additionally, it is demonstrated how the quality of the test set ups corresponds with the achieved buckling load. Finally, the suitability of selected design approaches is determined based on the test results. Based on that, recommendations for the choice of a suitable approach are given.

Deformation of Cylindrical Shell Made of 9X2 Steel Under Complex Loading

The development of the construction industry in terms of the design and manufacture of shell structures of non-standard architectural forms made of materials with complex mechanical properties requires using modern integrated computer-aided design systems with step-by-step modeling of deformation of structural elements under operating conditions, as well as taking into account their subsequent behavior after accumulation of residual strains during plastic deformation. The purpose of the study is to simulate the process of plastic deformation of a thin-walled cylindrical shell made of 9X2 GOST 5950-2000 (Interstate Standard) steel under compression and torsion with theoretical calculations based on the general theory of elastoplastic processes by A.A. Ilyushin. The constitutive equations of the theory of elastoplastic processes by A.A. Ilyushin for complex loading path and deformation of materials in the deviatoric strain space are presented. Based on the presented solutions, according to the strain path of the 9X2 steel shell implemented in the model, the graphs showing the relation of the vector and scalar properties of the material to the arc length of the strain path are constructed. A conclusion is made about the degree of hardening of the material in question and its dependence on the magnitude of the angle of convergence at the kink point of the complex path. The graphs of changes in the constitutive plasticity functions with respect to the increments of the arc length of the strain path are presented.

Dynamic response of clamped metallic thin-walled cylindrical shells under lateral shock loading

A combined experimental and numerical study was carried out to explore the dynamic response of Q235 thin-walled cylindrical shells under lateral shock loading. The machined Q235 specimens were clamped on both sides and subjected to centered lateral simulated shock loading via foam projectile impact tests, with their dynamic deformation evolution, mid-point deflections, and final deformation modes experimentally measured. The mid-point deflections of the impact side are all positive (the direction of deformation is the same as the impact direction) while those of the rear side all exhibit negative values (the direction of deformation is opposite to the impact direction). To further explore this phenomenon, the method of finite element (FE) was employed to simulate the foam projectile impact, with good agreement against experimental measurements achieved. Using the validated numerical model, the effects of impact velocity, length-to-diameter ratio, and thickness-to-diameter ratio on the dynamic response of the thin-walled cylindrical shell were further analyzed. The direction of both side deflections and deformation modes are significantly affected by the impact level and the shell geometries. For the rear side, within the given range of impact momentum and geometric parameters, the numerically predicted deflection varies from −1.775 mm to 2.45 mm. Thereupon, the coupling of indentation and bulge deformation patterns are indicated, and their corresponding contribution changes are considered the main mechanism for determining the final deformation of the thin-walled cylindrical shell's rear side.

Nonlinear Vibrations Analysis of Hyperelastic Cylindrical Shells Utilizing the Method of Multiple Scales

In this study, the primary resonance of a hyperelastic thin-walled cylindrical shell subjected to external excitation is examined. The incompressible Moony–Rivlin model, nonlinear Donnell’s shell theory, and Hamilton principle are employed to extract the fundamental equations in three directions. The Galerkin approach is employed to reduce the governing equation into ordinary differential equations form. Then, by neglecting the membrane inertia, three equations are reduced to one equation to analyze the transverse vibrations of the hyperelastic shells. Natural frequencies of different asymmetric modes are used to define the fundamental mode. Then, the multiple scales method is applied to evaluate the frequency–amplitude curves for various parameters. In addition, the model’s accuracy is validated with those presented in the literature for a cylindrical shell and the comparison shows good arrangement results. In the simulation part, the effects of the amplitude of excitation, the ratio of thickness–radius, and the ratio of radius–length on the primary resonances of shells are evaluated. The simulation plots show that for small values of radius-to-length ratios, increasing its value causes to decrease in the stiffness of the thin hyperelastic shell. Also, by increasing the radius–length ratios from 0.3 to 1.18 the hardening of the shell is decreased, and by increasing the radius–length ratios from 1.18 to 2 the hardening behavior is increased.

Computer modelling of thin-walled shell structures with geometric imperfections

The study presented in the article focuses on modelling of thin-walled cylindrical shell structures with initial geometrical imperfections under external radial pressure. The critical pressure of the perfect shell obtained using linear analysis significantly exceeded that calculated by the Papkovich formula. This discrepancy can be attributed to the shell displacement constraints and the fact that linear analysis provides non-conservative estimates. Initially, the geometric imperfections were assumed to follow an eigenmode-affine pattern with varying amplitudes. Critical pressure values iteratively determined using the modified Ricks method were found to be lower than the critical pressure of the first buckling mode. Importantly, all these values remained notably higher than the normative value. Subsequently, the initial imperfections were modelled as combinations of sinusoidal deviations with different amplitudes and varying numbers of waves along the perimeter. Short-wavelength eigenmode-affine imperfections were superimposed on longer-wavelength deviations. The research indicated that while the long-wavelength imperfections had a marginal impact on the critical pressure values, they notably altered the post-buckling behaviour of the shell, as depicted in load-deflection figures in the form of loops. These processes occurred at pressure levels considerably higher than the normative value. The simulation results are in good agreement with established theories regarding the pre- and post-buckling behaviour of thin-walled shells. Nonlinear analysis revealed that the actual critical pressure values exceeded the normative value by 30-45%, and the post-buckling pressure values exhibited a gradual decrease without posing a threat to abrupt changes in the geometry of the shells. This outcome provides a basis for a more accurate estimation of the load-carrying capacity of the shell structures.

CRITICAL STATES OF THIN-WALLED CYLINDRICAL SHELLS WITH ANNULAR SEAMS UNDER AXIAL COMPRESSION AND INTERNAL PRESSURE

We consider the loading conditions of a thin-walled cylindrical shell containing an annular layer of less durable material under its axial compression and internal pressure. The main pipeline of seamless pipes of large diameter containing annular mounting seams is considered as an application. The main material of the shell and the material of the layer are elastoplastic hardenable. The limits of strength and yield strength of the layer are lower than these values of the base material. The purpose of the article is to establish the dependences of critical deformations, stresses and pressures on the shell on its mechanical and geometric parameters and loading conditions. The research method is based on the application of the Swift - Marciniak criterion for the loss of stability of the process of plastic deformation of the material using new approximations of deformation diagrams. Explicit analytical expressions for the required quantities are obtained. The results make it possible to determine the critical pressures under given loading conditions and the pipeline wall thicknesses at a given operating pressure.

Critical circumferential wavelength of elastic buckling of longitudinal compressed thin-walled cylindrical shells

The classical theory of elastic critical buckling stress works well for slender columns and thin flat plates under compression; however, the situation is different for longitudinally compressed thin-walled circular cylindrical shells, and the issue has plagued us despite considerable efforts over the last 100 years. We noticed that all such buckling analyses thus far, both linear and nonlinear, in terms of the main philosophy, inherited and were confined to Euler’s pioneering solution for the slender column model that focuses on the longitudinal buckling deformation mode and should be classified as the ‘longitudinal open-loop’ eigenmode because the deformations of the two longitudinal ends are physically independent of each other. In view of this, for an ideal linear-elastic buckling model of a thin-walled perfectly circular cylindrical shell under uniform longitudinal compression on the foundation of the longitudinal open-loop eigenmode solution, it is also necessary to consider a ‘circumferential closed-loop’ eigenmode simultaneously to physically avoid violating the reality of its ideal periodic deformation on the entire perimeter and to mathematically redefine the biunique and precise relationship for each distinct eigenmode by the critical circumferential wavelength. Originating from such a case study, the mathematical uniqueness issue hidden in the general solution of the Donnell equation is further discussed. The authenticity of the competing eigenmode characterized by the Koiter circle is also discussed. Furthermore, a preliminary attempt was conducted to interpret the discrepancy between theoretical and experimental buckling loads, mainly initiated by the characteristic type of longitudinally generated circumferential local inward displacement in initial geometric imperfections, using the insights herein.

Dynamic buckling of thin-walled cylindrical shells under radial impact pressures randomly distributed in the circumferential direction

Dynamic buckling of thin-walled cylindrical shells under radial impact pressures randomly distributed in the circumferential direction

Seismic experiments on short coaxial multi-layered cylindrical shells with fluid–structure interaction in fast reactors

As the most important component of pool-type fast reactors, the main vessel contains most of the equipment for the primary circuit and thousands of tons of liquid sodium. The fluid–structure interaction effects of the coaxial multi-layer thin-walled cylindrical shells formed by the main vessel and its thermal shield cannot be neglected. Though the research on the fluid–structure interaction of the liquid in the pool is sufficient, the research on the short coaxial multi-layer cylindrical shells is not enough, especially the axial and circumferential mode shapes and the ratio of each mode under seismic conditions. So, it is necessary to study the fluid–structure interaction of short coaxial multilayer shells. This paper presents shaking table tests performed on double- and triple-layered cylindrical shells to investigate fluid–structure interaction and seismic response, respectively. The experiments reveal that when the aspect ratio is less than 2, Mode (1,6) exhibits the most significant response under sine wave excitation conditions, while Mode (1,1) demonstrates the highest response under seismic conditions. The first three modes are characterized as out-of-phase modes. Additionally, the pressure component of the first circumferential mode contributes 20% to the overall response of the first 12 modes under seismic conditions.

Limit state analysis of the thin-walled shell using a forming limit diagram and finite element modeling

The study considers the problem of estimating the limiting state of thin-walled cylindrical shells loaded with internal pressure. A diagram of limiting deformations is used as a method for estimating the limiting state of shells. The upper limit of permissible deformations satisfying the kinematic criterion of limiting deformation is determined based on the Side-Rice criterion. Using the finite element method, a series of numerical experiments on the loading of the inner shell at different heights of the loaded region in comparison with the diameter of the shell were carried out. Thus, the formulation of the problem made it possible to evaluate the effect of edge effects on the deformed state of a thin-walled shell. The results of the calculation of the limiting state of the shell can be used to develop a system for detecting cracks in turbine blades due to a system of thin-walled capsules under internal pressure.

Thermal-vibration ageing characteristics of three thin-walled cylindrical shells covered with a functionally graded protective coating: Modeling, analysis and test

In this study, the thermal-vibration ageing characteristics of three thin-walled cylindrical shells (TCSs) covered with a functionally graded protective coating (FGPC) are investigated for the first time, including fiber reinforced polymer (FRP), metal and fiber metal hybrid (FMH) shell structures with the FGPC. Initially, a dynamic model of an FGPC-TCS structure in a thermal-vibration ageing environment is developed by employing the first-order shear deformation principle enriched by the improved exponential function approach, the complex modulus method, the Rayleigh-Ritz method, etc. In this model, the ageing-related material parameters of the FGPC and the TCS structure are assumed to be affected by both environmental temperature and aging time. After the solution procedures of the vibration parameters of the above three coated shells are clarified, the determining method of fitting coefficients of the coating and different materials in the shells studied is provided. Also, the detailed experimental validation is undertaken on the uncoated and coated FRP, metal, and FMH shell specimens, which indicates that the present model is reliable for predicting the key dynamic ageing parameters when the complex thermal-vibration ageing effect is considered. From the measured and calculated data, it is proved that the suppression contribution of the FGPC is obvious no matter whether these shell structures are at room temperature or thermal degradation environment. Furthermore, some important application suggestions of the FGPC are summarized to improve the degradation resistance of such coated shell structures.