Thin-walled Cylindrical Shells Research Articles

Impact experiment and buckling criterion analysis of thin-walled cylindrical shells

Impact experiment and buckling criterion analysis of thin-walled cylindrical shells

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.

Thin-walled cylindrical shells in engineering designs and critical infrastructures: A systematic review based on the loading response

Abstract Cylindrical shell structures are ubiquitous and essential supporting structures in various engineering applications. The aim of this research work is to provide a comprehensive overview of the behavior of cylindrical shell structures under different loading conditions, including external pressure, axial compression, and bending moment. The study found that the behavior of cylindrical shells was affected by their geometry, including diameter, length, thickness, and imperfections. These factors should be carefully considered in the design and analysis of cylindrical shells. Additionally, stiffeners and sandwich structures can be applied to improve the structural performance of cylindrical shells under different loading conditions. The work also highlighted the latest research trends in the field, such as the use of advanced materials, and numerical simulations to improve the understanding and design of cylindrical shell structures. Overall, this study has provided a valuable resource for engineers and researchers working on cylindrical shell structures, helping them to design and analyze the cylindrical shell structures more efficiently and effectively.

On the Discussions of Nonlinear Terms in the Large Deformation Model of Thin-Walled Cylindrical Shells

On the Discussions of Nonlinear Terms in the Large Deformation Model of Thin-Walled Cylindrical Shells

BUCKLING BEHAVIOR OF RING STIFFENED-ALUMINUM CYLINDERS SUBJECTED TO EXTERNAL PRESSURE

Ring stiffeners are preferably used to enhance thin-walled cylindrical shell buckling resistance while subjected to external lateral pressure. A comprehensive finite element (FE) numerical study investigated the influence of external ring stiffeners varying from 3 to 17 on the buckling strength of thin-walled stiffened aluminum cylinders. Ten ring-stiffened cylinders were modelled using an ANSYS workbench 2021, whose stiffener dimensions were varied such that the overall weight for all ring-stiffened cylinders remained constant. The FE results indicate that specimens with nine and a larger number of stiffeners with lower strength failed in the overall flexural buckling mode (OFBM), and the other with seven and a lesser number of stiffeners with higher strength failed in the local shell buckling mode (LSBM). The optimum number of stiffeners is obtained when both failure modes occur simultaneously. Experimental results and the theoretical solution with reasonable accuracy substantiate the FE results. The experimental, theoretical, and finite element (FE) results indicate that the ring stiffener’s optimum size and spacing can improve the stiffened cylinder buckling strength since critical buckling pressure and failure mode shape were influenced by the ring stiffener’s size and spacing.

Buckling of Thin-Walled Cylindrical Shell Structures with Axially Variable Elastic Modulus Under Axial Compression

This paper conducts the analytical investigation on the buckling of cylindrical shells with axially variable elastic modulus subjected to axial compressive load for the first time. First, it proves that the axially distributed elastic modulus can be expressed as the combination of constant and variable component. Then, governing differential equations for buckling analysis are derived and exactly solved by the combined perturbation method and Fourier analysis. Accordingly, the closed analytical solutions for the cylinder with arbitrarily variable elastic modulus are obtained, which reveal the explicit relations among buckling load, shell sizes and elastic modulus functions. Based on the presented analytical formulas, four types of elastic modulus variations for shell material which are uniform, periodic, linear and combined are studied in detail, and the results are also well verified. The derived analytical solutions in this paper can serve as benchmarks for buckling analyses of thin-walled cylinders with elastic modulus variations resulted from design, material manufacturing process, material imperfections and so on.

Computer simulation of the stress-strain state of thin plates and cylindrical shells with a circular hole reinforced by an inclusion from functionally graded material

Computer simulation and FEM analysis of the stress-strain state of thin plates and thin-walled cylindrical shells, weakened by a circular hole in the presence of an annular inclusion of a functionally graded material (FGM) surrounding it, have been carried out. The influence of the dimensions of the FGM-inclusion and the law of change of its elastic modulus on the concentration of the parameters of the stress-strain state of plates and shells in the vicinity of the hole is studied. The distribution of stress and strain intensities in the zones of local stress concentration is obtained. It has been established that when using a radially inhomogeneous FGM-inclusion with certain mechanical properties, it is possible to reduce the stress concentration factor by more than 35%. The law of change in the modulus of elasticity of the FGM-inclusion and the width of the inclusion have a significant effect not only on the concentration of the parameters of the stress-strain state of the plate and shell, but also on the nature of the stress distribution over their surfaces. The results of a series of large-scale computational experiments show that the use of an FGM annular inclusion makes it possible to reduce the intensity of both stresses and deformations around the hole.

On the mechanochemical dissolution of shells and its temperature dependence: Discussion of different models

Phenomenological models of mechanochemical corrosion kinetics and their application to the prediction of lifetime of thin-walled cylindrical and spherical shells under internal and external pressures and temperatures are discussed. Closed-form solutions for one- and double-sided corrosion are developed in a compact form that, nevertheless, may reflect various temperature effects such as its influence on the corrosion rate, corrosion inhibition, maximal allowable stress of the shell material, coating lifetimes, and, by changing the thermo-elastic stresses, on the mechanochemical effect and the bearing capacity factor.

Buckling Behavior Analysis of Thin-Walled Cylindrical Shell Structure Under Localized Axial Compression Load Based on Initial Imperfection Sensitivity

In practical engineering, a thin-walled cylindrical shell structure is more easily subjected to localized axial compression loads caused by external adjacent structures or devices. However, until now there are few studies to reveal the buckling behavior of cylindrical shells under such nonuniform loading conditions based on initial imperfection sensitivity. Therefore, buckling analysis of cylindrical shell under localized axial compression loads is investigated in this paper. Based on the buckling test, the influence of the morphology and amplitude of measured initial geometric imperfection are studied using the finite element method. Meanwhile, the inherent reason for initial geometric imperfection affecting the buckling load is elaborated. The influence of amplitude, distribution range, and different combinations of local dent imperfections are also elucidated. In addition, the effects of inclined loading imperfection and uneven shell thickness distribution imperfection are analyzed in the form of deterministic numerical simulation. Finally, a new buckling load knockdown factor that can reasonably consider the influence of loading imperfection and shell thickness variation imperfection is proposed. This work elucidates the initial imperfection sensitivity of the thin-walled cylindrical shell structures under localized axial compression load and can provide useful guidance for the buckling design and preventing buckling failure of these structures.

Effect of potting support design on compression buckling of composite cylindrical shells

The design of thin-walled cylindrical shells under compression loading is mostly driven by buckling considerations. However, accurate experimental evaluation of the buckling load is challenging due to small variations in boundary conditions due to manufacturing tolerances in support conditions. To test a cylindrical shell under compression loading, potting support is usually created around its bottom circumference to avoid edge crippling that could otherwise drastically reduce its critical buckling load. Therefore, investigating the effects of the potting support on the buckling response of cylindrical shell structures is important to mimic boundary conditions as close as possible to real structural constraints of the boundary. The main objective of this work is to investigate the effects of single and double-sided potting supports on the critical linear buckling load of composite cylindrical shells under compression loading. Then, this paper provides insights into understanding underlying reasons for the deviations of theoretical buckling loads from their corresponding experimental values due to boundary conditions, which can occur independently from, or in combination with, geometric imperfection sensitivity. Finally, robust linear buckling expressions that can help designers estimate the reduction due to support conditions are presented. These expressions can be used for evaluating initial safety margins for the potting support design used for testing cylindrical shells.