Buckling Of Cylindrical Shells Research Articles

Analytical Study on the Buckling of Cylindrical Shells With Circumferential Thickness Variation Under Varying External Pressure

Abstract In this article, the analytical buckling load coefficient formula for a cylinder with circumferential thickness variation subjected to varying external pressure is established for the first time by developing a quadratic perturbation method. Based on the presented formula, some specific examples that consider either circumferential shell thickness variation or varying lateral pressure are studied and compared with those in the published literature. First, classical cosine thickness variation is analyzed. The computed results of buckling load coefficients indicate that most of differences between the proposed formula and finite element (FE) analyses in previous literature are less than 5%. Second, wind-type pressure load is discussed, and the maximum difference of predicted buckling load coefficients between our formula and results in published article is 2.3%. Third, both circumferential thickness variation and linear liquid pressure are analyzed by the proposed analytical formula and validated by the Galerkin method when both thickness and load variations are small. Therefore, accuracy and reliability of the established formula are validated. For the purpose of engineering application, buckling of a circular shell with local circumferential thickness variation due to weld shrinkage under wind-type pressure is analytically investigated. The effects of thickness variation amplitude, load parameter, half angle of thickness variation, and shell dimensions on buckling load coefficients are studied in detail.

Odd elastic stability of cylindrical shells

Biologically active shells typically exhibit complex mechanical behaviors, with their morphogenesis involving rich symmetry breaking events and non-conservative biological forces. In this article, an accurate buckling solution model of active cylindrical shells is established based on the odd elasticity theory. The tension buckling, non-reciprocal torsional buckling and stress-free active buckling of odd elastic cylindrical shells are reported, which are an anomalous instability caused by odd elastic effects. The result shows that the anomalous buckling of cylindrical shells can only occur in the form of chiral deformation, because the energy required for instability can be obtained based on the odd elastic effects.

Experimental study on the wind-induced buckling of open-top storage tanks with wind girders via 3D-DIC technique

Large open-top storage tanks are susceptible to buckling failure under the combination of external and internal wind pressures. Therefore, wind girders are recommended to be installed on the tank wall to improve its buckling capacity. Most previous experiments on buckling of cylindrical shells typically measured the response at a certain point with a single displacement sensor, and the buckling modes are not readily available. In this study, a measurement technique based on the three-dimensional digital image correlation method is utilized to analyze the buckling behavior of several elastic tank models with aspect ratios of 0.5 and 0.2 in the boundary layer turbulence. The critical buckling pressure and instantaneous displacement field on the windward side of models with and without wind girders are presented and compared with the results of finite element analysis. In addition, the effects of wind girders and imperfections are further discussed. The results indicate that the deformation of the tank wall can change the wind pressure, making it more difficult to return to the pre-buckling state. The wind girders can significantly restrain the buckling deformation and increase the critical buckling load. However, as the wind girders become rigid, the strengthening effect becomes almost constant, and the stiffened tanks are more sensitive to initial geometric imperfections. Based on the cylindrical shell buckling theory and existing calculation methods, an empirical formula for the critical buckling wind pressure of open-top storage tanks with different numbers of wind girders in the boundary layer is proposed.

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.

Analytical investigation on the buckling of cylindrical shells under combined non-uniform axial compression and external pressure

This paper focuses on the buckling problem of cylindrical shells under combined non-uniform axial compression and external pressure. To obtain buckling loads, a completely new method called two-parameter perturbation method is established. Using this method, governing differential equations are solved and buckling loads expressed by load functions, load parameters, and shell dimensions are derived for the first time. Comparative studies show that buckling loads by the analytical formulas coincide with those for combined uniform loads or single wind load in literatures. Buckling of a cylinder subjected to combined bending and wind loads is analyzed, and confirmed by the Galerkin method for the case of small load variations. Therefore, the presented formulas are adequately validated. The numerical calculations are carried out to analyze the effects of non-uniform load parameters on buckling load coefficient. The obtained results in this paper can be applied to evaluate buckling loads for cylinders subjected to combined non-uniform loads in actual engineering.

Foreword to the special issue on new developments in structural stability.

Foreword to the special issue on new developments in structural stability.

A Symplectic Analytical Approach for Torsional Buckling of Cylindrical Shells with Asymmetric Local Defects

A torsional buckling model of cylindrical shells with asymmetric local thickness defect is established based on the Hamiltonian system. The critical load and torsional buckling mode of cylindrical shells with defects are obtained by the symplectic eigensolution expansion method, which overcomes the difficulty of constructing the deflection function of the traditional semi-inverse method. Local buckling modes can be captured by this new analytical model with the superposition of symplectic eigensolutions. To ensure accuracy and validity of the symplectic method, the analytical solution with torsional buckling of a cylindrical shell is compared with the classical solution and the finite element method (FEM) solution. The results show that the most detrimental position of the defect is only related to the width of the defect, not to the depth. The local defect changes the circumferential buckling wave number of the cylindrical shell and concentrates the torsional corrugation on the side containing the defect. Torque symmetry is broken due to the asymmetric defect, and the most detrimental defect direction for buckling is the same as the direction of torsional buckling wavelet.

Characterization of blast waves using solid and gaseous explosives: application to dynamic buckling of cylindrical shells

Characterization of blast waves using solid and gaseous explosives: application to dynamic buckling of cylindrical shells

A novel analytical study on the buckling of cylindrical shells subjected to arbitrarily distributed external pressure

A completely new analytical method to solve the fourth-order governing partial differential equations with variable coefficients is proposed for the buckling of cylindrical shells subjected to distributed external pressure. Unlike the present energy method in literatures, pressure distribution needs not be assumed beforehand and be simple, which is arbitrary in this manuscript. The present novel method makes the buckling analysis for the complicated external pressure distributions (including discontinuous loads) possible. Furthermore, general buckling load formulas related to geometrical sizes of the shell and pressure distribution functions are obtained by the combined perturbation method and Fourier series expansion for the first time. The first and second order asymptotic terms of buckling loads are directly given for the purpose of engineering application. Based on the presented method, three types of external pressure loads (namely, linear liquid pressure, wind type pressure and discontinuous stepwise external pressure)are considered. Validity and accuracy are demonstrated by comparing with the results in published literatures for linear liquid pressure and wind type pressure, and it is also the first time to derive the buckling load for a shell under discontinuous stepwise external pressure. Parametric discussion is also performed to investigate the effects of load distribution types and parameters on buckling resistance capacity.

Teaching buckling of cylindrical shells through an effective laboratory demonstration

A laboratory demonstration for a Stability of Structures course is presented, consisting in the buckling test of two cylindrical shells: a 3 D-printed and a composite cylinder. The learning outcomes have been formulated by comparing what can be learnt from theoretical lessons and buckling tests. The activity follows the Interactive Lecture Demonstration approach. Main results show that the activity helped students’ understanding of shell buckling and it increased their enthusiasm for the topic. This demonstration is easily implementable, and the presented step-by-step development methodology provides guidelines to develop similar activities for different engineering subjects.

Buckling of a Cylindrical Shell Joint with Annular Plates under External Pressure

The buckling of a thin cylindrical shell supported by identical annular plates under uniform external pressure is analyzed using an asymptotic method. The boundary conditions on an internal parallel of the shell joined to a thin plate are obtained. The free support conditions are introduced at the edges of the shell. The approximate solutions to the eigenvalue problem are sought as a sum of slowly varying functions and edge effect integrals. For the formulation of the zero-order eigenvalue problem, the main boundary conditions are obtained on the parallel of the interface between the plate and the shell. This problem also describes vibrations of a simply supported beam stiffened by springs. Its solution is sought as linear combinations of Krylov’s functions. It is shown that in the zeroth approximation it is possible to replace a narrow plate with a circular beam. As the plate width increases, the stiffness of the corresponding spring tends to a constant. It occurs because of localized plate deformations in the proximity of the internal edge of the plate. As an example, the dimensionless critical pressure is determined in the case when the shell is supported by a single plate. Replacing a narrow plate with a circular beam does not lead to substantial variation in the critical pressure; however, for a wide plate the beam model provides an overestimated value of the critical pressure.

Analytical study on thermal buckling of cylindrical shells with non-uniform thickness

This paper presents an analytical study on thermal buckling of cylindrical shells with non-uniform thickness, which is common in engineering practice. Firstly, the shell thickness is assumed to be arbitrary in the axial direction. After solving the basic partial differential equations by the perturbation method, buckling temperature and modes in terms of thickness function and geometric sizes of the shell are obtained. Using the presented formulas, this paper deeply analyzes and discusses cosine distributed and stepwise thicknesses. For simple cosine distributed thickness, the classical Galerkin method is applied to derive buckling temperature factors, while stepwise thickness is verified by the finite difference method. Results from the Galerkin method and the finite difference method are in accordance with those by presented formulas in this paper. Furthermore, the influence of parameters in thickness functions and buckling modes on buckling temperature factors is discussed, and some interesting conclusions are drawn. The presented buckling temperature formulas can be applied to evaluate stability capacity of the cylinder used in thermal environment.

Local–global buckling of cylindrical shells with wall thinning defects

The influence of local thinning thickness defects on the buckling of cylindrical shells is investigated. A static buckling model of cylindrical shells with defects is established based on the Hamiltonian system. The complete symplectic eigensolutions of the cylindrical shell are superimposed to derive the buckling modes of the cylindrical shell with defects. A total of seven different cylindrical shells with axisymmetric and non-axisymmetric defects are considered. Local buckling modes can be captured by this new analytical model with symplectic methodology. By constraining the defect volume, the influence of different defect shapes on buckling of the cylindrical shell is investigated. Comparing with step defects and parabolic defects, the analysis concludes that defects of exponential function are more harmful to buckling of cylindrical shells. Highlights This article establishes a cylindrical shell model with arbitrary thickness changes under the Hamiltonian system and evaluates the buckling characteristics of cylindrical shells with thickness defects. A new symplectic approach is developed where the symplectic eigensolutions of the complete cylindrical shell are superimposed to obtain the corresponding buckling modes. Local buckling modes can be captured by this new analytical model. The occurrence of local buckling often drives a significant decrease in critical buckling load. The effects of defect parameters including location, depth, and shape on structure buckling are determined and analyzed.

Energy Method on Dynamic Buckling of Cylindrical Shell with Simply-Fixed Supported subjected to Axial Impact of Rigid Mass

Based on the energy method, considering the stress wave effect, the buckling problem of cylindrical shell subjected to impact is studied. Substituting the Lagrange function and the trial function satisfied the boundary condition into the second Lagrange equation. After the second-order linear partial differential equation is obtained, the analytical expression of the critical buckling speed of a rigid mass impacting cylindrical shell is obtained by analyzing the properties of the equations. The influence of critical length, impact mass, axial mode number, circumferential mode number and diameter-thickness ratio on buckling is discussed by analyzing the examples. The results show that the stress wave effect, initial kinetic energy and diameter-thickness ratio have a significant effect on the dynamic buckling of cylindrical shells; the higher-order modes of buckling and the buckling of cylindrical shell are easily motivated by high-speed impact.

Analytical Study on Dynamic Buckling of Cylindrical Shells with General Thickness Variations Subjected to Exponentially Increasing External Pressure

This paper presents an analytical investigation on dynamic buckling of cylindrical shells with general thickness variations under exponentially increasing external pressure over the time. Different from the previous studies in literatures, the shell thickness varies arbitrarily and is common in actual engineering, which leads to failure of the existing methods. A new analytical method is first developed to solve the fourth-order governing partial differential equations with variable coefficients for the shell subjected to varying external pressure. Then the asymptotic formulae for dynamic buckling loads considering general thickness variations are derived and expressed by geometry sizes of the shell and thickness variation functions. To validate the presented results, two specific non-axisymmetric thickness cases are discussed in detail. The critical dynamic buckling loads show a great agreement with the previous ones by other researchers for simple and axial thickness variation situation. Finally, example calculations and parametric discussion are performed, and influences of thickness variation types, speed of external pressure and the power exponent of time on the critical dynamic buckling loads are discussed.

Cross-sectional bending strength of steel Elliptical-Hollow-Sections (EHSs) based on Equivalent-Resistance-Capacity-Method (ERCM)

An expression for cross-sectional bending capacity prediction curve is proposed in this study based on the Direct-Strength-Method (DSM) approach using a comprehensive data from the literature on structural carbon steel Circular-Hollow-Sections (CHSs). Later, according to the Equivalent-Resistance-Capacity-Method (ERCM), improved empirical expressions for the equivalent CHS diameter of Elliptical-Hollow-Section (EHS) are derived using the proposed CHS bending capacity prediction curve and the data of EHSs from the literature. A unified set of cross-section slenderness limits for assessing the CHS and EHS members under bending is proposed. Also, the proposed expression for the bending resistance curve based on DSM is transformed into the generalized form of the traditional cylindrical shell buckling capacity curve as a practical solution in harmony with the newly introduced Reference-Resistance-Design (RRD) guidelines. Finally, the behaviour of EHS cantilever members under cyclic bending is assessed in terms of cyclic moment resistance and rotation capacities based on the authors' previous study.

Eigenvectors for a Cylindrical Shell under Axial Impact

A lot of research on dnamic buckling of cylindrical shells has been carried out, which greatly promotes the development of dynamic stability theory of shells. However, the existing theoretical analysis methods belong to the Lagrangian system, so it is difficult to apply the traditional variable separation method. In this paper, a symplectic system method for the dynamic buckling of elastic cylindrical shells under axial impact is presented. In symplectic space, the critical buckling load and dynamic buckling mode are simplified as general eigensolutions. In numerical results, the critical buckling load modes of elastic shells under different boundary conditions are given.

An analytical solution to the buckling of cylindrical shells under arbitrarily distributed axial loads

This paper presents an analytical study on the buckling of cylindrical shells under arbitrarily distributed axial loads. It has three main innovation points. First, different from the previous studies, the axial loads need not be assumed to be specific forms beforehand and be simple ones such as cosine type, which are arbitrary in this paper (including continuous and discontinuous distributions). Second, combining the separation of variables and perturbation methods, it develops a novel general method to solve the fourth-order partial differential equations with unknown variable coefficients for cylindrical shells under distributed axial loads. Last, it derives the asymptotic formula of buckling loads with respect to shell geometry sizes and load functions for the first time. Using the presented formula, two continuous axial load distributions are analyzed first and the results show a good agreement with previous studies and those by the Bubnov-Galerkin method. Furthermore, one discontinuous axial load distribution is investigated. Comparative study on effects of load distribution parameters and types is also performed. The study has sufficient accuracy and significant engineering application value.

Confined elasticae and the buckling of cylindrical shells

Abstract For curves of prescribed length embedded into the unit disk in two dimensions, we obtain scaling results for the minimal elastic energy as the length just exceeds 2 ⁢ π {2\pi} and in the large length limit. In the small excess length case, we prove convergence to a fourth-order obstacle-type problem with integral constraint on the real line which we then solve. From the solution, we obtain the energy expansion 2 ⁢ π + Θ ⁢ δ 1 3 + o ⁢ ( δ 1 3 ) {2\pi+\Theta\delta^{\frac{1}{3}}+o(\delta^{\frac{1}{3}})} when a curve has length 2 ⁢ π + δ {2\pi+\delta} and determine first order coefficient Θ ≈ 37 {\Theta\approx 37} . We present an application of the scaling result to buckling in two-layer cylindrical shells where we can determine an explicit bifurcation point between compression and buckling in terms of universal constants and material parameters scaling with the thickness of the inner shell.

Harnessing energy landscape exploration to control the buckling of cylindrical shells

Even for relatively simple thin shell morphologies, many different buckled configurations can be stable simultaneously. Which state is observed in practice is highly sensitive to both environmental perturbations and shell imperfections. The complexity and unpredictability of postbuckling responses has therefore raised great challenges to emerging technologies exploiting buckling transitions. Here we show how the buckling landscapes can be explored through a comprehensive survey of the stable states and the transition mechanisms between them, which we demonstrate for cylindrical shells. This is achieved by combining a simple and versatile triangulated lattice model with efficient high-dimensional free-energy minimisation and transition path finding algorithms. We then introduce the method of landscape biasing to show how the landscapes can be exploited to exert control over the postbuckling response, and develop structures which are resistant to lateral perturbations. These methods now offer the potential for studying complex buckling phenomena on a range of elastic shells.