Buckling Of Shells Research Articles

Buckling of cylindrical metal shells on discretely supported ring beams

Silos in the form of cylindrical metal shells are usually supported on evenly spaced columns in applications where an access space is needed for the discharge of contained solids. In large silos a ring beam is used to distribute the column forces into the shell. The presence of discrete supports results in a circumferential non-uniformity of axial stresses in the shell. This non-uniformity leads to high local stresses that must be considered in assessing the possibility of shell buckling. Design standards provide recommendations for the buckling of shells under uniform axial compression, but are largely silent concerning stress peaks that may vary in width. Designers must resort either to onerous finite element analyses that include both geometric and material nonlinearities with imperfections (GMNIA) or trust to their own judgment. This paper presents a parametric study to develop resistance or capacity curves which can be used directly in design without the need for complicated analysis. The proposed design method uses only hand calculations apart from a simple linear finite element analysis to determine the degree of non-uniformity in the axial stresses.

Dynamic Buckling of Cylindrical Shells with Arbitrary Axisymmetric Thickness Variation under Time Dependent External Pressure

This paper presents an analytical study on the critical dynamic buckling load of cylindrical shells with arbitrary axisymmetric thickness variation under uniform external pressure which is a function of time. Based on the Donnell simplified principle, the equilibrium and compatibility equations of cylindrical shells with arbitrary axisymmetric wall thickness under dynamic external pressure were derived. By using the method of separation of variables, the equations were transformed into ordinary differential equations in nondimensional form. Combining Fourier series expansion and the regular perturbation method, as well as the Sachenkov–Baktieva method, analytical formulas of the critical buckling load of cylindrical shells with arbitrary axisymmetric thickness variation under dynamic external pressure that varies as a power function of time were obtained. Using these analytical formulas, the critical dynamic buckling load of cylindrical shells with linearly and parbolically varying thickness were computed. The influences of thickness variation parameter and loading speed of external pressure on the critical buckling load were also discussed. The method was also applied to cylindrical shells with a classical cosine form thickness variation, by introducing the reduction factor of critical dynamic buckling load. The buckling capacity of these cylindrical shells under dynamic external pressure was discussed considering the effects of loading speed and thickness variation parameter.

Optimal Structure Design of Elliptical Deep-Submersible Pressure Hull

Geometric configurations such as hull shape, shell thickness, stiffener layout, and type of materials are the key factors influencing the structural performance of pressure hulls. The aim of this study is to maximize the structural efficiency of elliptical deep-submerged pressure hull under hydrostatic pressure. Minimize the buoyancy factor of a submarine pressure hull under hydrostatic pressure was proposed as an objective function for both composite and steel models. The thickness and the orientation angle of each layer, the radii of the ellipse and the operating depth are taken as design variables. Also, the shell buckling strength and the angle-ply laminated failure strength are considered in the case of composite model. In the other hand, the shell thickness, the radii of the ellipse, the stiffeners offsets, the stiffeners dimensions, and the operating depth, are selected as design variables for steel model with shell buckling and materials yielding constraints. The analysis is performed using commercial finite element analysis software ANSYS. Additionally, a sensitivity analysis is performed to study the influence of the design variables on the structural optimum design. Results of this study provide a valuable reference for designers of underwater vehicles.

The Computer Simulation of the Dynamic Buckling of Cyclindrical Shells under Pulse Load

The computer simulation of the dynamic buckling on the cylindrical shell subjected to pulse load was carried out by ABAQUS/Expliect. The value of the rectangle and triangle pulse load is the same and the shape is different, and they are applied on the impact end of the cyclindrical shell. The influence of the load amplitude, the shape of load and the effect of the stress wave on the critical buckling time of cylindrical shell were discussed. The radial displacement curve was obtained which indicates that stress wave propagate along the length of the cylindrical shells, and the curve of strain time history is also acquired which is used to judge bifurcation and give the critical time.

Nonlinear Deformation of Shells with Finite Angles of Rotation and Low Elastoplastic Strains

An incremental approach to the statement and solution of the problem of the nonlinear deformation of shells under loads that cause buckling and strong bending in the plastic range is developed. The relations between strains and displacements for great angles of rotation are used. A system of differential equations for the rates of the unknown functions is derived and represented in Cauchy operator form. To solve the boundary-value problem, the discrete-orthogonalization method is used assuming that the unknown functions and the loads are equivalent. The problem of the buckling and postbuckling behavior of a long D16T-alloy shell with a local initial deflection is solved as an example

Analysis of the Particle Formation Process of Structured Microparticles.

The particle formation process for microparticles of cellulose acetate butyrate dried from an acetone solution was investigated experimentally and theoretically. A monodisperse droplet chain was used to produce solution microdroplets in a size range of 55-70 μm with solution concentrations of 0.37 and 10 mg/mL. As the droplets dried in a laminar air flow with a temperature of 30, 40, or 55 °C, the particle formation process was recorded by two independent optical methods. Dried particles in a size range of 10-30 μm were collected for morphology analysis, showing hollow, elongated particles whose structure was dependent on the drying gas temperature and initial solution concentration. The setup allowed comprehensive measurements of the particle formation process to be made, including the period after initial shell formation. The early particle formation process for this system was controlled by the diffusion of cellulose acetate butyrate in the liquid phase, whereas later stages of the process were dominated by shell buckling and folding.

Snap-Through Buckling Problem of Spherical Shell Structure

This paper presents results of a numerical study on the nonlinear behavior of shells undergoing snap-through instability. This research investigates the problem of snap-through buckling of spherical shells applying nonlinear finite element analysis utilizing ANSYS Program. The shell structure was modeled by axisymmetric thin shell of finite elements. Shells undergoing snap-through buckling meet with significant geometric change of their physical configuration, i.e. enduring large deflections during their deformation process. Therefore snap-through buckling of shells basically is a nonlinear problem. Nonlinear numerical operations need to be applied in their analysis. The problem was solved by a scheme of incremental iterative procedures applying Newton-Raphson method in combination with the known line search as well as the arc- length methods. The effects of thickness and depth variation of the shell is taken care of by considering their geometrical parameter l . The results of this study reveal that spherical shell structures subjected to pressure loading experience snap-through instability for values of l ≥2.15. A form of ‘turn-back’ of the load-displacement curve took place at load levels prior to the achievement of the critical point. This phenomenon was observed for values of l =5.0 to l =7.0.

Failure mechanisms in thin-walled nanocrystalline cylinders under uniaxial compression

Lattice materials composed of hollow nanocrystalline struts have recently made it possible to access new regions of material property space, by exploiting structural efficiencies along multiple length scales (nanometre to centimetre range). An important design issue for these materials is to understand how the failure mechanisms that act at these scales affect the macroscopic mechanical properties. In this study, we tested hollow nanocrystalline cylinders of two different grain sizes (20nm and 100nm) in uniaxial compression to investigate the effect of grain size on dominant failure mechanisms, and the influence of the latter on the compressive strength. The finite element method was used to model the interaction of the three observed failure mechanisms: shell buckling (SB), yielding (Y) and fracture (F). Depending on the grain size and geometry, the failure sequence can be SB–Y–F, Y–SB–F, SB–Y or Y–SB, the order of which has important implications in defining the limits of mechanical performance. One such implication is that when shell buckling occurs in the inelastic regime of the material, the macroscopic strength increase due to grain size refinement can be greater than the inherent yield strength increase of the material. Second, material fracture and shell buckling may not be competing failure mechanisms, which means that the effectiveness of grain size reduction in increasing the structural efficiency of cylindrical strut members can span the entire Hall–Petch range of the material.

Computer simulation of local and global buckling of thin-walled shells

Stability of thin-walled structures is investigated on the basis of the geometrically nonlinear theory of shells. This allows us to monitor a series of shell deformation processes under different load changes. The local and general loss of stability can be determined by observing changes in the shape of the shell curved surface before and after critical loads. The shell material can be isotropic or orthotropic, but linear-elastic. A mathematical model of deformation of a shell is the functional of total potential energy of deformation of the shell. Two methods are applied to minimize the total energy functional of deformation of the shell. One is based on the method of L-BFGS with discrete approximation of the unknown functions by NURBS-surfaces. This enables taking into account various forms of fixing of the shell contour and the complex shape of this circuit. The other employs the Ritz method and the best parameter continuation method in the continuous approximation of the unknown displacement functions and the angles of rotation of the normal. This technique allows us to find the upper and lower critical loads and the bifurcation point. A combination of these techniques makes it possible to study both the subcritical and supercritical behavior of the structure and to identify the local and global buckling of the shell and their relationship. On the curve of equilibrium states versus “load q - deflection W ” one can see all moments of buckling of the shell caused by “swatting” of some part of it. Thus, after each buckling a significant change in the shape of the curved surface is observed. For illustration purposes the changes in the shell shape at subcritical and supercritical stages are plotted against its three-dimensional surface. After the general loss of stability the shell deforms under loading without any significant change in its shape, i.e. it behaves as a plate.

外圧を受けるリング補強円筒殻の胴板座屈強度および補強リングの横倒れ座屈強度に関する研究

Ring stiffened cylinder is generally used as main structural members of offshore and submergible structures. In designing of such structures, it is very important to estimate the buckling strength of ring stiffened cylinder under external pressure accurately. The buckling mode of ring stiffened cylinder under external pressure can be divided into the following four modes. The first is the general buckling mode which occurs over the entire length of the cylinder involving ring stiffeners. The second is the shell buckling mode which is the buckling of cylindrical shell between the ring stiffeners. The third is the frame tripping mode of ring stiffener. The fourth is the local buckling mode of ring stiffener’s web or face. The purpose of this research is to propose the simplified formula for predicting the elastic shell buckling strength included the influence of stress ratio of shell and ring stiffener, and to propose the simplified formula for predicting the elastic ring frame tripping strength combined the proposed formula of the elastic shell buckling strength. The elastic shell buckling strength and the elastic ring frame tripping strength predicted by these simplified formulas are compared with the result of finite element analysis by changing various parameters, such as the scantling of ring stiffener and shell thickness. From the comparison of these results, accuracy of these simplified formulas is examined.

Comparison of Buckling of Aboveground Oil Storage Tanks and Cylindrical Shells under both Internal and External Liquid Pressure

Comparison of Buckling of Aboveground Oil Storage Tanks and Cylindrical Shells under both Internal and External Liquid Pressure

Mechanical Behavior of Single-Layer Two-Way Grid Cylindrical Latticed Shell with Out-of-Plane Tension Members

Single layer two-way grid shell with in-plane and out-of-plane tension members is a new type of single-layer latticed shell roof. This study treats the effects of tension member installation on the buckling load and strength of a single layer two-way grid cylindrical shell roof by the numerical method. The tension members are installed to stiffen the rigidity of a single layer two-way grid shell roof and improve its stability behavior. Tension member installation and placement pattern is focused as both diagonal members of two-way grids and out-of-plane stiffened members in a cylindrical surface. The diagonal member and the out-of-plane member are used to increase the in-plane and the out-of-plane rigidity of a single layer two-way grid shell, respectively. The tension member placement pattern, the load distribution patterns, the initial imperfections and the initial axial force are considered for the numerical calculation parameters. It is confirmed by the numerical analysis that the tension members in out-of-plane and diagonals caused the increase in the buckling and strength of two-way grid shell.

Accurate buckling analysis for shear deformable FGM cylindrical shells under axial compression and thermal loads

Based on the Reddy’s high-order shear deformation theory, buckling behaviors of the FGM cylindrical shells subjected to an axial compression in thermal environment are investigated analytically. Considering the temperature-dependent FGMs properties, the constituent distribution across the shell thickness is assumed to follow the volume fraction rule of mixture. Through the variational principle, basic equations are derived for shear deformable FGM cylindrical shell with the initial geometric imperfection. Method of separation of variables and Galerkin’s solving process are employed in dealing with the stability governing equations of perfect and imperfect shells, respectively. By changing the boundary conditions, material types, composition distributions, thermal load and temperature fields, the effect of the transverse shear deformation is evaluated by comparing with the results of the classical Donnell’s theory. Meanwhile, imperfection sensitivity for buckling of the shear deformable FGM cylindrical shell is discussed in detail.

Postbuckling behavior of stringer versus ring reinforced geometrically imperfect cylindrical shells under pure torsion

This paper deals with the buckling and initial-postbuckling behavior and imperfection-sensitivity of stringer or ring stiffened cylindrical shells under pure torsion. In particular, the effectiveness of stringer versus ring reinforced shells is examined for various types of stiffener and shell parameters under different boundary condition. The initial-postbuckling single-mode analysis is performed using Koiter’s general theory of elastic stability. By changing the parameters of stringer or ring, we are able to find out how does the stringer or ring affecting the buckling and post-buckling behavior of cylindrical shells.

Nonlinear post-buckling of thin FGM annular spherical shells under mechanical loads and resting on elastic foundations

This paper presents an analytical approach to investigate the nonlinear buckling and post-buckling of thin annular spherical shells made of functionally graded materials (FGM) and subjected to mechanical load and resting on Winkler-Pasternak type elastic foundations. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for annular spherical shells are derived by using the classical thin shell theory in terms of the shell deflection and the stress function. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain closed-form of load-deflection paths. An analysis is carried out to show the effects of material and geometrical properties and combination of loads on the stability of the annular spherical shells.

Nonlinear buckling of higher deformable S-FGM thick circular cylindrical shells with metal–ceramic–metal layers surrounded on elastic foundations in thermal environment

An analytical approach on the nonlinear response of thick functionally graded circular cylindrical shells with temperature independent material property surrounded on elastic foundations subjected to mechanical and thermal loads is presented. Material properties are graded in the thickness direction according to a Sigmoid power law distribution in terms of the volume fractions of constituents (S-FGM). The formulations are based on the third order shear deformation shell theory taking into account von Karman nonlinearity, initial geometrical imperfection and Pasternak type elastic foundation. By applying Galerkin method and using stress function, explicit relations of thermal load–deflection curves of the S-FGM shells are determined. Detailed parametric studies are carried out to investigate effects of volume fraction index, material properties and geometrical shapes, axial compressions and thermal load, foundation stiffness and imperfection on nonlinear buckling behaviors of S-FGM thick circular cylindrical shells. The present analysis is validated by comparing results with other publications.

Influence of Cutout Position on Buckling of Large-Scale Thin-Walled Cylindrical Shell of Desulphurizing Tower with Welding Induced Imperfection under Wind Loading

Not only the geometrical imperfection induced by welding but also cutouts will influence the buckling of large-scale thin-walled steel cylindrical shell under wind loading. Based on the practical cylindrical shells of a desulphurizing absorption tower, in consideration of the correlation between welding induced imperfection and circular cutouts, the influence of cutout position on buckling of cylinder under wind loading is investigated by nonlinear finite element method. The results indicate that the buckling capacity varies slightly when the cutout position moves along meridional direction in the neighboring region of welding imperfection. The buckling capacity varies significantly when the cutout position moves circumferentially as the cutout is located in the welding imperfection. The buckling capacity reaches the minimum value as the cutout is located in the buckle center of cylindrical shells without cutout.

Buckling and postbuckling of anisotropic laminated cylindrical shells under combined external pressure and axial compression in thermal environments

The buckling and postbuckling analysis for an anisotropic laminated thin cylindrical shell of finite length subjected to combined loading of external pressure and axial compression using the boundary layer theory is presented. The material of each layer in the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are obtained utilizing classical shell theory and von Kármán–Donnell strain displacement relations. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfection of the shell, is extended to the case of anisotropic laminated thin cylindrical shells under combined loading cases. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. Postbuckling response of perfect and imperfect, anisotropic laminated cylindrical shells with respect to the material and geometric properties and load-proportional parameters under different sets of thermal environmental conditions is numerically illustrated. The analytical model developed can be used as a versatile and accurate tool to study the buckling and postbuckling behavior of composite structures.

Analytical Study on the Buckling of Cylindrical Shells With Arbitrary Thickness Imperfections Under Axial Compression

This paper presents an analytical study on the buckling of axially compressed cylindrical shells with arbitrary thickness imperfections (nonaxisymmetric and axisymmetric). First, the basic governing partial differential equations, which consider thickness imperfections, are obtained. Second, a unified method that combines the perturbation method and Fourier series expansion is developed to derive buckling load, radial displacement and stress function, that are expressed by triple series in terms of thickness imperfection parameter and buckling modes up to arbitrary order. Third, two patterns of nonaxisymmetric thickness imperfections, which are modal and exponential, are, respectively, investigated. These results are absolutely new to literature. When modal thickness imperfection becomes axisymmetric, the buckling loads degenerate to the known results. In addition to the analytical investigation, analyses and comparisons are also carried out.

Thermal buckling of temperature-dependent FGM conical shells with arbitrary edge supports

Bifurcation behavior of heated conical shell made of a through-the-thickness functionally graded material is investigated in the present research. Properties of the shell are obtained based on a power law form across the thickness. Temperature dependency of the constituents is also taken into account. The heat conduction equation of the shell is solved based on an iterative generalized differential quadrature method (GDQM). General nonlinear equilibrium equations and the associated boundary conditions are obtained using the virtual displacement principle in the Donnell sense. The prebuckling solution of the shell is obtained under the assumption of linear membrane deformations. The stability equations are extracted via the concept of the adjacent equilibrium criterion. A semi-analytical solution employing the GDQM and trigonometric expansion is implemented to solve the stability equations. Numerical results of the present research are compared and validated with the known available data through the open literature. Some parametric studies are conducted to investigate the influences of various involved parameters, such as the cone semi-vertex angle, boundary conditions, power law index of composition rule, length to thickness ratio, and the radius to thickness ratio.