Paradoxical buckling behaviour of a thin cylindrical shell under axial compression

The widely accepted theory of buckling of thin cylindrical shells under axial compressive loading emphasises the sensitivity of the buckling load to the presence of initial imperfections. These imperfections are conventionally taken to be minor geometric perturbations of a shell which is initially stress-free. The original aim of the present study was to investigate the effect on the buckling load of imperfections in the form of local initial stress, which are probably more typical of practice than purely geometric ones. Experiments were performed on a vertical “melinex” cylinder of diameter 0.9 m and height 0.7 m, with radius/thickness ratio 1800. The upper and lower edges of the cylinder were clamped to end discs by means of circumferential belts — an arrangement that allowed states of self-stress to be introduced to the shell readily by means of local “uplift” at the base. The upper disc was made sufficiently heavy to buckle the shell, and it was supported by a vertical central rod under screw control. Many buckling tests were performed. Surprisingly, the buckling loads were generally at the upper end of the range of fractions of the classical buckling load that have been found in many previous experimental studies. Even when the local uplift at the base caused a local “dimple” to be formed before the shell was loaded, the buckling load was relatively high. A surface-scanning apparatus allowed the geometric form of the shell to be monitored, and the progress of such a dimple to be followed; and it was found that a dimple generally grew in size and migrated in a stable fashion up the shell as the load increased, until a point was reached when unstable buckling occurred. These unexpected and paradoxical features of the behaviour of the experimental shell may be attributed to the particular boundary conditions of the shell, which provide in effect statically determinate support conditions. This study raises some new issues in the field of shell buckling, both for the understanding of buckling phenomena and for the rational design of shells by engineers against buckling.     

Flat-topped conical shell under axial compression

Based on experimental observations of a grid-domed textile composite under axial compression, the large deformation mechanisms of a flat-topped conical shell are identified. Accordingly, both elastic model and rigid-plastic model are proposed to describe the collapse process and predict the load–displacement characteristics. In the rigid-plastic analysis, the energies dissipated in bending along plastic hinge lines and in stretching of the thin-wall segments between the plastic hinge lines are taken into account. Analytical expressions describing the load–displacement and energy–displacement relationships during the large deformation process are derived. Illustrated by typical numerical examples, the effects of apical angle of a flat-topped conical shell on its energy absorption capacity are revealed. The respective strain distributions on the conical shell resulted from bending deformation and membrane deformation are presented. A good agreement is shown between the theoretical predictions and experimental results.     

Diffraction of sound on an elastic cylindrical shell with a covering

Diffraction of a hydroacoustic field on an elastic cylindrical shell with a covering was considered. Conditions allowing minimization of the scattered field at combined selection of impedances were obtained.     

An efficient method to improve the stability of submerged functionally graded cylindrical shell

Journal of Mechanical Science and Technology - An efficient method is presented to improve the stability of a submerged functionally graded (FG) cylindrical shell which is subjected to external...     

Postbuckling of shear deformable cross-ply laminated cylindrical shells under combined external pressure and axial compression

A postbuckling analysis is presented for a shear deformable cross-ply laminated cylindrical shell of finite length subjected to combined loading of external pressure and axial compression. The governing equations are based on Reddy's higher order shear deformation shell theory with von Kármán–Donnell type of kinematic nonlinearity. 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 imperfections of the shell, is extended to the case of shear deformable laminated cylindrical shells under combined loading cases. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, unstiffened or stiffened, moderately thick, antisymmetric and symmetric cross-ply laminated cylindrical shells for different values of load-proportional parameters.     

Finite deformations of an initially stressed cylindrical shell under internal pressure

This paper investigates the large deformations of an extended thick cylindrical tube under internal pressure, with emphasis on the static nonlinear behavior and instabilities of the shell. Thick elastic tubes that undergo large elastic deformations under internal pressure can exhibit novel instabilities. After some deformation, part of the tube becomes highly deformed taking the form of a bulge, while the remainder appears almost unchanged. This local instability phenomenon corresponds to a limit point along the nonlinear equilibrium path. After the onset of these highly nonuniform deformations, the local bulge initially grows with a marked decrease in internal pressure while the rest of the tube unloads. First, a detailed experimental analysis is carried out involving different geometries and initial axial forces and the influence of the axial force and of the internal pressure on the critical pressure is investigated. The shell used in the experiments is composed of an isotropic, homogeneous and hyperelastic rubber, which is modeled as a Mooney–Rivlin incompressible material, described by two elastic constants. These constants are obtained by comparing the experimental and numerical solutions for the shell under axial tension. The governing shell equations are solved numerically using the finite-element method, using the program ABAQUS. The experimental results are, as shown in the paper, in satisfactory agreement with the numerical analysis.     

Limit pressure of a cylindrical shell with a two-dimensional array of nozzles with associated axial cracks

The limit pressure of a cylindrical shell with a two-dimensional array of penetrating nozzles and associated defects covering the whole shell has been calculated and compared with the limit pressure of the plain cylindrical shell. A lower-bound method was used. The conventional ligament efficiency method of calculating the limit pressure is too conservative. It is necessary to claim some strength from the nozzles. Hence a more elaborate method has been used here. If there are axial cracks in the main vessel tangential to some nozzles, the limit pressure is reduced to a value which is between the ligament efficiency and the value for a single crack in a plain cylinder. The actual reduction has been calculated for a range of crack lengths for a typical geometry.     

Linear and nonlinear vibration analysis of sandwich cylindrical shell with constrained viscoelastic core layer

Damping characteristics of three-layered sandwich cylindrical shell for thin and thick core viscoelastic layers are studied using semi-analytical finite element method. The finite element method is developed based on the linear and nonlinear variations of the displacement distribution through the thickness of the core layer. Transient vibration has been conducted using the developed linear and nonlinear models and shown that the nonlinear formulation exhibits more damping property than the linear model. The effect of geometric nonlinearity due to the large deformation of the shell has also been considered assuming small strain and moderate rotation. Different assumptions based on the continuity and discontinuity in transverse shear stresses and slope of in-plane displacements are considered in the finite element formulation and their effects have been investigated. Considering nonlinearity of eigenvalue problem due to the frequency dependent property of viscoelastic material, an efficient algorithm has been developed to find the natural frequencies and loss factors of the viscoelastic cylindrical shell considering large deformation. The effect of imperfect bonding between the layers has also been investigated in the modeling and it is shown that slippage between layers at the interfaces leads to reduction in loss factor at the majority of modes.     

Assessment of shell theories for hybrid piezoelectric cylindrical shell under electromechanical load

The assessment of classical lamination shell theory and first-order shear deformation theory is presented for simply supported finite circular cylindrical hybrid shell with cross-ply composite laminate as elastic substrate under electromechanical static load. Navier-type solutions are obtained and used in threedimensional equilibrium equations and transverse strain—displacement relation to obtain transverse stress components and improved value of deflection. These solutions are assessed by comparison with the threedimensional solution. The error in the two-dimensional shell theories increases as the shell becomes thicker and it is more for the patch loads in comparison to the uniformly distributed and sinusoidal loads.     

Vibrational energy flow analysis of coupled cylindrical thin shell structures

In this study, a method for energy flow analysis was developed to predict the vibrational responses of coupled cylindrical thin shell structures in the medium-to-high frequency ranges. To extend the application of the energy flow model for out-of-plane waves in the thin shell to coupled structures, the wave transmission analyses of general coupled cylindrical thin shell structures are performed. Power reflection and transmission coefficients on the coupled line were calculated using the coupling relationships established for coupled cylindrical thin shells. Using these coefficients, an energy flow analysis in which a junction was considered, was performed for coupled cylindrical thin shell structures. The junction consisted of an arbitrary number of cylindrical thin shells coupled along a junction line. Through numerical simulations, the energy flow solutions of coupled cylindrical thin shell structures were compared with those of classical displacement solutions, and they showed well-developed energy density global propagation and decay patterns.     

Postbuckling of 3D braided composite cylindrical shells under combined external pressure and axial compression in thermal environments

A postbuckling analysis is presented for a three-dimensional (3D) braided composite cylindrical shell of finite length subjected to combined loading of external pressure and axial compression in thermal environments. Based on a micro–macro-mechanical model, a 3D braided composite may be a cell system and the geometry of each cell is highly dependent on its position in the cross-section of the cylindrical shell. The material properties of epoxy are expressed as a linear function of temperature. The governing equations are based on a higher order shear deformation shell theory with a von Kármán–Donnell-type kinematic nonlinearity and includes thermal effects. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, braided composite cylindrical shells with different values of shell geometric parameter and of fiber volume fraction under combined loading conditions. The results show that the shell has lower buckling loads and postbuckling paths when the temperature-dependent properties are taken into account. The effects of temperature rise, fiber volume fraction, shell geometric parameter, load-proportional parameter, as well as initial geometric imperfections are studied.     

Plastic buckling of conical shells under axial compression

Analysis and experimental results are presented on the plastic axisymmetric buckling of steep, truncated conical shells under axial compression. Specimens of 6061-T6 aluminum and type 416 stainless steel were tested; in spite of the considerable difference in the stress-strain curves for the two materials, the buckling modes observed in the experiments for geometrically identical cones were the same. Perturbation analysis, which takes account of the continuous change in direction of the plastic strain rate vector during buckling, is found to describe the essential features of the observed buckling deformation.     

A method to calculate the reliability of the gas pipeline segment under axial compression

An algorithm is presented for probabilistic calculation of the gas pipeline strength reliability for the case when the ultimate strength of the pipe steel, compressing force, gas pressure, Young’s modulus, temperature drop, pipe thickness, and diameter are distributed normally.     

Stability of a trunk pipeline under axial seismic compression

Models for analysis of deformations of a trunk pipeline under axial seismic compression are developed. Two algorithms for calculating the main parameters of this phenomenon in the two limiting cases of a purely elastic state and the rigid-plastic pipeline model are constructed. The adequacy of these algorithms is confirmed by calculations with parameters acceptable for practice.     

轴心受压高强钢圆管稳定承载性能研究

对770MPa级高强钢管件的初始几何缺陷、残余应力和本构关系进行了测试,完成了66根770MPa级不同规格高强钢管件的轴压极限承载力试验,结合仿真分析,验证了添加初始缺陷的一致模态法分析高强钢管件极限承载力的准确性。     

弹性压杆稳定计算的方块脉冲函数法

弹性压杆特别是变截面压杆，要推导出其稳定方程和计算临界载荷是十分繁琐甚至是不可能的。这里利用方块脉冲函数(BPF)的良好运算性质直接求解弹性压杆稳定的能量泛函极值，将计算临界载荷转化为求矩阵的特征值问题，从而得到了计算弹性压杆失稳临界载荷的一种新的数值方法。该方法对于等截面压杆和变截面压杆均适用，具有计算简洁、便于计算机处理等优点，有很好的工程应用价值。     

Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium

This paper presents a study on the postbuckling response of a shear deformable functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to axial compressive loads in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless Pasternak foundation, from which the postbuckling results for FGM shells with conventional elastic foundations are also obtained for comparison purposes. The results reveal that the unilateral constraint has a significant effect on the postbuckling responses of shells subjected to axial compression in thermal environments when the foundation stiffness is sufficiently large.     

Dynamic stability of a rotor with shear-flexible shaft under axial loads

The dynamic stability of shear-flexible rotating shaft with a disk under axial forces has been studied by employing the transfer matrix method. The conventional transfer matrix was modified to include both the applied axial force and the shear deformation. The shear effect is considered based on Engesser’s and Haringx’s buckling theories for shear-flexible beam. A computer program was developed to investigate the influence of both the axial force and the shear deformation on the stability and the natural frequencies of general rotor systems. Two rotor system models are considered: the overhung rotor with or without an intermediate support and the simply supported Jeffcott rotor. The effect of shear deformation and the difference between the Engesser and Haringx approaches increase with an intermediate support for an overhung rotor.     

Steady-state thermo-hydrodynamic analysis of cylindrical fluid film journal bearing with an axial groove

A steady-state thermohydrodynamic analysis of an axial groove journal bearings in which oil is supplied at constant pressure is performed theoretically. Thermohydrodynamic analysis requires simultaneous solution of Reynolds equation, energy equation and heat conduction equations in the bush and the shaft. From parametric study it is found that the temperature of the fluid film raises due to frictional heat thereby viscosity, load capacity decreases. Increased shaft speed resulted in increased load carrying capacity, bush temperature, flow rate and friction variable. It is difficult to obtain the solution due to numerical instability when the bearing is operated at high eccentricity ratios.     

Classification of the axial collapse of cylindrical tubes under quasi-static loading

The results of an experimental investigation of the axial crushing modes and energy absorption properties of quasi-statically compressed aluminium alloy tubes are presented. In particular, the influence of tube length on these properties is discussed and quantified and a classification chart presented. This chart together with other experimental data, enables a designer to predict the energy absorbing properties of a given tube as well as its mode of crushing.