Perfect Cylindrical Shells Research Articles

Nonlinear resonant responses of a novel FGM sandwich cylindrical shell structure for supersonic flight vehicles based on 1:1 internal resonance between conjugate modes

A new design scheme for the functionally graded material (FGM) sandwich cylindrical shell structure made of ceramic-FGM-carbon fiber composites is proposed, which is geared towards supersonic flight vehicles and has high specific stiffness and high-temperature resistance. We focus on analyzing the nonlinear resonant responses of the novel FGM sandwich cylindrical shell subjected to external excitation and aerodynamic force. Firstly, the mechanical properties of the novel FGM sandwich material are calculated, and then the nonlinear dynamic model of the FGM sandwich cylindrical shell is established based on the first order shear deformation theory (FSDT) and Hamilton's principle. Due to the axisymmetric property of the cylindrical shell, a 1:1 internal resonance between the driven and companion modes always exists in the perfect cylindrical shell. Taking this into consideration, the nonlinear resonant response problems of the FGM sandwich cylindrical shell are numerically simulated by combining the Galerkin method and the pseudo-arc length continuation method. Finally, the effects of complex parameters such as external excitation, aerodynamic force, aspect ratio, gradient index, and skin-core-skin ratio on the nonlinear resonant responses of the FGM sandwich cylindrical shell are investigated.

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

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

Stability analysis of a cylindrical shell with axially symmetric defects under axial compression based on the reduction stiffness method

Initial imperfections can greatly reduce critical buckling load of axially compressed thin-walled cylindrical shells. During the buckling process of a cylindrical shell, the total potential energy of cylindrical shell can be divided into a constant linear component and a square nonlinear component. In this study, based on deriving the buckling load of a perfect cylindrical shell under axial compression, the role of different stiffness reductions in the evaluation of stable load carrying capacity was assessed with reference to the Reduction Stiffness Method (RSM). Then the influence of initial axisymmetric defects on stiffness of each part of compressed cylindrical shell was discussed. The mechanism by which axially symmetric initial imperfections affected the stability of axially compressed cylindrical shells was analyzed. The results show that (1) Initial axisymmetric defects affected the membrane stiffness of cylindrical shell. (2) The stability carrying capacity of axially compressed cylindrical shell was reduced. (3) The initial defect was amplified by the square of instability wavenumber of cylindrical shell. Hence, a small defect could have a significant influence on stability carrying capacity of axially compressed cylindrical shell. The results presented in this paper provide a useful reference for the design of axially compressed cylindrical shell structures.

Critical buckling load prediction of axially compressed cylindrical shell based on non-destructive probing method

Critical buckling load prediction of axially compressed cylindrical shell is investigated based on the non-destructive probing method in this paper. Finite element model of the cylindrical shell under combined axial load and radial probe is established using ABAQUS and the static modified Newton-Raphson method that uses artificial damping is chosen in the geometrically and materially nonlinear buckling analysis. By the means of repeatedly probing the shell under different prescribed axial loads, the three-dimensional representation of probe force, probe displacement and prescribed axial load is established. Based on that, the critical buckling load of the shell is predicted by the fitting curve that reflecting the relationship between the maximum probe force and the prescribed axial load. Applying this prediction method, the perfect cylindrical shell, the cylindrical shells with dimple-shape imperfections and the cylindrical shell with measured imperfections have been studied. All of the predicted results are compared with the real critical loads in buckling behavior of the shells under axial compression. Effects of poker size and probing location on the prediction results are analyzed. Results show that the critical loads for the first buckling pattern of the cylindrical shells with notable local imperfections can be predicted accurately when the shell is probed at the location with the largest imperfection amplitude. If the shell is probed away from that area, the predicted result will become much larger. Compared to the probing location, the poker size has little effect on the prediction results. For the cylindrical shell with measured imperfections, probing at the location with largest imperfection amplitude has achieved the most accurate prediction result. Besides, the predicted critical buckling loads obtained by probing at other locations are also acceptable. It is believed that for a general cylindrical shell without notable local defects, the smallest one of different predicted results obtained by probing a series of representative locations on the cylindrical shell could be regarded as the critical buckling load.

ASTER Shell: a simple concept to significantly increase the plastic buckling strength of short cylinders subjected to combined external pressure and axial compression

This paper proposes a new type of shell, similar to a cylindrical shell, which has significantly higher buckling strength when subjected to an arbitrary combination of uniform external pressure and axial compression. The underlying principle consists in a slight modification of the perfect cylinder in order to counteract the natural deformations which get larger and larger and lead to the collapse of the structure. Such shells are called ASTER shells. The concept has been validated through experiments, then analyzed numerically in order to explain what was observed and to propose avenues for improvements. The shells were made of electrodeposited nickel. The material was characterized. The chosen specimens were carefully measured to characterize their thickness and initial imperfections, then tested under the various types of loading. Then they were analyzed using finite elements. Thus, we were able to compare the finite element predictions with the experimental results. This comparison shows that plasticity has a decisive influence on the critical load and that linear elastic dimensioning leads to a serious overestimation of the experimental critical load. Contrary to perfect cylindrical shells, this type of shell is not significantly affected by geometric imperfections: this is another advantage of this type of design. Finally, we propose a numerical analysis in order to optimize the choice of the shape and propose shapes which resist buckling much better than a smooth cylinder when subjected to uniform external pressure, axial compression or a combination of both.

A novel method for studying the buckling of nanotubes considering geometrical imperfections

Buckling of nanotubes has been studied using many methods such as molecular dynamics (MD), molecular mechanics, and continuum-based shell theories. In MD, motion of the individual atoms is tracked under applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics-based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that the direct application of shell theories to study nanotube buckling often leads to erroneous results. The present study reveals that a major source of this error can be attributed to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work, the nanotube is modeled as a thin-shell with initial imperfection. Then, a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this can prove to be a robust method for a continuum analysis of nanosystems taking in the effect of variation of temperature as well.

Stability of perfect and imperfect cylindrical shells under axial compression and torsion

Stability analyses of perfect and imperfect cylindrical shells under axial compression and torsion were presented. Finite element method for the stability analysis of perfect cylindrical shells was put forward through comparing critical loads and the first buckling modes with those obtained through theoretical analysis. Two typical initial defects, non-circularity and uneven thickness distribution, were studied. Critical loads decline with the increase of non-circularity, which exist in imperfect cylindrical shells under both axial compression and torsion. Non-circularity defect has no effect on the first buckling mode when cylindrical shell is under torsion. Unfortunately, it has a completely different buckling mode when cylindrical shell is under axial compression. Critical loads decline with the increase of thickness defect amplitude, which exist in imperfect cylindrical shells under both axial compression and torsion, too. A greater wave number is conducive to the stability of cylindrical shells. The first buckling mode of imperfect cylindrical shells under torsion maintains its original shape, but it changes with wave number when the cylindrical shell is under axial compression.

NUMERICAL INVESTIGATION OF INFLUENCING PARAMETER OF IMPERFECTIONS ON THIN SHORT CARBON STEEL CYLINDRICAL SHELL UNDER AXIAL COMPRESSION

Thin cylindrical shell structures have wide variety of applications due to their favorable stiffness-to-mass ratio and under axial compressive loading, these shell structures fail by their buckling instability. Hence, their load carrying capacity is decided by its buckling strength which in turn predominantly depends on the geometrical imperfections present on the shell structure. The main aim of the present study is to determine the more influential geometrical parameter out of two geometrical imperfection parameters namely, "the extent of imperfection present over a surface area" and its "amplitude". To account for these geometrical parameters simultaneously, the imperfection pattern is assumed as a dent having the shape of extent of surface area as a nearly square. The side length of extent of surface area can be considered as proportional to extent of imperfection present over an area and the dent depth can be considered as proportional to amplitude of imperfections. For the present numerical study, FE models of thin short carbon steel perfect cylindrical shells with different sizes of dent are generated at 1/3rd and half the height of cylindrical shells and analyzed using ANSYS nonlinear FE buckling analysis.

Postbuckling of functionally graded cylindrical shells based on improved Donnell equations

This paper presents an analytical approach to investigate the buckling and postbuckling of functionally graded cylindrical shells subjected to axial and transversemechanical loads incorporating the effects of temperature. Material properties are assumed to be temperature independent, and graded in the thickness direction accordingto a simple power law distribution in terms of the volume fractions of constituents. Equilibrium equations for perfect cylindrical shells are derived by using improved Donnell shell theory taking into account geometrical nonlinearity. One-term approximate solution is assumed to satisfy simply supported boundary conditions and closed-form expressions of buckling loads and load-deflection curves are determined by Galerkin method. Analysis shows the effects of material and the geometric parameters, buckling mode, pre-existent axial compressive and thermal loads on the nonlinear response of the shells.

Solving nonlinear stability problem of imperfect functionally graded circular cylindrical shells under axial compression by Galerkin's method

This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection. Equations to find the critical load and the load-deflection curve are established by Galerkin's method. Effects of buckling modes, of imperfection, of dimensional parameters and of volume fraction indexes to buckling loads and postbuckling load-deflection curves of cylindrical shells are investigated. In case of perfect cylindrical shell, the present results coincide with the ones of the paper [13] which were solved by Ritz energy method.

Neighbourhood effect of two short dents on buckling behaviour of short thin stainless steel cylindrical shells

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells. In this work, neighbourhood effect of two circumferential short dents on the buckling behaviour of thin short stainless steel cylindrical shell is studied in detail. The dents are modelled on the FE surface of perfect cylindrical shell at half the height of the cylindrical shell by varying the centre distance between the dents. These cylindrical shells are analysed using non linear FE static buckling analysis and their buckling behaviours are compared with that of cylindrical shell with a short circumferential dent. It is found that the effect of two short dents and its nearness effect seem to be negligible compared with the effect of single dent in reducing the buckling strength of cylindrical shell.

PROBABILISTIC DESIGN OF AXIALLY COMPRESSED COMPOSITE CYLINDERS WITH GEOMETRIC AND LOADING IMPERFECTIONS

The discrepancy between the analytically determined buckling load of perfect cylindrical shells and experimental test results is traced back to imperfections. The most frequently used guideline for design of cylindrical shells, NASA SP-8007, proposes a deterministic calculation of a knockdown factor with respect to the ratio of radius and wall thickness, which turned out to be very conservative in numerous cases and which is not intended for composite shells. In order to determine a lower bound for the buckling load of an arbitrary type of shell, probabilistic design methods have been developed. Measured imperfection patterns are described using double Fourier series, whereas the Fourier coefficients characterize the scattering of geometry. In this paper, probabilistic analyses of buckling loads are performed regarding Fourier coefficients as random variables. A nonlinear finite element model is used to determine buckling loads, and Monte Carlo simulations are executed. The probabilistic approach is used for a set of six similarly manufactured composite shells. The results indicate that not only geometric but also nontraditional imperfections like loading imperfections have to be considered for obtaining a reliable lower limit of the buckling load. Finally, further Monte Carlo simulations are executed including traditional as well as loading imperfections, and lower bounds of buckling loads are obtained, which are less conservative than NASA SP-8007.

Parametric study on buckling behaviour of dented short carbon steel cylindrical shell subjected to uniform axial compression

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings, etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short ( Lc/ Rc∼1, Rc/ t=117, 175, 280) cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination of dents do not have much effect on static buckling strength of thin cylindrical shells, whereas in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically. It is also found that the reduction in buckling strength of thin cylindrical shell with a dent of same size and orientation increases with increase in shell thickness.

Effect of a Dent of Different Sizes and Angles of Inclination on Buckling Strength of a Short Stainless Steel Cylindrical Shell Subjected to Uniform Axial Compression

Generally, thin cylindrical shells are susceptible for geometrical imperfections like non-circularity, non-cylindricity, dents, swellings etc. All these geometrical imperfections decrease the static buckling strength of thin cylindrical shells, but in this paper only effect of a dent on strength of a short (L / D ∼1 and R/t = 280) stainless steel cylindrical shell is considered for analysis. The dent is modeled on the FE surface of perfect cylindrical shell for different angles of inclination and sizes at half the height of cylindrical shell. The cylindrical shells with a dent are analyzed using non-linear static buckling analysis. From the results it is found that in case of shorter dents, size and angle of inclination dents do not have much effect on static buckling strength of thin cylindrical shells, where as in the case of long dents, size and angle of inclination of dents have significant effect. But both short and long dents reduce the static buckling strength drastically.

Plastic Buckling Transition Modes in Moderately Thick Cylindrical Shells

Moderately thick perfect cylindrical shells under axial compression first exhibit an axisymmetric buckling mode, where a localization of buckling patterns, referred to as an elephant foot bulge, is caused by the first plastic bifurcation. However, the transition from the axisymmetric buckling mode to a nonaxisymmetric buckling mode, referred to as a diamond buckling mode, may occur due to the next bifurcation if we continue the loading under displacement control. Herein, this phenomenon is examined, based on a rigorous plastic bifurcation analysis. As a result, it is observed that the circumferential wave number of the diamond buckling mode increases with the decrease of the wall thickness. The boundary conditions also considerably influence the occurrence of diamond buckling. It is found that the strain concentration is intensified for the diamond buckling modes, compared with the axisymmetric modes.

Buckling analysis for design of pressurized cylindrical shell panels

In contrast with the pressure buckling of a complete cylinder, even a perfect cylindrical shell panel displays a complex form of nonlinear snap buckling behaviour. The prebuckling nonlinearity has been understood to be induced by the total equivalent imperfections involving the potential-load-induced imperfection and the actual geometric imperfection. Based on this concept, an alternative estimation procedure of the elastic and elastoplastic buckling load-carrying capacities is proposed and the resulting simple equations and formulae for design are represented.

Vibrations of a fluid filled cylindrical shell excited by an oscillating piston in the fluid: Comparison between measurements and calculations

A water filled thin walled cylindrical shell was excited to vibrate by a piston displacing the water. The near-wall water pressures and the accelerations of the wall were measured and compared with corresponding computations. It was stated that the dynamic system behavior was dominated by the structure dynamics. A major finding was that a relatively small imperfection caused by a weld seam of the cylindrical shell (out-of-roundness 0.36% of the diameter) exerted a decisive influence on the dynamic behavior of the shell. Pressures and accelerations were changed by a multiple of the value calculated for the perfect cylindrical shell.

Interactive Buckling Tests on Cylindrical Shells Subjected to Axial Compression and External Pressure—A Comparison of Experiment, Theory and Various Codes

The buckling of welded steel cylindrical shells under the combined action of external pressure and axial compressive loads is of considerable interest to the offshore oil and nuclear industries. However, test results on this subject are scarce and some design rules which have been proposed recently have not been validated experimentally, especially in the plastic buckling region. In order to check these rules, and suggest others, interactive buckling tests were conducted at Liverpool University on cylindrical shells having R/t ≍ 100. One series of tests consisted of 19 machined and stress-relieved steel models having L/R ratios of 0.33, 0.74 and 1.45. The results obtained on these near-perfect machined models were compared with theoretical predictions of the behaviour of perfect cylindrical shells and the agreement between the two was good The other series consisted of 21 welded steel models and had geometric ratios which were similar to the machined ones. The linear interaction equation Sp + Sx = 1 was used to predict the failure loads of these welded steel models and the predictions were safe in all cases. However, for some combined loading cases the linear equation was rather conservative and, in consequence, some non-linear interaction equations were investigated. These seem promising for design purposes. Irrespective of whether a linear or a non-linear equation is chosen for design, more tests will be needed to establish the scatter bands of the interactive buckling curves for various values of R/t. Some tests were also carried out on (a) the effect of the loading path on the failure loads and (b) models with localized dents. Other topics discussed in the paper are: the effects of residual stresses and initial geometric imperfections, the general procedure adopted by Codes to predict buckling loads and some discrepancies between the predictions of various Codes.

Shell Buckling of Circular Cylindrical Shells With Initial Deflection

An Experimental and analytical invetigation of shell buckling of circular cylindrical shells under hydrostatic pressure was carried out in order to clarify the effect of initial deflection.Fifty-nine models with one bay and two rings, which consisted of 32-models without the initial deflection and 27-models with that, were fabricated with machine tools and were tested. The geometrical characteristics of those models are shown in Table 1.The analyses of shell buckling of those models were carried out by finite element method.The following results were obtained from the experiments and the analyses.1) It seems, from comparison of the analytical results with the experiments, that the shell buckling strength of the cylindrical shells with fixed ends will be predicted by the finite element method.2) In the lower range of the thinness factor λ (that is, 0. 7<λ<1.0) the buckling strength of the cylindrical shells with the initial deflection being one-half to equel size of the shell thicknness were 30% to 40% lower than the buckling strength of the perfect cylindrical shells having same geometrical characteristics, but, in the higher range of λ (λ>2.0), the initial deflection did not apeares to be very important.3) The cylindrical shells, in the lower range of λ (0.7<λ<0.9), could resist to higher pressure than that at which the shell buckling was caused, and those pressure almost equal to the shell buckling pressure of the perfect cylindrical shells having the same geometrical characteristics.