Imperfect Cylindrical Shells Research Articles

A probabilistic identification of the buckling resistance of imperfect cylindrical shells in axial compression

The buckling resistance of imperfect circular cylindrical shells of elastic and isotropic material subject to axial compression is studied focusing on initial geometric imperfections. Considering the imperfections as a random field, the suggested probabilistic representation of the buckling resistance parallels the deterministic dependence of buckling loads on the size and shape of imperfections. It derives from the probability density function of an imperfection size measure and the conditional probability density functions of the resistance confined to the realizations of imperfections given their size levels. The separated representation of the buckling resistance allows: (1) supplementary checking the accuracy of the random field representation, (2) classifying measured and simulated imperfections by their size and shape effects on buckling loads, (3) prospective delimiting the range of working imperfections for fabrication tolerance classes, and (4) defining the characteristic imperfection for the semi-probabilistic design. Introductory calculations illustrate the dependence of the normalized buckling loads of a shell on the shape and size of imperfections.

Nonlinear three-dimensional stability characteristics of geometrically imperfect nanoshells under axial compression and surface residual stress

Abstract Through reduction of thickness value in nanostructures, the features of surface elasticity become more prominent due to having a high surface-to-volume ratio. The main aim of this research work was to examine the surface residual stress effect on the three-dimensional nonlinear stability characteristics of geometrically perfect and imperfect cylindrical shells at nanoscale under axial compression. To do so, an unconventional three-dimensional shell model was established via combination of the three-dimensional shell formulations and the Gurtin–Murdoch theory of elasticity. The silicon material is selected as a case study, which is the most utilized material in the design of micro-electromechanically systems. Then, the moving Kriging meshfree approach was applied to take numerically into account the surface free energy effects and the initial geometrical imperfection in the three-dimensional nonlinear stability curves. Accordingly, the considered cylindrical shell domain was discretized via a set of nodes together using the quadratic polynomial type of basis shape functions and an appropriate correlation function. It was found that the surface stress effects lead to an increase the critical axial buckling load of a perfect silicon nanoshell about 82.4 % 82.4 \% for the shell thickness of 2 nm 2{\rm{nm}} , about 32.4 % 32.4 \% for the shell thickness of 5 nm 5{\rm{nm}} , about 15.8 % 15.8 \% for the shell thickness of 10 nm 10{\rm{nm}} , and about 7.5 % 7.5 \% for the shell thickness of 20 nm 20{\rm{nm}} . These enhancements in the value of the critical axial buckling load for a geometrically imperfect silicon nanoshell become about 92.9 % 92.9 \% for the shell thickness of 2 nm 2{\rm{nm}} , about 36.5 % 36.5 \% for the shell thickness of 5 nm 5{\rm{nm}} , about 17.7 % 17.7 \% for the shell thickness of 10 nm 10{\rm{nm}} , and about 8.8 % 8.8 \% for the shell thickness of 20 nm 20{\rm{nm}} .

Imperfection Sensitivity of Cylindrical Shells Under Shear Loading

AbstractOne of the basic load cases relevant for the design of shell structures is torsion, which can occur exemplary in silos and tanks under seismic actions or even under wind loading. To address the stability problem of cylindrical shells under this load case, the relevant design standard EN 1993‐1‐6 and the European Recommendation ECCS EDR5 provide simple approaches for the buckling design of cylindrical shells. In order to improve the current hand calculation rules given in the above documents, this numerical study attempts to include the imperfection sensitivity of cylindrical shells subjected to uniform torsion.In the present paper, theoretical, numerical, and experimental results from the literature are reviewed, and new systematic computational analyses and evaluations are introduced regarding the imperfection sensitivity of cylindrical shells under shear loading. For this purpose, a comprehensive computational study was performed using linear and nonlinear buckling analyses on perfect and imperfect shells. Since the influence of imperfections on the buckling strength of cylindrical shells is highly dependent on the imperfection pattern used in the numerical models, nonlinear buckling analyses were performed on imperfect cylindrical shells with three imperfection types: (i) eigenmode‐affine shape from torsion, (ii) longitudinal eigenmode‐affine pattern, and (iii) eigenmode‐affine shape from external pressure.

Imperfection Sensitivity of Large Cylindrical Shells Under Vacuum Considering Different Geometric Ratios

AbstractThe prediction of the buckling resistance of shells is subject to uncertainty since it depends significantly on the initial geometric imperfections caused by the fabrication process. However, the load case of vacuum or uniform external pressure has not yet been extensively studied. Stress design approaches implement a reduction factor alpha that accounts for the effect of imperfections. This factor is assumed to be a general lower bound but does not account for different geometric ratios. However, it is to be expected that different imperfection sensitivities prevail for different cylinder lengths or length to thickness ratios. To better understand this aspect, a comprehensive numerical study of buckling resistances of imperfect cylindrical shells is conducted, which covers a range of different length, radius and thickness ratios with focus on thicker and shorter cylinders. Within this study, three different geometric imperfection forms are investigated: linear bifurcation eigenmodes, and ovalisation and weld depressions, which represent typical imperfections of manufacturing processes. Further, a formulation for longitudinal weld depressions is introduced, since this direction of the imperfection is more deleterious than axisymmetric circumferential weld depressions. The results of this comprehensive study contribute to understanding the effect of different imperfection forms and amplitudes on different cylinder dimensions.

Stochastic analysis of geometrically imperfect thin cylindrical shells using topology-aware uncertainty models

Buckling of thin-shell structures is one of the most canonical problems in mechanics. In practice, the buckling load and its deviation from theoretical prediction is often handled through the development of knock-down factors in shell structure design. Uncertainty-informed analysis based design is an alternative path that has been aggressively pursued in recent years. In this study, we use a novel representation of the stochastically imperfect shell geometry to investigate the buckling behavior of imperfect cylindrical shells. The representations rest on a non-Gaussian random field model, obtained by translating a latent Gaussian field defined as the solution to a stochastic partial differential equation and allows for the construction of topology-aware spatially correlated imperfections on nonconvex domains. We perform finite element analysis of buckling for imperfect shells and gain new insights into how the interplay between random imperfections and topological features influences buckling behavior.

Alternative approach for imperfection-tolerant design optimization of stiffened cylindrical shells via energy barrier method

Imperfection sensitivity analysis of stiffened shells generally involves high computational cost, thus imperfection-tolerant design is a challenging issue. The concept of using the energy barrier to predict the buckling load of imperfect cylindrical shells has exhibited potential for practical application. In this study, the energy barrier method is used for stiffened cylindrical shells to obtain the minimum post-buckling load, and the numerical-based smeared stiffener method (NSSM) is employed to accelerate the analysis process. Then, an imperfection-tolerant design optimization framework for stiffened cylindrical shells is established via energy barrier method. Results show that the design configuration of a stiffened cylindrical shell with higher imperfection tolerance capacity can be obtained by the proposed method in a more efficient manner.

Effect of geometric imperfections and circumferential symmetry on the internal resonances of cylindrical shells

In the present work the resonant response of an imperfect cylindrical shell is investigated using Donnell’s nonlinear shallow shell theory. For this, a reduced order multi degree of freedom model is obtained by discretizing the partial differential equation of motion using the Galerkin procedure and a consistent modal expansion which captures the nonlinear modal interactions and couplings between two asymmetric vibration modes with near commensurable natural frequencies in a 1:2 ratio. As a result of the circumferential symmetry each mode exhibits a 1:1 internal resonance, leading to a possible 1:1:2:2 multiple internal resonances. These modes are coupled through quadratic and cubic nonlinearities arising from the shell curvature and nonlinear strain–displacement relation. The existence and stability of solutions and their bifurcations are investigated using numerical continuation methods for bifurcation analysis and their stability are studied using Floquet theory. It is known that geometric imperfections have a strong influence on the response of thin shell structures. Here, a detailed parametric analysis shows the influence of different forms of geometric imperfections on the shell natural frequencies and bifurcations in the main resonance region. Several branches of solutions due to multiple bifurcations are detected leading to dynamic jumps under increasing and decreasing frequency sweep. Steady-state harmonic and quasi-periodic responses resulting from Neimark–Sacker bifurcations are detected. The reduced order model demonstrates the influence of the geometric imperfection shape and magnitude on the bifurcation scenario and the energy transfer among the four interacting modes.

Non-destructive prediction of buckling load of axially compressed cylindrical shells using Least Resistance Path to Probing

Stability properties of localized states is of great significance in the determination of nonlinear buckling characteristics of an axially loaded cylindrical shell. We have analyzed these localized states with the help of carefully carried out experiments by using an external poker. The focus of this study is on assessing the practical feasibility for obtaining the peak load carrying capacity of an imperfect (near perfect) cylindrical shell, for which no prior knowledge of the location of dominant defect is present. Three different methods are attempted: Method 1- Probing at a single arbitrary location, Method 2 – Probing at multiple locations, Method 3- Probing at multiple locations to find the Least Resistant Path (LRP). The results indicate that the determination of LRP and hence the location which corresponds to the least energy barrier can significantly improve the efficacy of the probing procedure.

Imperfection sensitivity of unstiffened cylindrical shells under external pressure

AbstractThe design rules for cylindrical shells subjected to uniform external pressure can be found in corresponding codes and recommendations, e.g. in EN 1993‐1‐6 (2007) or European Recommendation ECCS EDR5 (2008). Although the buckling strength of thin‐walled shells is highly dependent on the imperfections caused by various fabrication or manufacturing processes, the sensitivity of the buckling resistance of an imperfect shell to the amplitude of the geometric imperfections is not taken into account in design rules of standards.This paper investigates in detail the effect of boundary conditions and cylinder length on the linear buckling behaviour of cylindrical shells subjected to uniform external pressure. Following this, a comprehensive computational study is performed using geometrically nonlinear analyses on imperfect cylindrical shells with two‐imperfection types: (i) eigenmode‐affine form and (ii) longitudinal eigenmode‐affine pattern. Based on the numerical results obtained from eigenvalue analyses, the existing formulae of EN 1993‐1‐6 for the external pressure buckling factor Cβs of short cylindrical shells are modified to provide a more accurate prediction of the elastic critical circumferential buckling stress. The effects of geometric nonlinearity and imperfection sensitivity on the buckling strength are also briefly explored.

Static and dynamic postbuckling analysis of imperfect SSFG cylindrical shells surrounded by nonlinear elastic foundation subjected to an axial compression

In this article, the semianalytical method based on the Galerkin technique and fourth-order Runge-Kutta method is utilized to investigate the static and dynamic postbuckling analysis of internal/external spiral stiffened functionally graded (ISSFG/ESSFG) cylindrical shells, respectively. The simply supported SSFG shell subjected to an axial compression is resting on a nonlinear elastic foundation (EF) which is including the Pasternak and Winkler foundation parameters augmented by a softening/hardening cubic nonlinearity. The material constitutes of both the stiffeners and the shells that are continuously changed along the thickness. The discretized motion equation is extracted utilizing the Galerkin method regarding to the Donnel’s shells theory and nonlinear strain-displacement von Kármán. To obtain the responses of dynamic postbuckling (DPB) analysis, the fourth-order Runge-Kutta method is utilized. To validate the results, comparisons are made with the available solutions for both static postbuckling (SPB) and DPB analysis of stiffened homogeneous and functionally graded cylindrical shells. The influences of various material and geometrical parameters with the inclusion of the supporting nonlinear EF on the SPB and DPB behavior of imperfect ISSFG/ESSFG cylindrical shells are presented. As one of the most interesting results, for the ISSFG cylindrical shells with the stiffeners angle and ESSFG cylindrical shells with the stiffeners angle the buckling load-bearing capacity is the most.

Incomplete reduced stiffness method for imperfection sensitivity of cylindrical shells

Cylindrical shells are commonly used in the industry structures, and they are prone to buckling under axial compression load. However, the practical critical loads are often lower than the theoretical value of buckling load due to the presence of imperfections. In this paper, an incomplete reduced stiffness method (iRSM) is proposed to perform the imperfection sensitivity analysis of cylindrical shells. In the iRSM, it is assumed that membrane stiffness components of the shell would be eroded at the critical buckling state, and a reduction function with two parameters is proposed to describe the mapping between membrane stiffness components and the geometric imperfections of the shell. Then, the buckling load of imperfect cylindrical shells can be obtained by solving the linear buckling problem of the reduced-stiffness system. For typical cylindrical shells, the reduction function is determined according to the measured imperfection and experimental results. By comparison with the experimental results and other conventional methods, it is demonstrated that the iRSM is a high-accurate, slightly conservative and fast method to perform the imperfection sensitivity of cylindrical shells.

Elastic Imperfect Cylindrical Shells of Varying Length under Combined Axial Compression and Bending

AbstractThis paper presents a comprehensive computational investigation of the elastic nonlinear buckling response of near-perfect and highly imperfect uniform-thickness thin cylindrical shells of ...

Combination resonances of imperfect SSFG cylindrical shells rested on viscoelastic foundations

The present paper investigates the combination resonance behavior of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal and external functionally graded stiffeners under two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. With regard to classical plate theory of shells, von-Karman equation and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The combination resonance is obtained by using the multiple scales method. Finally, the influences of the stiffeners angles, foundation type, the nonlinear elastic foundation coefficients, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

Modelling of Random Geometrical Imperfections and Reliability Calculations for Thin Cylindrical Shell Subjected to Lateral Pressure

It is well known that it is very difficult to manufacture perfect thin cylindrical shell. Initial geometrical imperfections existing in the shell structure is one of the main determining factor for load bearing capacity of thin cylindrical shell under uniform lateral pressure. As these imperfections are random, the strength of same size cylindrical shell will also random and a statistical method can be preferred to find the allowable load of these shell structures and therefore a In this work the cylindrical shell of size R/t = 228, L/R = 2 and t=1mm is taken for study. The random geometrical imperfections are modeled by linearly adding the first 10 eigen mode shapes using 2kfullfactorial design matrix of DoE. By adopting this method 1024 FE random imperfect cylindrical shell models are generated with tolerance limit of ± 1 mm. Nonlinear static FE analysis of ANSYS is used to find the buckling strength of these 1024 models. FE results of 1024 models are used to predict the reliability based on MVFOSM method.

Computation of worst geometric imperfection profiles of composite cylindrical shell panels by minimizing the non-linear buckling load

• Semi-analytical method is used to compute limit point loads of imperfect cylindrical shell panel. • Global imperfection is represented by double Fourier series . • The unknown Fourier coefficients are determined using genetic algorithm which gives the lowest limit point load. • The “worst imperfection” profile is reported for various stacking sequences of laminated composite cylindrical panel. In this article the “most unfavorable” shape of initial geometric imperfection profile for laminated cylindrical shell panel is obtained analytically by minimizing the limit point load. The partial differential equations governing the shell stability problem are reduced to a set of non-linear algebraic equations using Galerkin's technique. The non-linear equilibrium path is traced by employing Newton–Raphson method in conjunction with the Riks approach. A double Fourier series is used to represent the initial geometric imperfection profile for the cylindrical shell panel. The optimum values of these Fourier coefficients are determined by minimizing the limit point load using genetic algorithm. The results are determined for simply supported composite cylindrical shell panel. Numerical results show that more number of terms is needed in Fourier series representation to obtain the “worst” geometric imperfection profile which gives lower limit load compared to single term representation of imperfection. We have incorporated constraints on the shape of imperfection to avoid unrealistic limit point loads (due to imperfection shape) as we have assumed that the imperfection is due to machining/manufactuting.

BUCKLING ASSESSMENT OF IMPERFECT CYLINDRICAL SHELLS UNDER AXIAL LOADS USING A GEP TECHNIQUE

Determination of buckling behavior of shell structures has long been identified as a challenging task. This is largely because the buckling behavior is masked by local large deformations, which occur once the critical load is reached. This research proposes a novel technique to accurately predict the buckling load of imperfect cylindrical shells using gene expression programming (GEP), which is an evolutionary artificial intelligence method. An existing experimental data bank was employed for training and testing the program, and the obtained buckling load of shell structures were accordingly verified. From the results, it is concluded that GEP is a promising and reliable method to determine the buckling load of shell structures subjected to axial compression.

Mechanical stability of metal foam cylindrical shells with various porosity distributions

The paper deals with the nonlinear buckling analysis of imperfect cylindrical shells made of porous metal foam subjected to axial compression. For the metal foam shells, porosities are dispersed by uniform, symmetric, and asymmetric distributions in the thickness direction. Using Donnell shell theory and von-Karman nonlinear kinematics, nonlinear equilibrium equations are derived. The critical buckling load and buckling equilibrium curves for both perfect and imperfect shells are solved by using the Galerkin's procedure. A comprehensive investigation into the influence of porosity coefficient, imperfections, porosity distribution, and geometry on the buckling behaviors of the cylindrical shell is performed.

Investigation of imperfect effect on thermal buckling of cylindrical shell with FGM coating

Abstract The shell with functionally graded material (FGM) thermal barrier coating is a novel high temperature resistant structure, which has been increasingly applied in the aerospace, nuclear, turbo machinery and other engineering fields. However, there are some defects for the practical structures due to the limitation of manufacturing technique. But relevant theoretical research on the thermal buckling behavior of the imperfect cylindrical shell is limited in most open literature. Therefore, this work proposed to establish the theoretical solution of the critical temperature of buckling for the cylindrical shell with an axisymmetric imperfect and FGM coating based on the Donnell shell theory, Koiter model and Galerkin method. The theoretical solution deduced in this work agrees well with the existing literature. In addition, the influences of the profile of the axisymmetric imperfection, the volume fraction of the ceramic phase and the types of the thermal loading on the thermal buckling behavior of the coated imperfect cylindrical are further analyzed. The study provides a scientific solution and better understanding for the thermal buckling problem of the coated imperfect cylindrical shells.

Nonlinear thermo-mechanical response of eccentrically stiffened Sigmoid FGM circular cylindrical shells subjected to compressive and uniform radial loads using the Reddy's third-order shear deformation shell theory

ABSTRACTBased on Reddy's third-order shear deformation shell theory, this paper presents an analytical approach to investigate the nonlinear thermo-mechanical response of imperfect Sigmoid FGM circular cylindrical shells surrounded on elastic foundations and reinforced by outside metal stiffeners. The eccentrically stiffened S-FGM shells are subjected to axial compressive load and uniform radial load in thermal environment. Using the stress function, Bubnov–Galerkin method, the paper proposes the formula for forces and moments taking into account the thermal stress in both the shells and stiffeners. The obtained results are validated by comparing with other results reported in the literature.

Nonlinear Vibrations of Fluid-Filled Cylindrical Shells with Initial Imperfections

Theoretical approaches to studying the free vibrations of imperfect (with small geometrical imperfections) orthotropic cylindrical shells filled with a fluid are proposed. A geometrically nonlinear problem is solved. The emphasis is on the interaction and energy exchange between the “conjugate” flexural modes in the dynamic radial deflection. The effect of initial deflections on the interaction of the initial deflection modes is analyzed