Perfect Shell Research Articles

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.

Special Issue on Stability of Composite Structures

The increased use of composites in aerospace and civil engineering has resulted in growing demand for engineers versed in the advanced design of composite structures. Composite structures are understood in the wide sense, including microstructured materials, composite structural shapes, composite members built up by subelements of various materials, laminate or sandwich members, small-scale composite structures, etc. Compositelike structural elements are increasingly used in traditional engineeringfields, such as civil engineering, mechanical engineering, or aeronautical engineering, and they have also found some new applications with some recent developments, such as biomedical engineering or biomechanics, nanotechnology, etc. This special issue is primarily based on the presentations given in the symposium on the stability of composite structures organized by the EngineeringMechanics Institute (EMI) Stability Committee during the ASCE EMI Annual Conference held in Boston on June 2–4, 2011. This symposium has provided a forum to discuss recent advances and address the future prospects in the area of the stability of composite structures. The symposium has covered a large number of topics related to the stability of composite structures including the following: • Buckling of composite members; • Plate buckling; • Buckling and vibration of thin-walled structures; • Shear and large displacement analysis; • Interactive buckling and nonlocal mechanics; • Shear effects for in-plane and out-of-plane analyses; • Inelastic buckling; • Anisotropic effects, microstructured materials, and stability problems; • Buckling of sandwich structures; • Stability of partially composite members and delamination effects; • Postbuckling; and • Dynamic buckling. After going through an external review process, the following papers have been accepted and are included in this special issue on the stability of composite structures. As indicated by the title of this special issue, most of the presented papers uniquely deal with the challenges in stability analysis brought by the complexity of composite materials and structures. Their specific advances by these contributions are briefly summarized as follows: 1. In “Local Buckling Analysis of Restrained Orthotropic Plates under Generic In-Plane Loading,” Qiao et al. investigated analytically and numerically the local buckling of composite orthotropic plates under generic in-plane loading and with rotationally restrained boundary conditions. They used both semianalytical and finite-element method (FEM) numerical approaches to characterize the stability behavior of laminated plates or panels of fiber-reinforced plastic structural shapes. The approximated semianalytical solution is obtained from the variationally based Rayleigh-Ritz method, and it is successively compared with available results published in the literature. 2. In “Modeling of Interactive Buckling in Sandwich Struts with Functionally Graded Cores,” Yiatros et al. studied the interactive buckling in sandwich struts with functionally graded cores. The postbuckling behavior is analyzed for this sandwich column composed of two Euler-Bernoulli extensible columns connected with a shear functionally graded core. Linearized and nonlinear analyses are presented for this nonlinear elastic structural problem, and the possibility of capturing secondary bifurcations for such nonlinear systems is numerically shown. This nonlinear model is compared successively to some FEM results based on two-dimensional analyses for the core behavior. 3. In “Buckling Loads of Two-Layer Composite Columns with Interlayer Slip and Stochastic Material Properties,” Schnabl et al. presented an efficient stochastic buckling model for studying the structural reliability of layered composite columns with interlayer slip between the layers and random material and loading parameters. The deterministic model is composed of two connected elastic columns with the shear effect neglected for each column. The nonderterministic approach is based on the exact buckling model, response surface method, and Monte Carlo simulations. The probability of failure for this stochastic buckling problem is computed, and it is shown to be very sensitive to loading and material distribution parameters. 4. In “Effect of Fiber Orientation on Buckling and First-Ply Failures of Cylindrical Shear-Deformable Laminates,” Cagdas and Adali investigated the effect of fiber orientation on buckling and first-ply failures of cylindrical shear-deformable laminates using an 8-node shell finite element (FE). The best ply angle is optimized for each stacking sequence to maximize the failure load. They identified that the rotational restraints at the curved edges have a pronounced effect on the failure load. 5. In “Thermal Postbuckling of Shear Deformable FGM Cylindrical Shells Surrounded by an Elastic Medium,” Shen incorporated the additional effect of an elastic medium on the thermal postbuckling of shear deformable functionally graded material (FGM) cylindrical shells. The surrounding elastic medium is modeled as a Pasternak foundation. The nonlinear governing equations are solved using a singular perturbation technique. The numerical results show that in some cases the FGM cylindrical shell with an intermediate volume fraction index does not have an intermediate buckling temperature and thermal postbuckling strength. In the case of heat conduction, the nonlinear equilibrium path for geometrically perfect FGM shells with simply supported boundary conditions is no longer of the bifurcation type. 6. In “Generalized Beam Theory to Analyze the Vibration of Open-Section Thin-Walled Composite Members,” Silvestre

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.

Buckling of cylindrical shells with general axisymmetric thickness imperfections under external pressure

Abstract This study focuses on the buckling of cylindrical shells under external pressure with general axisymmetric thickness imperfections. Firstly, the result of uniform thickness imperfection and recent study result of axisymmetric modal thickness imperfection are reviewed briefly. Secondly, asymptotic formulas of the buckling load, which are in terms of the thickness imperfection parameter up to arbitrary order, are determined through asymptotic analyses. The analyses are based on a system of linearized governing partial differential equations of perfect shells with variable thickness. Thirdly, the effects led by three patterns of thickness imperfections on the buckling of the laterally pressured cylindrical shells, which are uniform, axisymmetric modal and parabolic, are respectively investigated. Buckling loads of uniform and axisymmetric modal thickness imperfections coincide with the known results. In addition to the analytic investigation, numerical analyses and comparisons are also carried out. The analytical study results presented in the paper can be utilized to evaluate the stabilities of cylindrical shells under external pressure with general axisymmetric imperfections in thickness, once the thickness imperfection is known.

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.

Complementary cloak based on conventional cloak with axial symmetrical cloaked region

Based on the concept of complementary medium, a method which can make the conventional cylindrical cloak with axial symmetrical cloaked region to be not blind by filling the isotropic complementary in inner cloaked region is proposed. Firstly, the perfect electric conductor cylindrical shell was removed. Secondly, the symmetrical cloaked region was separated into two symmetrical regions along the symmetry axis and filled with isotropic complementary medium according to folding transformation. Full wave simulations are performed to confirm the effectiveness of the proposed method. The simulation results show that the converted cloak not only can exchange information with the outside, but also its presence cannot be detected.

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.

RELIABILITY ASSESSMENT OF AXIALLY COMPRESSED COMPOSITE CYLINDRICAL SHELLS WITH RANDOM IMPERFECTIONS

Cylindrical shells under axial compression are susceptible to buckling and hence require the development of enhanced underlying mathematical models in order to accurately predict the buckling load. Imperfections of the geometry of the cylinders may cause a drastic decrease of the buckling load and give rise to the need of advanced techniques in order to consider these imperfections in a buckling analysis. A deterministic buckling analysis is based on the use of the so-called knockdown factors, which specifies the reduction of the buckling load of the perfect shell in order to account for the inherent uncertainties in the geometry. In this paper, it is shown that these knockdown factors are overly conservative and that the fields of probability and statistics provide a mathematical vehicle for realistically modeling the imperfections. Furthermore, the influence of different types of imperfection on the buckling load are examined and validated with experimental results.

Synthesis of Single Crystal Hollow Silver Nanoparticles in a Fast Reaction-Diffusion Process

Colloidal hollow silver nanoparticles were produced by a fast chemical reduction of silver oxide nanoparticles capped with glutathione. These hollow silver particles were surprisingly single crystalline and had almost perfect spherical shells. The reaction was further tested for the transformation of silver oxide nanoparticles to hollow silver sulfide nanoparticles by a reaction with sulfide ions. Analysis of the dimensions of the precursor Ag2O nanoparticles and product hollow Ag nanoparticles as well as the sensitivity of the reduction process to the nature of reducing agent and its concentration hints that the reaction had to proceed through inward diffusion of reducing agent versus fast outward diffusion/dissolution of silver ions. We believe that this type of reactions resembles transformation reactions that have been associated with the nanoscale Kirkendall effect in its broader sense.

Generation of three-dimensional dark spots with a perfect light shell with a radially polarized Laguerre–Gaussian beam

The theoretical analyses in this paper show that a highly focused double-ring radially polarized Laguerre-Gaussian beam with a topological charge of 1 (R-LG(11)) can generate a small three-dimensional (3D) dark spot surrounded by an almost 100% uniform light shell in all directions. The cleanness and size of the 3D dark spot, the uniformity and strength of the light shell surrounding the dark spot, and the light efficiency all depend on the truncation parameter β of the R-LG(11) beam and the numerical aperture (NA) of the system. When β=1.6 and the NA is close to its utmost, an almost 100% uniform light shell surrounding the 3D dark spot can be achieved and the dark spot is very clean. If the NA is lowered but β is increased to 1.95, we can also achieve an almost 100% uniform light shell and light efficiency can reach 90%, but the disadvantage is that the center of the dark spot is not too clean. A not-too-clean 3D dark spot, if the light shell surrounding it is very uniform, is acceptable for many applications. Therefore, 3D dark spots surrounded by a high uniform light shell, generated by simply adjusting the truncation parameter of the R-LG(11) beam and the NA of the system, are useful for superresolution fluorescence microscopy, dark spot microscopy, and the dark spot trap.

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.

Non-linear dynamic thermo-mechanical buckling analysis of the imperfect laminated and sandwich cylindrical shells based on a global-local theory inherently suitable for non-linear analyses

The available accurate shell theories satisfy the interlaminar transverse stress continuity conditions based on linear strain–displacement relations. Furthermore, in majority of these theories, either influence of the transverse normal stress and strain or the transverse flexibility of the shell has been ignored. These effects remarkably influence the non-linear behavior of the shells especially in the postbuckling region. Furthermore, majority of the buckling analyses performed so far for the laminated composite and sandwich shells have been restricted to linear, static analysis of the perfect shells. Moreover, almost all the available shell theories have employed the Love–Timoshenko assumption, which may lead to remarkable errors for thick and relatively thick shells. In the present paper, a novel three-dimensional high-order global-local theory that satisfies all the kinematic and the interlaminar stress continuity conditions at the layer interfaces is developed for imperfect cylindrical shells subjected to thermo-mechanical loads.In comparison with the layerwise, mixed, and available global-local theories, the present theory has the advantages of: (1) suitability for non-linear analyses, (2) higher accuracy due to satisfying the complete interlaminar kinematic and transverse stress continuity conditions, considering the transverse flexibility, and releasing the Love–Timoshenko assumption, (3) less required computational time due to using the global-local technique and matrix formulations, and (4) capability of investigating the local phenomena. To enhance the accuracy of the results, compatible Hermitian quadrilateral elements are employed. The buckling loads are determined based on a criterion previously published by the author.

Nonepitaxial Growth of Hybrid Core-Shell Nanostructures with Large Lattice Mismatches

We report a synthetic route to achieving nanoscale heterostructures consisting of a metal core and monocrystalline semiconductor shell with substantial lattice mismatches between them, which cannot be obtained by conventional epitaxial techniques. By controlling soft acid-base coordination reactions between molecular complexes and colloidal nanostructures, we show that chemical thermodynamics can drive nanoscale monocrystalline growth of the semiconductor shell with a lattice structure incommensurate with that of the core. More complex hybrid core-shell structures with azimuthal and radial nanotailoring of structures and compositions of the monocrystalline semiconductor shell are also demonstrated.

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.

Nonlinear Buckling and Postbuckling Behavior of 3D Braided Composite Cylindrical Shells Under External Pressure Loads in Thermal Environments

Nonlinear buckling and postbuckling behavior for a 3D braided composite cylindrical shell of finite length subjected to lateral pressure, hydrostatic pressure, or external liquid pressure in thermal environments have been presented in this paper. Based on a new micromacromechanical model, a 3D braided composite may be treated as a cell system and the geometry of each cell is deeply dependent on its position in the cross section of the cylindrical shell. The material properties of the epoxy are expressed as a linear function of temperature. The governing equations are based on Reddy’s higher order shear deformation shell theory with a von Kármán–Donnell type of kinematic nonlinearity and including thermal effects. A singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect braided composite cylindrical shells with different values of geometric parameter and of fiber volume fraction in different cases of thermal environmental conditions. The results show that the shell has lower buckling pressures and postbuckling paths when the temperature-dependent properties are taken into account. The results reveal that the temperature changes, the fiber volume fraction, and the shell geometric parameter have a significant effect on the buckling pressure and postbuckling behavior of braided composite cylindrical shells.

Critical loads of shells with high-modulus reinforcement

The analytical method developed to determine the upper and lower critical stresses is applied to cylindrical shells reinforced with stringers and rings. Buckling modes typical of shells reinforced with discrete ribs are considered. The minimum critical loads are determined and compared with available experimental data. Perfect and imperfect ribbed shells with high-modulus reinforcement are studied. It is proved that the effect of small axisymmetric imperfections in such shells is not so drastic as in isotropic shells. Ribs made of a high-modulus material can enhance the stability of shells by a factor of tens

A Comparison of Post-buckling Behavior for FGM Cylindrical Shells With Piezoelectric Fiber Reinforced Composite Actuators

Compressive post-buckling under thermal environments and thermal post-buckling due to uniform temperature field or heat conduction are presented for a shear deformable functionally graded cylindrical shell with piezoelectric fiber reinforced composite (PFRC) actuators. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and PFRC layers are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation shell theory that includes thermopiezoelectric effects. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine buckling loads (temperature) and post-buckling equilibrium paths. The numerical illustrations concern the compressive and thermal post-buckling behavior of perfect and imperfect FGM cylindrical shells with fully covered PFRC actuators under different sets of thermal and electric loading conditions, from which results for monolithic piezoelectric actuators are obtained as comparators. The results reveal that, in the compressive buckling case, the control voltage only has a small effect on the post-buckling load-deflection curves of the shell with PFRC actuators, whereas in the thermal buckling case, the effect of control voltage is more pronounced for the shell with PFRC actuators, compared with the results of the same shell with monolithic piezoelectric actuators.

Non-linear vibrations of imperfect free-edge circular plates and shells

Large-amplitude, geometrically non-linear vibrations of free-edge circular plates with geometric imperfections are addressed in this work. The dynamic analog of the von Kármán equations for thin plates, with a stress-free initial deflection, is used to derive the imperfect plate equations of motion. An expansion onto the eigenmode basis of the perfect plate allows discretization of the equations of motion. The associated non-linear coupling coefficients for the imperfect plate with an arbitrary shape are analytically expressed as functions of the cubic coefficients of a perfect plate. The convergence of the numerical solutions are systematically addressed by comparisons with other models obtained for specific imperfections, showing that the method is accurate to handle shallow shells, which can be viewed as imperfect plate. Finally, comparisons with a real shell are shown, showing good agreement on eigenfrequencies and mode shapes. Frequency-response curves in the non-linear range are compared in a very peculiar regime displayed by the shell with a 1:1:2 internal resonance. An important improvement is obtained compared to a perfect spherical shell model, however some discrepancies subsist and are discussed.

Quantitative Analysis of Scanning Transmission X-ray Microscopy Images of Gas-Filled PVA-Based Microballoons

We report on the quantitative analysis of scanning transmission X-ray microscopy (STXM) images of gas-filled, poly(vinyl alcohol) (PVA)-based microballoons (MB) in a water environment. A model for the transmitted intensity is proposed on the basis of a perfect spherical shell stabilizing the microballoon. An extension of this model to take into account the deformation of the MBs is also presented. Taking into consideration a density gradient of the shell and the STXM resolution, we were able to explain very precisely two types of experimental STXM profiles observed on gas-filled MBs. This enables the detailed characterization of MB properties such as radius and wall thickness and the determination of their wall density with unprecedented high resolution.