Imperfection Sensitivity Research Articles

Buckling enhancement of laminated composite structures partially covered by piezoelectric actuators

The buckling (eigenvalue) problem of biaxially compressed laminated plates and shallow cylindrical panels having two symmetric piezoelectrical (PZT) patches on the top and the bottom of laminates is considered. The analysis is carried out with the use of the classical laminate theory and of the first order shear deformation theory. The variable thickness of structures (the local positions of PZT patches) is described by piecewise constant step functions in one direction or in both directions due. Three different methods of the solution of the linear eigenvalue problem are proposed: the exact analytical solution, the approximate solution based on the definition of the Rayleigh quotient and the numerical 3D finite element analysis. For the approximate Donnell's theory of shallow panels two variational formulations of the eigenvalue problem are derived in the form of the Hu-Washizu functional (the Airy stress functions and transverse normal displacements) and in the form of the Legendre functional (displacements). The influence of geometric parameters of composite panels and PZT patches, piezoelectric effect, external electric voltage and laminate configurations (symmetric angle-ply and cross-ply laminates) on buckling characteristics are discussed in detail. The analysis demonstrates evidently that the use of the local piezopatches should be considered as the buckling problem for structures with the non-uniform thickness distribution. The appropriate use of the local PZT patches should be always combined with the appropriate choice of the best (optimal) laminate configuration. The formulation system developed is suitable to other shell theories and to account for the analysis of thermal effects or the imperfection sensitivity.

A comparison of the test-negative and traditional case-control study designs with respect to the bias of estimates of rotavirus vaccine effectiveness

Estimation of the effectiveness of rotavirus vaccines via the test-negative control study design has gained popularity over the past few years. In this study design, children with severe diarrhea who test positive for rotavirus infection are considered as cases, while children who test negative serve as controls. We use a simple probability model to evaluate and compare the test-negative control and the traditional case-control designs with respect to the bias of resulting estimates of rotavirus vaccine effectiveness (VE). Comparisons are performed under two scenarios, corresponding to studies performed in high-income and low-income countries. We consider two potential sources of bias: (a) misclassification bias resulting from imperfect sensitivity and specificity of the test used to diagnose rotavirus infection, and (b) selection bias associated with possible effect of rotavirus vaccination on the probability of contracting severe non-rotavirus diarrhea.Our results suggest that both sources of bias may produce VE estimates with substantial bias. Particularly, lack of perfect specificity is associated with severe negative bias. For example, if the specificity of the diagnostic test is 90% then VE estimates from both types of case-control studies may under-estimate the true VE by more than 20%. If the vaccine protects children against non-rotavirus diarrhea then VE estimates from test-negative control studies may be close to zero even though the true VE is 50%. However, the sensitivity and specificity of the enzyme immunoassay test currently used to diagnose rotavirus infections are both over 99%, and there is no solid evidence that the existing rotavirus vaccines affect the rates of non-rotavirus diarrhea. We therefore conclude that the test-negative control study design is a convenient and reliable alternative for estimation of rotavirus VE.

Searching for imperfection insensitive externally pressurized near-spherical thin shells

This paper studies the buckling behavior and imperfection sensitivity of geodesic and stellated shells subject to external pressure. It is shown that these structures can completely eliminate the severe imperfection sensitivity of spherical shells and can achieve buckling pressure and mass efficiency higher than the perfect sphere. Key results of this paper are as follows. First, a shell with the shape of an icosahedron can carry external pressure significantly higher than a spherical shell, when the effects of geometric imperfections are considered. Second, stellated shells are generally insensitive to imperfections. For pyramids with height-to-radius ratios greater than 35% the buckling pressure is greater than for a perfect sphere. The specific ratio 45% gives the highest buckling pressure, 28% higher than the perfect sphere. Third, stellated icosahedra with concave pyramids have higher mass efficiency than the perfect sphere. Fourth, in terms of volume efficiency, geodesic shells are comparable to spherical shells with a knockdown factor of 0.2 and convex stellated shells are comparable to spherical shells with a knockdown factor of 0.65.

Experimental and numerical studies on stainless steel tubular members under axial cyclic loading

The fundamental behaviour of stainless steel tubular hollow section members under axial cyclic loading is presented in this paper. An experimental investigation on eight test specimens with varying global and local slenderness is conducted first, where the strength, fracture life, ductility, and energy dissipation capability are discussed in detail. A numerical study is then carried out to further elaborate the deformation/stress pattern, global and local buckling behaviour, and imperfection sensitivity of the members. The subsequent parametric study considers a broadened parameter matrix and thus enables a more comprehensive understanding of the global and local buckling behaviour of stainless steel tubular hollow section members. It is generally observed that the major stainless steel design codes provide conservative predictions for the compressive resistance of the members under cyclic loading, and a large dispersion of the FE-to-predicted ratio exists. A Continuous Strength Method (CSM) is shown to provide more consistent predictions. Due to the diverse failure modes observed in the parametric study models, large inconsistency also exists in the prediction of the post-buckling resistance of the FE models. A ductility-oriented design approach is proposed to enable a quick yet reliable prediction of the available compressive ductility of cyclically loaded stainless steel members.

Development and first evaluation of a novel multiplex real-time PCR on whole blood samples for rapid pathogen identification in critically ill patients with sepsis

Molecular tests may enable early adjustment of antimicrobial therapy and be complementary to blood culture (BC) which has imperfect sensitivity in critically ill patients. We evaluated a novel multiplex real-time PCR assay to diagnose bloodstream pathogens directly in whole blood samples (BSI-PCR). BSI-PCR included 11 species- and four genus-specific PCRs, a molecular Gram-stain PCR, and two antibiotic resistance markers. We collected 5 mL blood from critically ill patients simultaneously with clinically indicated BC. Microbial DNA was isolated using the Polaris method followed by automated DNA extraction. Sensitivity and specificity were calculated using BC as reference. BSI-PCR was evaluated in 347 BC-positive samples (representing up to 50 instances of each pathogen covered by the test) and 200 BC-negative samples. Bacterial species-specific PCR sensitivities ranged from 65 to 100%. Sensitivity was 26% for the Gram-positive PCR, 32% for the Gram-negative PCR, and ranged 0 to 7% for yeast PCRs. Yeast detection was improved to 40% in a smaller set-up. There was no overall association between BSI-PCR sensitivity and time-to-positivity of BC (which was highly variable), yet Ct-values were lower for true-positive versus false-positive PCR results. False-positive results were observed in 84 (4%) of the 2200 species-specific PCRs in 200 culture-negative samples, and ranged from 0 to 6% for generic PCRs. Sensitivity of BSI-PCR was promising for individual bacterial pathogens, but still insufficient for yeasts and generic PCRs. Further development of BSI-PCR will focus on improving sensitivity by increasing input volumes and on subsequent implementation as a bedside test.

Imperfection sensitivity analysis of steel columns at ultimate limit state

The present paper applies Sobol's variance-based global sensitivity analysis (SSA) to quantify the contribution of input imperfections to the load-carrying capacity (LCC) of an IPN 200 steel compressed member. LCC is evaluated using the geometrically and materially non-linear finite element solution with regard to the effects of initial random imperfections including residual stresses. Comparison of results of SSA for (i) buckling about the minor principal axis, (ii) buckling about the major principal axis and (iii) lateral–torsional buckling due to bending moment is performed on the non-dimensional slenderness interval of 0–2. SSA for (i) and (ii) is performed for steel grade (a) S235 and (b) S355, SSA for (iii) is performed only for steel grade S235. SSA found similarities in results (ia) and (ib), (iia) and (iib) and identified significant differences between results (ia) and (iiia), (iia) and (iiia), where sensitivity to the initial axial curvature is more than two times higher in (ia) than in (iiia). The relationships between the effects of initial imperfections on LCC and the design criteria of reliability of Eurocode 3 are discussed.

Imperfection Sensitivity of Post-Buckling Behavior and Vibration Response in Pre- and Post-Buckled Regions of Nanoscale Plates Considering Surface Effects

This paper aims to investigate the imperfection sensitivity of the post-buckling behavior and the free vibration response under pre- and post-buckling of nanoplates with various edge supports in the thermal environment. Formulation is based on the higher-order shear deformation plate theory, von Kármán kinematic hypothesis including an initial geometrical imperfection and Gurtin–Murdoch surface stress elasticity theory. The discretized nonlinear coupled in-plane and out-of-plane equations of motion are simultaneously obtained using the variational differential quadrature (VDQ) method and Hamilton’s principle. To this end, the displacement vector and nonlinear strain–displacement relations corresponding to the bulk and surface layers are matricized. Also, the variations of potential strain energies, kinetic energies and external work are obtained in matrix form. Then, the VDQ method is employed to discretize the obtained energy functional on space domain. By Hamilton’s principle, the discretized quadratic form of nonlinear governing equations is derived. The resulting equations are solved employing the pseudo-arc-length technique for the post-buckling problem. Moreover, considering a time-dependent small disturbance around the buckled configuration, the vibrational characteristics of pre- and post-buckled nanoplates are determined. The influences of initial imperfection, thickness, surface residual stress and temperature rise are examined in the numerical results.

Modal nudging in nonlinear elasticity: Tailoring the elastic post-buckling behaviour of engineering structures

The buckling and post-buckling behaviour of slender structures is increasingly being harnessed for smart functionalities. Equally, the post-buckling regime of many traditional engineering structures is not being used for design and may therefore harbour latent load-bearing capacity for further structural efficiency. Both applications can benefit from a robust means of modifying and controlling the post-buckling behaviour for a specific purpose. To this end, we introduce a structural design paradigm termed modal nudging, which can be used to tailor the post-buckling response of slender engineering structures without any significant increase in mass. Modal nudging uses deformation modes of stable post-buckled equilibria to perturb the undeformed baseline geometry of the structure imperceptibly, thereby favouring the seeded post-buckling response over potential alternatives. The benefits of this technique are enhanced control over the post-buckling behaviour, such as modal differentiation for smart structures that use snap-buckling for shape adaptation, or alternatively, increased load-carrying capacity, increased compliance or a shift from imperfection sensitivity to imperfection insensitivity. Although these concepts are, in theory, of general applicability, we concentrate here on planar frame structures analysed using the nonlinear finite element method and numerical continuation procedures. Using these computational techniques, we show that planar frame structures may exhibit isolated regions of stable equilibria in otherwise unstable post-buckling regimes, or indeed stable equilibria entirely disconnected from the natural structural response. In both cases, the load-carrying capacity of these isolated stable equilibria is greater than the natural structural response of the frames. Using the concept of modal nudging it is possible to “nudge” the frames onto these equilibrium paths of greater load-carrying capacity. Due to the scale invariance of modal nudging, these findings may impact the design of structures from the micro- to the macro-scale.

3D wind buckling analysis of long steel corrugated silos with vertical stiffeners

Abstract Thin-walled cylindrical steel silos are susceptible to instability under wind pressure when they are empty or only partially filled. This paper investigates numerically the wind buckling behavior of a real steel corrugated silo with 8.02 m diameter and 17.62 m height, strengthened by open-section vertical stiffeners. Accordingly, comprehensive 3D finite element models were used and detailed linear and non-linear buckling analyses were conducted. The effects of sinusoidal corrugated sheet profile dimensions on this issue were specially explored. Wind load vertical and circumferential distributions were adopted from Eurocode. Two proposed circumferential pressure distributions for an isolated silo and a silo in a group were taken into consideration. To investigate the material efficiency of corrugated steel silos, a comparison between a full-scale corrugated silo and an equivalent flat sheets one was performed. Additionally, imperfection sensitivity analyses for both structures were carried out.

Investigation on imperfection sensitivity of composite cylindrical shells using the nonlinearity reduction technique and the polynomial chaos method

The theoretical buckling load of a perfect cylinder must be reduced by a knock-down factor to account for structural imperfections. The EU project DESICOS proposed a new robust design for imperfection-sensitive composite cylindrical shells using the combination of deterministic and stochastic simulations, however the high computational complexity seriously affects its wider application in aerospace structures design. In this paper, the nonlinearity reduction technique and the polynomial chaos method are implemented into the robust design process, to significantly lower computational costs. The modified Newton-type Koiter-Newton approach which largely reduces the number of degrees of freedom in the nonlinear finite element model, serves as the nonlinear buckling solver to trace the equilibrium paths of geometrically nonlinear structures efficiently. The non-intrusive polynomial chaos method provides the buckling load with an approximate chaos response surface with respect to imperfections and uses buckling solver codes as black boxes. A fast large-sample study can be applied using the approximate chaos response surface to achieve probability characteristics of buckling loads. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with an unstiffened CFRP cylinder.

Post-buckling behavior of fluid-storage steel horizontal tanks

This paper focuses on the buckling and post-buckling of horizontal steel tanks with conical end-caps, supported on discrete saddles, under pressure caused by internal vacuum and liquid pressure. Linear bifurcation, as well as geometrically nonlinear analyses with imperfections, was performed on a single geometric configuration in order to highlight modeling differences, imperfection sensitivity, and post-buckling behavior. Results are presented for (a) increasing uniform external pressure; (b) increasing pressure under fixed fluid level; (c) coupled increasing pressure and decreasing fluid. For perfect shells, the lowest maximum loads are reached at the conical end-caps; however, imperfection-sensitivity is more stringent for the cylindrical shell than for the conical caps, with the consequence that the buckling mode has displacements in the cylinder and in the conical caps. The influence of radius to thickness ratio and fluid level are investigated by means of parametric studies.

Post-buckling of a pressured biopolymer spherical shell with the mode interaction.

Imperfection sensitivity is essential for mechanical behaviour of biopolymer shells characterized by high geometric heterogeneity. The present work studies initial post-buckling and imperfection sensitivity of a pressured biopolymer spherical shell based on non-axisymmetric buckling modes and associated mode interaction. Our results indicate that for biopolymer spherical shells with moderate radius-to-thickness ratio (say, less than 30) and smaller effective bending thickness (say, less than 0.2 times average shell thickness), the imperfection sensitivity predicted based on the axisymmetric mode without the mode interaction is close to the present results based on non-axisymmetric modes with the mode interaction with a small (typically, less than 10%) relative errors. However, for biopolymer spherical shells with larger effective bending thickness, the maximum load an imperfect shell can sustain predicted by the present non-axisymmetric analysis can be significantly (typically, around 30%) lower than those predicted based on the axisymmetric mode without the mode interaction. In such cases, a more accurate non-axisymmetric analysis with the mode interaction, as given in the present work, is required for imperfection sensitivity of pressured buckling of biopolymer spherical shells. Finally, the implications of the present study to two specific types of biopolymer spherical shells (viral capsids and ultrasound contrast agents) are discussed.

Imperfection sensitivity of the post-buckling characteristics of functionally gradient plates using higher-order shear and normal deformation theory

The aim of the present paper is to investigate the post-buckling responses of geometrically imperfect gradient plate using hybrid deformation plate theory (HHDT). This theory is accountable for realistic transverse shear distribution along with thickness stretching effect. The geometric imperfection is incorporated using various imperfection functions in the transverse direction only. Parametric studies have been carried out to present new results using finite element method with C0 continuous element. The consequences of geometric nonlinearity, various geometric imperfection, and geometric configuration on the Post-buckling characteristics of FGM plate is investigated.

Shell buckling, without ‘imperfections’

The buckling behaviour of thin shell structures under load has been a persistent challenge to engineering designers and researchers over many decades. In this article I consider two unusual experimental studies on the buckling of thin-walled elastic cylindrical shells, each of which sheds intriguing light on the buckling phenomena. The classical theory of buckling of thin cylindrical shells under axial compression predicts that the buckling stress will be proportional to t/ R– the ratio of thickness to radius – other things being equal. But collected results of experimental studies from many laboratories, when plotted on log–log scales, show clearly that the buckling stress is actually proportional to ( t/ R)1.5, with the measured buckling stresses being scattered through a factor of about 4 for shells with R/ t > 200. Such scatter is commonly judged to be in accord with Koiter’s theory of ‘imperfection sensitivity’. But that theory lays no claim to an understanding of the empirical 1.5-power law. I claim that a key to this situation is the experimental performance of some small-scale open-topped silicone rubber shells, buckling under their own weight, which clearly demonstrates a 1.5-power law, but with very little scatter. The buckling mode of these shells involves almost entirely inextensional deformation, with a single small dimple growing near the base, separated from the rest of the shell by a narrow boundary layer that accounts for almost all of the dimple’s elastic strain energy. A straightforward, simple analysis of the mechanics of the dimple is consistent with the experimental 1.5-power law. As noted above, experimental buckling loads of shells that are closed at both ends also show the empirical 1.5-power law, but now with significant statistical scatter. A second aim of the paper is to throw light on that phenomenon. I venture to attribute it to the effect of the boundary conditions of the shell. I adduce support for this view from experimental observations on the buckling of a shell with special, frictional end-fittings. That feature produces significantly higher collapse loads, and with much smaller scatter, than for corresponding shells with fixed boundaries; and it permits striking pre-buckled deformations to occur, of a kind not previously noted. It will be appreciated that neither of the two parts of this article depends on the widely accepted theory of imperfection-sensitivity; hence my choice of title. It is a pleasure for me to submit this article to a special publication in honour of Michael Rotter, with whom I have discussed matters of this sort through three decades.

Effect of shape imperfection on the buckling of large-scale thin-walled ellipsoidal head in steel nuclear containment

Buckling is a failure mode of a large-scale thin-walled ellipsoidal head for a cylindrical steel containment vessel, which is widely used in nuclear power plants such as AP1000 and CAP1400. Manufacturing processes always induce shape imperfections in large-scale thin-walled ellipsoidal heads. However, the study on the effect of shape imperfections on the buckling of a large-scale thin-walled ellipsoidal head subjected to internal pressure is still lacking. In this work, we first used a 3D laser scanner to measure the overall shape of the ellipsoidal head which has a diameter of 5000mm, a radius-to-height ratio of 2.0 and a thickness of 5.5mm. On the basis of the measured overall shape, shape imperfections were determined, and an equation was proposed to quantitatively characterize bulging of weld in the knuckle. Secondly, the measured overall shape and the equation were used to develop FEA models with shape imperfections. Buckling pressures were predicted by using nonlinear FEA. Good agreement between the predictions of the FEA models with shape imperfections indicates that bulging of weld has a considerable effect on buckling pressure. Thirdly, a buckling experiment was performed on the ellipsoidal head and buckling behavior was obtained. The experimental results show that all the buckles occurred at the bulgings of welds. The agreement between the experimental results and the predictions based on the models with shape imperfections is good. At last, FEA models, including different bulging heights of welds characterized by the equation, were established to perform an imperfection sensitivity analysis. Thin-walled ellipsoidal heads subjected to internal pressure demonstrate a significant sensitivity to the bulging height of weld in the knuckle.

Elastoplastic buckling and collapse of spherical shells under combined loadings

In this paper, the buckling behavior of a complete spherical shell under external pressure and of a half-sphere under torsion are first investigated. Several parametric studies are performed, which rely on the European Recommendations framework (ECCS text), so as to identify the different key parameters of the corresponding buckling capacity curves and lead up to both a qualitative and quantitative discussion about the imperfection sensitivity of such structures under each fundamental load. The related results allow us to completely describe the buckling behavior of a spherical shell under combined external pressure and circumferential shear by means of interactive buckling curves, without the need of many supplementary computations for any arbitrary combined loading case.

Buckling and post-buckling behaviors of 1/3 composite cylindrical shell with an opening

A 1/3 composite cylindrical shell with a central rectangular opening was axially compressed experimentally, and its critical buckling load and displacement, and strains were measured. A finite element model (FEM) of the shell with Hashin failure criteria was established to analyze its buckling and post-buckling behaviors by nonlinear Newton-Raphson method. The geometric imperfection sensitivity and the effect of side supported conditions of the shell were investigated. It was found that the Newton-Raphson method can be used to analyze the buckling and post-buckling behaviors of the shell. The shell is not sensitive to initial geometric imperfection. And the support design of the shell by side stiffeners is a good way to obtain the critical buckling load and simplify the experimental fixture.

Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

This paper addresses testing of compressed structures, such as shells, that exhibit catastrophic buckling and notorious imperfection sensitivity. The central concept is the probing of a loaded structural specimen by a controlled lateral displacement to gain quantitative insight into its buckling behavior and to measure the energy barrier against buckling. This can provide design information about a structure’s stiffness and robustness against buckling in terms of energy and force landscapes. Developments in this area are relatively new but have proceeded rapidly with encouraging progress.Recent experimental tests on uniformly compressed spherical shells, and axially loaded cylinders, show excellent agreement with theoretical solutions. The probing technique could be a valuable experimental procedure for testing prototype structures, but before it can be used a range of potential problems must be examined and solved. The probing response is highly nonlinear and a variety of complications can occur. Here, we make a careful assessment of unexpected limit points and bifurcations, that could accompany probing, causing complications and possibly even collapse of a test specimen. First, a limit point in the probe displacement (associated with a cusp instability and fold) can result in dynamic buckling as probing progresses, as demonstrated in the buckling of a spherical shell under volume control. Second, various types of bifurcations which can occur on the probing path which result in the probing response becoming unstable are also discussed. To overcome these problems, we outline the extra controls over the entire structure that may be needed to stabilize the response.

Imperfection and tangential edge constraint sensitivities of thermomechanical nonlinear response of pressure-loaded carbon nanotube-reinforced composite cylindrical panels

Initial geometrical imperfection and elasticity of tangential edge constraints are inherent in real structures in general and composite cylindrical panels in particular. This paper investigates the nonlinear response of functionally graded nanocomposite cylindrical panels reinforced by single-walled carbon nanotubes (SWCNTs), exposed to thermal environments and subjected to uniform external pressure. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRC) are assumed to be temperature dependent, graded in the thickness direction, and are estimated by the extended rule of mixture through a micromechanical model. The governing equations are based on classical shell theory taking von Karman–Donnell nonlinearity, initial geometrical imperfection and tangential constraints of boundary edges into consideration. Approximate solutions of deflection and stress functions are assumed to satisfy simply supported boundary conditions, and the Galerkin method is applied to obtain closed-form expressions of load–deflection relations. An analysis of separate and simultaneous influences of carbon nanotube volume fraction and distribution types, geometrical parameters, varying degree of tangential edge constraints, thermal environments, geometrical imperfection and temperature dependence of material properties on the buckling behavior and load-carrying capacity of FG-CNTRC cylindrical panels results in interesting remarks and novelty of the present study.

Assessing robustness of hazard ratio estimates to outcome misclassification in longitudinal panel studies with application to Alzheimer's disease.

Analyses of imperfectly assessed time to event outcomes give rise to biased hazard ratio estimates. This bias is a common challenge for studies of Alzheimer’s Disease (AD) because AD neuropathology can only be identified through brain autopsy and is therefore not available for most study participants. Clinical AD diagnosis, although more widely available, has imperfect sensitivity and specificity relative to AD neuropathology. In this study we present a sensitivity analysis approach using a bias-adjusted discrete proportional hazards model to quantify robustness of results to misclassification of a time to event outcome and apply this method to data from a longitudinal panel study of AD. Using data on 1,955 participants from the Adult Changes in Thought study we analyzed the association between average glucose level and AD neuropathology and conducted sensitivity analyses to explore how estimated hazard ratios varied according to AD classification accuracy. Unadjusted hazard ratios were closer to the null than estimates obtained under most scenarios for misclassification investigated. Confidence interval estimates from the unadjusted model were substantially underestimated compared to adjusted estimates. This study demonstrates the importance of exploring outcome misclassification in time to event analyses and provides an approach that can be undertaken without requiring validation data.