Shape Imperfections Research Articles

Reliability of stability of single-layer latticed shells with spatially correlated initial geometric imperfection modeled using conditional autoregressive model

Latticed shells are extensively used for large-span structures. Their design is often governed by the global instability requirement stipulated in the Chinese design code for the specified gravity load and initial geometric imperfection (IGI). However, the reliability-basis for the recommended design requirement that a critical load factor of 2 need to be achieved is unknown. In the present study, it is proposed that the spatially varying IGI can be adequately modeled using the conditional autoregressive model. It is shown that this model is sufficiently flexible in modeling spatially varying correlated imperfection and can cope with irregular grid systems. By using this model for IGI and considering global instability, the probability distributions of the load capacity and the failure probabilities of spherical and cylindrical latticed shells designed according to the Chinese design code are evaluated. The evaluation is also carried out by representing the IGI shape using the spatially independent Gaussian model and the first eigen buckling mode (1EBM) that is recommended by the design code. It is shown that the use of the 1EBM to represent the IGI shape does not necessarily lead to conservative estimates of the failure probabilities as compared to those obtained by considering spatially varying stochastic imperfection shapes. The results shown that the estimated failure probability is sensitive to the assumed stochastic model for and standard deviation of the IGI at each joint of the latticed shells. Furthermore, the failure probability of the spherical latticed shell differs from that of the cylindrical latticed shell. The reliability analysis results also indicate that the use of a critical load factor of 2 implemented in the code for design of the latticed shell, in general, lead to an annual failure probability for global instability less than 10−5. A sensitivity analysis indicates that the code recommended critical load factor can be reduced to 1.75 while achieving a target reliability index often adopted for design code calibration.

Effect of spatially correlated initial geometric imperfection on reliability of spherical latticed shell considering global instability

Latticed shells are extensively used for large-span structures because of their good structural behaviour, lightweight and ease of construction. Their codified design is often governed by the global instability requirement for gravity load and specified shape and amplitude of maximum initial geometric imperfection (IGI). The reliability basis for the assigned shape and maximum IGI is unknown. In the present study, it is proposed that IGI is modelled using the simultaneous autoregressive model. It is shown that this model is flexible in modelling spatially varying correlated imperfection and can cope with irregular grid system. By using this model, the effect of the spatially correlated IGI on the probability distribution of the load capacity for global instability and the reliability of spherical latticed shell designed according to the Chinese design code is assessed. It is shown that the use of the prefixed shape of the IGI to assess the probability distribution of the load capacity is unconservative as compared to that by using spatially varying random imperfection. The shape of the probability distribution for the former differs from that for the latter. The reliability analysis results indicate that the use of a critical load factor of 2 implemented in the code leads to a failure probability less than about 10−6 for global instability if the specified maximum IGI defined in the code equals about two to three times the standard deviation of IGI. This failure probability becomes less than about 10−5 if a critical load factor of 1.5 is used for design. It is suggested that the code recommended critical load factor may be reduced to 1.5 while achieving target reliability index often adopted for design code calibration.

Combined Extinction and Absorption UV-Visible Spectroscopy as a Method for Revealing Shape Imperfections of Metallic Nanoparticles.

Metallic nanoparticle solutions are routinely characterized by measuring their extinction spectrum (with UV-vis spectroscopy). Theoretical predictions such as Mie theory for spheres can then be used to infer important properties, such as particle size and concentration. Here we highlight the benefits of measuring not only the extinction (the sum of absorption and scattering) but also the absorption spectrum (which excludes scattering) for routine characterization of metallic nanoparticles. We use an integrating sphere-based method to measure the combined extinction-absorption spectra of silver nanospheres and nanocubes. Using a suite of electromagnetic modeling tools (Mie theory, T-matrix, surface integral equation methods), we show that the absorption spectrum, in contrast to extinction, is particularly sensitive to shape imperfections such as roughness, faceting, or edge rounding. We study in detail the canonical case of silver nanospheres, where small discrepancies between experimental and calculated extinction spectra are still common and often overlooked. We show that this mismatch between theory and experiment becomes much more important when considering the absorption spectrum and can no longer be dismissed as experimental imperfections. We focus in particular on the quadrupolar localized plasmon resonance of silver nanospheres, which is predicted to be very prominent in the absorption spectrum but is not observed in our experiments. We consider and discuss a number of possible explanations to account for this discrepancy, including changes in the dielectric function of Ag, size polydispersity, and shape imperfections such as elongation, faceting, and roughness. We are able to pinpoint faceting and roughness as the likely causes for the observed discrepancy. A similar analysis is carried out on silver nanocubes to demonstrate the generality of this conclusion. We conclude that the absorption spectrum is in general much more sensitive to the fine details of a nanoparticle geometry, compared to the extinction spectrum. The ratio of extinction to absorption also provides a sensitive indicator of size for many types of nanoparticles, much more reliably than any observed plasmon resonance shifts. Overall, this work demonstrates that combined absorption-extinction measurements provide a much richer characterization tool for metallic nanoparticles.

Effect of eccentrically oblique stiffeners and temperature on the nonlinear static and dynamic response of S-FGM cylindrical panels

Abstract This work aims to study the effect of obique stiffeners on the nonlinear static and dynamic buckling behaviors of S-FGM cylindrical panels based on the classical shell theory (CST) with the geometrical nonlinearity in von Karman Donnell sense. The dynamic critical buckling load is obtainted by Budiansky-Roth criterion. The cylindrical panels are reinforced by oblique stiffeners on the top layer, and supported by elastic foundations on the bottom layer. Numerical results are given to evaluate effects of inhomogeneous, dimensional parameters, temperature increment, compressive pressure, oblique angles of stiffeners, the imperfection of original shape, and elastic foundations to the nonlinear static and dynamic response of S-FGM cylindrical panels in the thermal environment.

Numerical investigation on the influence of imperfections in the lateral-torsional buckling of beams with slender I-shaped welded sections

Abstract In this paper, a numerical investigation is carried out for determining the influence of imperfections on the lateral-torsional buckling of welded I-shaped slender section beams. The buckling resistance of unrestrained beams is calculated with nonlinear shell-element based FE analysis, including material and geometrical imperfections. The sensitivity to global and plate imperfections, as well as residual stresses, is presented for different amplitudes and shapes of geometrical imperfections and distributions of residual stresses available in the literature. The recommendations outlined in this work shall help the choice of these parameters on future numerical simulations and extend the observations of other authors in the context of studies for beams with non-slender sections. The comparison of the numerical results with the predictions of the North American design code, AISC360-16, and the European design code, Eurocode 3, suggests that the AISC360-16 provides an upper limit for the beam’s resistance and the Eurocode 3 a lower bound, mainly because residual stresses have a greater impact in the load-carrying capacity on the studied beams. Thus, these findings are expected to promote future developments and amendments to said design codes. Finally, this investigation also supports the need of more realistic definition of imperfections, especially for the case of residual stresses, and justifies a more comprehensive experimental campaign on the subject.

Post-Buckling Behaviour of laminated Cylindrical Panels with/without Cut-Outs

Buckling and post-buckling analysis of isotropic and laminated composite cylindrical plates/panels under compressive load has been done by equilibrium path approach (arc-length technique). The impact of cut outs on buckling and post-buckling load of an isotropic and laminated composite cylindrical plates/panels has been assessed by utilizing summed up generalized finite element programming ANSYS. In post-buckling Eigen mode imperfection shape is picked for creating geometric undulations on cylindrical panels with/without circular cut-outs. The impact of the area and size of the cut out and furthermore the composite utilize point on the buckling load of laminated composite cylindrical panel is explored with simply supported boundary conditions. The post-buckling consequences of laminated cylindrical panels have been validated with existing appropriate writing (18) and are additionally stretched out for analysis of sheets/plates with cutouts. It has been seen that the as the curvature of the panel increases load bearing capacity is increasing irrespective of the material and with/without cut out.

Peningkatan pengetahuan aneka olahan cabai merah besar untuk kemandirian ekonomi masyarakat

Large red chili is one of the mainstay agricultural commodities in Karanganyar Village. Production of 85 tons of large red chili can be obtained by farmers, if there is abundant production. Every time the harvest of large red chili is not always perfect, there is often an imperfect shape of chili. Farmers usually call a large red chili reject, with a percentage of 10% (8.5 tons) each time. The price of this large red chili is cheaper than the large red chili that looks perfect. The goal to be achieved in community service activities is to increase the income of the PKK group of women through the processing of various processed large red chilies into powder, shredded rice and sauce. The method is done by using lecture and demonstration methods accompanied by training materials, and delivered directly by conducting demonstration relating to the process of making powder, shredded and sauce starting from the handling of raw materials, how to use production equipment, the process of mixing materials, cooking to packaging. The overall results of partners can make a variety of processed large red chillies and can do the packaging well.

Shape morphing and adjustment of pantographic morphing aerofoil section structure

This study concerns with morphing structures, e.g. as applied in the aerospace industry. A morphing aerofoil structure capable of variable geometry was developed, which was shown to be able to cater for the different aerodynamic requirements at different stages of flight. In this work, the useful and relatively simple method has been applied, which provides a direct method for calculating required morphing shape displacements via finding the most effective bar through calculating bar sensitivity to displacement and calculating set of length actuations for bar assembly to control/adjust shape imperfection of prestressable structural assemblies including complex elements (macro-elements, e.g., the pantographic element), involving Matrix Condensation. The technique has been verified by experiments on the physical model of an aerofoil shaped morphing pantographic structure. Overall, experimental results agree well with theoretical prediction. Furthermore, the technique of multi-iteration adjustment was presented that effective in eliminating errors that occur in the practical adjustment process itself. It has been demonstrated by the experiments on the physical model of pantographic morphing structure. Finally, the study discusses identification of the most effective bars with the objective of minimal number of actuators or minimum actuation.

Calibration of Design Buckling Curves for Lateral-Torsional Buckling of Cantilever Beams Made of Glass—Experimental and Numerical Investigations

Using glass as a primary load-carrying element is becoming more and more popular in architecture. Probably the most used application is the single-span girder, but another important system is the cantilever beam, which is widely used, e.g., as a canopy in front of an entrance. Research on the lateral-torsional buckling behavior of glass beams has been typically performed on single-span girders. As a consequence, the design buckling curves provided in literature are usually too conservative for the widely used case of a cantilever beam, which is also related to the loading situation. Therefore, experimental and numerical investigations have been performed for this special case. Based on the obtained results, design buckling curves have been developed and resulted in being more economical than the curves already given in the literature. Among others, information on the shape and size of the real imperfections, a testing device for cantilever beams, and experimentally and numerically obtained load-deflection curves are additional outcomes of the investigations presented here.

A smeared stiffener based reduced-order modelling method for buckling analysis of isogrid-stiffened cylinder

• A reduced-order modelling method is proposed for nonlinear stability of isogrid-stiffened cylinders. • The reduced order model is constructed based on the smeared stiffener model. • Mode selection criteria are developed in the proposed method for imperfect cylinders. • Computational costs are significantly reduced in buckling and imperfection sensitivity analyses. Thin-walled isogrid-stiffened structures have been widely used as highly efficient structural components in aerospace engineering. In this work, the stability behavior of isogrid-stiffened cylinder is analyzed using the smeared stiffener model based reduced-order modelling (SSM-ROM) method. The smeared stiffener method proposed based on mechanical characteristics of isogrid-stiffener cell is applied to facilitate the finite element(FE) modelling of structure. The reduced-order models constructed based on Koiter asymptotic expansion are extended to be applicable for the smeared stiffener model. Mode selection criteria for cylinders with measured geometric-shape imperfections are developed to lower the computational cost in construction of the reduced-order model. The proposed method is implemented into the finite element framework and achieved completely using the in-house codes. The isogrid-stiffened cylinders with two different configurations(strong or weak stiffeners) are considered to validate the performance of the proposed method. Linear and nonlinear buckling analyses are first applied to test the numerical accuracy of the smeared stiffener model. The sensitivity of the buckling load in terms of magnitude of initial imperfections is then carefully studied using three different geometric imperfection shapes. Numerical results demonstrate the good performance of the proposed method in both structural buckling analysis and imperfection sensitivity analyses.

Fin Shape Dependence of Electrostatics and Variability in FinFETs

The performance of advanced nanoscale devices is limited by different process variability issues, including patterning proximity effects. Most manufactured fin-shaped field-effect transistors (FinFETs) have some imperfections in the fin shape due to imperfections in lithography and deformation due to other high-temperature process steps. In this work, full three-dimensional (3D) device simulations are performed to study the effects of such variability in the fin shape on the electrostatics of trigate FinFETs. Variability due to random discrete dopants (RDDs) and metal grain granularity (MGG) is considered separately and in combination. The device threshold voltage variation due to RDDs and MGG is critically examined. Finally, we calculate the mean and standard deviation of these parameters (QQ plots) to quantify the variability. It is shown that there is a strong correlation between the drain-induced barrier lowering (DIBL) and random discrete dopant position in the channel.

B2 stress index for structurally distorted pipe bends under in-plane opening bending moment

The present study determines the effect of shape imperfections on the B2 index of pipe bends subjected to in-plane opening moment using 3D nonlinear finite element (FE) methodology. The analysis considers the large strain formulation option and the material behavior is elastic-perfectly plastic. The reaction moment versus angular rotation curves are plotted for all the simulated pipe bends and the plastic collapsing moments are determined using Twice-elastic slope technique as recommended in ASME B&PV, section III (clause NB-3213.25). The B2 stress index was computed for each model from their respective collapse moment. The variable wall thickening in the pipe bend's cross section yields negligible effect and the presence of ovality has a momentous effect on B2 stress indices. A mathematical equation is suggested to compute B2 stress index for pipe bends with ovality subjected to in-plane opening bending moment.

A new formula to predict buckling pressure of steel ellipsoidal head under internal pressure

Abstract Buckling is a critical failure mode of ellipsoidal head under internal pressure. This study focuses on the prediction of buckling pressure of steel ellipsoidal heads subjected to internal pressure. First, finite element model of ellipsoidal head is generated, taking into account the effects of material and geometrical nonlinearity. The plastic bifurcation buckling pressure of ellipsoidal head is determined by nonlinear FEM. Second, we study the effects of diameter-thickness ratio, radius-height ratio, yield strength, strain hardening and attached cylinder on buckling pressure. Based on FE results of the models with elastic-perfectly plastic material, we propose a formula to predict buckling pressure of perfect ellipsoidal head. In addition, we summarize experimental results on the buckling of twenty-one ellipsoidal heads which cover different geometrical parameters, material types, and methods of fabrication. Eleven out of twenty-one ellipsoidal heads were tested by the authors recently. Finally, based on the formula for perfect ellipsoidal heads, a new formula is developed for the buckling pressure of actual ellipsoidal heads after considering a reduction factor that accounts for the effect of initial shape imperfection. The reduction factor depends on the methods of head fabrication, i.e. whether cold pressing and spinning or assembly of formed segments. It is shown that the new formula has comprehensive advantage in accuracy and applicability in comparison with other formulae.

Determination of plastic, shakedown and elastic limit loads of 90°pressurized pipe bends with shape imperfections

This study determines the plastic, shakedown and elastic limit loads and the corresponding regimes of 90° pressurized pipe bends with shape imperfections subjected to cyclic in-plane closing bending moment. Three dimensional FE analyses with small strain formulation was performed. The induced shape imperfections are ovality and thinning, which were varied from 0% to 20% with a 5% increment at every step. Plastic limit load was determined from the moment rotation curve while shakedown and elastic limit loads were determined by using Abdalla's simplified technique (ST). The analysis indicates that the presence of ovality produces considerable effect on plastic limit loads. Thinning alters plastic limit loads only for long bend radius models with no ovality when normalised internal pressure ratio is unity and in other cases its effect is minimal. Presence of ovality and thinning has a remarkable effect on shakedown and elastic limit loads and their regimes though the thinning effect is insignificant at higher ovality (10%–20%). Bree diagram was constructed for the reference pipe bend models. It was observed that the failure of pipe bends is due to either reversed plasticity or ratcheting. Mathematical equations are proposed to express the generated plastic, shakedown and elastic limit moment boundaries for the analyzed pipe bend models.

Oscillations of circular cylindrical shells with imperfections of shape

The impact of initial irregularities of ideal circular cylindrical shape on bending vibrations of thin shells is studied. For the first time ever, the possibility of appearance of the additional splitting zone of the flexural frequency spectrum caused by the shell having initial shape irregularities has been described. It is established that the splitting of the frequency spectrum happens not only when the number of waves of circular dynamic deformations is equal to the number of waves of shell shape irregularities (as it was previously thought), but also when the number of shape-generating waves is twice as low as the number of shape irregularity waves.

Nonlinear buckling optimization technique to predict critical imperfection wavelength of combined liquid-filled steel conical tanks

The shape of the imperfection induced by welding has an influence on the buckling resistance of thin shell structures, and many previous studies have come up with various models to estimate the critical imperfection shape. The aim of the current study is to assess the adequacy of three different approaches available in the literature, which consider that the imperfection wavelength matching the first buckling mode of a perfect tank to be the critical one. The first approach is based on buckling formulae calculated using a linear eigenvalue analysis performed on extensive experimental results of buckling of conical shells. The second approach assumes the critical wavelength, in view of the buckling mode profile detected from finite element analysis, as the distance between the inflection points of the elastic curve of the first buckling mode of a perfect tank. The third approach estimates the critical wavelength as double the distance between maximum and minimum points of the elastic curve. To determine the optimum wavelength that would lead to the minimum buckling capacity of the tank, the current study is conducted numerically by coupling a nonlinear finite element model, developed in house, and a direct search optimization technique. The results obtained from this numerical tool show good agreement with the first and the second approaches, which proves the adequacy of these two approaches in estimating the critical wavelength of the governing buckling mode, while the third approach yields a wavelength that overestimates the buckling capacity of the tank.

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.

Welding simulation of corrugated web girders - Part 2: Effect of manufacturing on shear buckling resistance

Residual stresses and initial geometric imperfections have important effect on the buckling resistance of slender plated steel structures. Despite their large importance, the actual knowledge on residual stresses and exact geometric imperfections are limited, especially for corrugated web girders. In the accompanying paper [1] (Part 1) a finite element model of corrugated web girders is introduced and verified, which is able to virtually simulate the manufacturing process (cold-forming; cutting, welding) of corrugated web girders. The presented numerical model is able to determine the actual imperfection shape and residual stresses which are specific for the actual girder geometry and manufacturing method. The numerical model is further developed for simulating geometrically and materially nonlinear analysis with imperfections (GMNIA) on the virtually manufactured specimens to determine the shear buckling resistance. The effect of manufacturing imperfections on the shear buckling resistance is evaluated for several different corrugation geometries and the obtained tendencies are evaluated and discussed in the current paper.

Buckling behavior of large-scale thin-walled ellipsoidal head under internal pressure

Compressive stresses present in the knuckle of ellipsoidal heads subjected to internal pressure. The presence of such stresses may make buckling possible. In this study, we combine experimental and numerical methods to investigate the buckling behavior of large-scale thin-walled ellipsoidal heads. Buckling experiments were conducted on three thin large-scale ellipsoidal heads with diameters up to 5 m and thicknesses of 5.5 mm. Finite element models of the ellipsoidal heads with measured initial shapes were generated to simulate the buckling behavior, which is compatible with the experimental observation that one or more buckles first occur at local positions in the knuckle and more ones form progressively with increasing pressure. Furthermore, the buckles become smaller or even disappear at relatively higher pressure, indicating that buckling is self-limited. These buckling behaviors are explained by changes in compressive stresses and shapes of ellipsoidal heads. In addition, we performed numerical simulation to investigate the effects of material properties, radius-to-height ratio, diameter-to-thickness ratio, and shape imperfection on buckling behavior.

Bifurcation analysis of the rotating axially compressed nano‐rod with imperfections

AbstractStatic stability problem for axially compressed rotating nano‐rod clamped at one and free at the other end is analyzed by the use of bifurcation theory. It is obtained that the pitchfork bifurcation may be either super‐ or sub‐critical. Considering the imperfections in rod's shape and loading, it is proved that they constitute the two‐parameter universal unfolding of the problem. Numerical analysis also revealed that for non‐locality parameters having higher value than the critical one interaction curves have two branches, so that for a single critical value of angular velocity there exist two critical values of horizontal force.