Initial Imperfection Amplitude Research Articles

A homotopy-based wavelet method for extreme large bending analysis of heterogeneous anisotropic plate with variable thickness on orthotropic foundation

A novel homotopy-based decoupled wavelet numerical strategy is developed to investigate the large-deflection bending of variable-thickness anisotropic thin plate constituted by heterogeneous material resting on orthotropic foundation. The anisotropic plates are described undergoing sinusoidally initial imperfections with inhomogeneous thickness and exponentially varying elastic modules, while the subgrade reaction involves the nonlinear support effects by Winkler-type foundation along with Pasternak-type orthotropy. Geometric nonlinearity by uneven thickness and large deformation, material nonlinearity by heterogeneity and contact nonlinearity of orthotropic foundation are simultaneously considered with the highly coupled and strongly nonlinear variable-coefficient Von Kármán equations derived. The accuracy and convergence of the present formulation are validated in excellent agreement with published results, while the new results of extreme bending solutions are provided, which are few given by other methods and further verify the effectiveness and superiority of proposed wavelet procedures. Parametric investigations of influences of material orthotropy and inhomogeneity, unevenness of thickness, amplitude of initial imperfection along with orthotropy of nonlinear Winkler–Pasternak foundation have been studied, which are of great significance on the extremely large bending properties.

Experimental and numerical study on the axial compression performance of the prestressed sleeved members

The progressive collapse of large-span spatial structures can be triggered by the buckling of compression members. To further improve the stable load capacity of compression members, this study proposes a prestressed sleeved member by combining a prestressed stayed column system with a sleeved member. The experimental results show that the prestressed sleeved members possess a high load capacity, large secondary stiffness and moderate recovery performance, with the buckling modes of the members including first-order and second-order buckling. A nonlinear finite element (FE) model for the prestressed sleeved members is developed based on the experimental model. In addition, a series of parametric analyses are conducted to investigate the effects of the initial imperfection amplitude ratio, inner tube length to slenderness ratio, strand cross-sectional area ratio, inner and outer tube cross-sectional stiffness ratio and central support plate equivalent height ratio on the axial compression performance of the specimens. Furthermore, a simplified calculation model of the prestressed sleeved members is proposed for the case of second-order buckling, and theoretical calculation formulas are presented for three key points of the axial force–displacement curves of specimens. In contrast to the theoretical and FE results, the maximum errors of axial displacement and axial force do not exceed 15%. In addition, the steel strand tension, the contact force, and the lateral deflection of the middle section of the inner half-tube are highly consistent, which verifies the proposed relevant assumptions and theoretical calculation formulae.

Snap-through instability of helicoidal composite imperfect beams surrounded by nonlinear elastic foundation

Bernstein polynomials are exploited, for the first time, in investigation of the nonlinear bending and snap-through instability phenomena of geometrically imperfect bioinspired composite beams with helicoidal orientation scheme. The curved bioinspired beam subjected to different types of lateral loading and embedded on three parameters elastic foundations is considered in formulation and analysis. The nonlinear equilibrium equation of the system based on Euler-Bernoulli beam hypothesis, von Kármán nonlinear strain, and initial imperfect curvature is developed. The equilibrium equation portrayed by nonlinear fourth order integro-differential equation is solved by Bernstein polynomials method and closed form solution of the load-deflection relationship is obtained. The accuracy of the present model and solution procedure is examined by comparing our results with previous results. The developed model is exploited to present the influence of lamination scheme, amplitude of initial imperfection and elastic foundation constants on the nonlinear bending and snap-through/reverse snap-through behaviors in detail. The numerical results show that the Bernstein polynomials approach can capture successfully the nonlinear equilibrium path and overcoming limit (turning) points, which usually appear in the nonlinear response of curved structures. The developed model can be used in design and control the snap-through response and open opportunities for this type of structures in many real applications.

Thermal Buckling of Railways

AbstractThis manuscript presents the results of numerical research regarding the thermal buckling on railway tracks. High temperatures may cause thermal buckling on the railways and due to this fact speed restrictions are often issued to reduce the probability of derailments. Railways are subject to thermal and mechanical loads in which, given some circumstances, buckling may take place. Continuous welded rail (CWR) is more prone to this effect than jointed rails since the longitudinal displacement is restrained. This research is focused on the effect of the track gauge, rail profile, initial imperfection amplitude, sleeper's elasticity modulus, torsional resistance of fastenings, and ballast resistance on the thermal buckling of railways. A total of 144 simulations were developed, concluding that the imperfection level and ballast resistance are the most affecting parameters on the buckling temperature.

Exact Solution of Nonlinear Behaviors of Imperfect Bioinspired Helicoidal Composite Beams Resting on Elastic Foundations

This paper presents exact solutions for the nonlinear bending problem, the buckling loads, and postbuckling configurations of a perfect and an imperfect bioinspired helicoidal composite beam with a linear rotation angle. The beam is embedded on an elastic medium, which is modeled by two elastic foundation parameters. The nonlinear integro-differential governing equation of the system is derived based on the Euler–Bernoulli beam hypothesis, von Kármán nonlinear strain, and initial curvature. The Laplace transform and its inversion are directly applied to solve the nonlinear integro-differential governing equations. The nonlinear bending deflections under point and uniform loads are derived. Closed-form formulas of critical buckling loads, as well as nonlinear postbuckling responses of perfect and imperfect beams are deduced in detail. The proposed model is validated with previous works. In the numerical results section, the effects of the rotation angle, amplitude of initial imperfection, elastic foundation constants, and boundary conditions on the nonlinear bending, critical buckling loads, and postbuckling configurations are discussed. The proposed model can be utilized in the analysis of bio-inspired beam structures that are used in many energy-absorption applications.

Imperfection Tolerances During the Erection of Steel Plate Girders and Geometrical Nonlinearities

This work aims to prove that the strict initial imperfection tolerance limits proposed by the American AWS D1.1/D1.1M and the European EN 1090-2 codes could be relaxed for the webs of the most encountered steel I-plate girders subjected to local bend-buckling during their erection phase. To achieve this scope, a parametric study was done involving 36 perfect and 612 imperfect web models with varying aspect ratio, slenderness ratio, initial imperfection amplitude, and stress ratio using Abaqus/CAE by Finite Element (FE) linear buckling analyses then FE geometrically and materially nonlinear analyses with imperfections included (GMNIA). After investigating the results, two main research novelties were found. An easily applicable equation to determine the ultimate strength of webs subjected to direct stresses, which is a function of not only the slenderness ratio and stress ratio (as in other research) but also a function of the initial imperfection amplitude, was derived. Secondly, a tolerance limit equation that is a function of not only the slenderness ratio but also the stress ratio, thus considering the symmetry of the section of plate girders, has been derived. The derived tolerance limit equation provides acceptable and inclusive parameter-wise imperfection tolerances for webs of plate girders so as to relax strict and costly tolerance limits. The results obtained show that for monosymmetric I-plate girders during erection, EN 1090-2 and AWS D1.1/D1.1M tolerance limits can be relaxed to around 40% and 80% in less slender webs and close to 60% and 200% in more slender webs, respectively.

Estimation of the critical buckling load of pile foundations during soil liquefaction

Buckling instability of slender piles may occur based on the effect of excessive axial loads acting on a pile with diminishing effective stress and shear strength owing to surrounding soil liquefaction. However, several guidelines for pile design often provide insufficient consideration of buckling failure, and it is significant to study the buckling failure of piles in liquefiable sites for the design and inspection of piles. In this paper, an efficient method of determining the critical buckling load of piles considering the material and geometric nonlinearities of piles based on the excess pore pressure distribution is proposed based on the beam-on nonlinear Winkler foundation (BNWF) model. Then, the method is verified and validated using results from centrifuge tests. Next, plots of the main effects and analysis of variance (ANOVA) were used for the sensitivity analysis of pile failure modes under axial loading. The initial imperfections and flexural rigidity of the pile have significant effects on the pile failure modes, and the pile is susceptible to buckling failure with low initial imperfections and flexural rigidity. Furthermore, the effects of the flexural rigidity of the pile, unsupported length ratio, initial imperfections, and degree of soil layer liquefaction on the critical buckling load of the pile in liquefiable soil are examined. The axial load-carrying capacity of the pile decreases with increasing initial imperfection amplitude, decreasing flexural rigidity of the pile, decreasing unsupported length ratio and severer degree of soil layer liquefaction. Finally, an estimating formula for predicting the critical buckling load of piles in liquefiable soil and an application example are presented.

Critical force of upheaval buckling for imperfect subsea pipe-in-pipe pipelines on nonlinear foundation

Upheaval buckling behaviors of imperfect subsea PIP (pipe-in-pipe) pipelines on nonlinear foundation are studied using finite element method. A parametric study is performed and the effects of the parameters on the critical force of upheaval buckling are discussed, including initial imperfection amplitude to wavelength ratio (AWR), the characteristic parameter of initial imperfection shape, stiffness ratio, clearance between outer and inner pipes, and soil condition as well as vertical pipe-soil interaction. A simplified empirical formula considering the above factors is presented to determine the critical force of upheaval buckling for subsea PIP pipelines based on dimensional analysis and the results of the parametric study. The results of case studies show that the proposed empirical formula has good accuracy.

Imperfection study on lateral thermal buckling of subsea pipeline triggered by a distributed buoyancy section

Controlled lateral buckling is triggered by distributed buoyancy section at predesigned sites to release the axial force induced by high temperature and high pressure in subsea pipelines. Due to the larger diameter and smaller submerged weight of distributed buoyancy section, compared to the normal pipe section, imperfections are more easily introduced at the location of distributed buoyancy section. In this study, an analytical model is proposed to simulate lateral buckling triggered by a distributed buoyancy section for an imperfect subsea pipeline, which is validated by test data. Semi-analytical solutions are derived. First, snap-through buckling behaviour is discussed. Then the influence of initial imperfections on buckled configurations, post-buckling behaviour, displacement amplitude and maximum stress is discussed in detail. The results show that there is no snap-through phenomenon for large amplitude of initial imperfections, which appears only when the amplitude of imperfection is small enough. The displacement amplitude increases with the amplitude of initial imperfections, and it first increases and then decreases with wavelength of initial imperfection. Compared to a perfect pipeline, the maximum stress amplifies for relative small wavelength of initial imperfections. Therefore, a large enough wavelength of initial imperfection should be introduced.

The Lateral Torsional Buckling Behavior of Laminated Glass Beams

In this paper, the lateral torsional buckling (LTB) behavior of multi-layered long-span laminated glass (LG) beams is investigated through full-scale model test and numerical simulation. In the test program, the LG beams consisting of up to four glass plies and spanning 5000[Formula: see text]mm are constructed and tested. The load-displacement curves and development of strain in glass plies are recorded, based on which the deformation and stress state of buckled LG beams are analyzed, and the strength checking criterion is provided. The test results are also used to determine the shape and amplitude of initial imperfection through statistical analysis and to validate a numerical model based on the finite element method (FEM). Parametric analysis based on the FEM model is then conducted to investigate influential factors on the LTB resistance of LG beams, among which the influence of shape and amplitude of initial imperfection is emphasized. For the LTB design of LG beams, the applicability of existing formula to determine the critical buckling moment through effective stiffnesses is evaluated for multi-layered LG beams with the test and numerical results. Finally, the design buckling curves adopting the Ayrton–Perry formula (APF) are proposed and validated for LG beams categorized with glass type and load duration.

Lateral buckling analysis of subsea pipelines on nonlinear foundation

Lateral soil resistance plays a significant role in lateral buckling, which is a main consideration in the design of subsea pipelines. In this study, a new lateral soil resistance model is proposed to describe the lateral resistance force-displacement relation. It shows a good agreement with existing test results. Based on the new lateral soil resistance model, analytical solution for the lateral buckling of subsea pipelines with initial imperfections is presented. The exact formula to determine the critical half-wavelength is also presented. The effects of initial imperfection parameters, soil properties and parameters, and lateral soil resistance models on critical force of lateral buckling are discussed. Results show that the capacity of subsea pipeline against lateral buckling increases with the increase of the initial half-wavelength, submerged unit weight of soil, and vertical load. It decreases with the increase of the initial imperfection amplitude, soil undrained shear strength, and breakout displacement. The critical forces of lateral buckling in and away from the buckled region both depend on the exact lateral soil resistance model and initial imperfection parameters.

Local web buckling of single-coped beam connections with slender web

This research study presents an investigation of the structural behaviour and local web buckling resistance of single-coped beam connections with slender web. Single-coped beams with slender web (SBSWs) can be used in long-span structures where the top flange of the beam is removed to provide clearance to connect the beam to the main girder. Eleven (11) full-scale tests of single-coped beam connections with slender web were carried out. In general, all the test specimens failed by local web buckling. It was observed that the ultimate connection resistance was decreased with increasing web slenderness ratio, cope length and cope depth. However, the slender web with significant cope length and cope depth could promote evident post-buckling strength for the connection. Finite element (FE) analyses were subsequently conducted to provide further understandings of the test results. The FE analysis results matched the test data reasonably, and the influences of the test parameters on the performance and ultimate resistance of the test connections were carefully studied. The FE results indicated that the ultimate resistances of the models with high web slenderness were insensitive to initial imperfection amplitude, and such trend was more pronounced for cases with large cope length and depth. Based on the test results, the current design methods for predicting the local web buckling resistance of single-coped beam connections were revisited. In general, overly conservative estimates were obtained using the available design guidelines for quantifying the ultimate connection resistance of the test connections with slender web.

Creep buckling of cylinders under uniform external pressure: Finite element simulation of buckling tests

This paper is dedicated to creep buckling predictions. Thin walled cylinders having an aspect ratio of one are subjected to an uniform external pressure. The material is a special type of nickel which “creeps” at ambient temperature. The material parameters for the creep law are identified from experimental results. The creep failure experiments are described and corresponding failure times are given. The paper then compares three alternatives of finite element modeling of the experiments (3D Shell with integration through the thickness with a periodic or non periodic initial imperfection are compared with COMU quasi axi-symmetric imperfect shell element). These 3 modeling show consistent predictions. The simulation time is a hundred times faster with the COMU model. It is shown that the prediction of failure time of these experiments is extremely sensitive to the initial imperfection amplitude. The effect of creep law modeling is also important. Finally a parametric analysis on different types of cylinders is given: some general trends are proposed for this type of delicate predictions.

Local web buckling of double-coped steel beam connections

This paper presents a comprehensive study on local web buckling behaviour of double-coped steel beam connections, cases which are common when beams of similar heights are joined. The study commenced with a series of full-scale tests on 11 specimens, covering a spectrum of cope lengths and cope depths. Local web buckling was observed as the main failure mode for most specimens. The ultimate load was found to decrease with increasing coped length and cope depth, and in addition, an increase of the rotational stiffness of the beam end connection could benefit the local web buckling capacity. A numerical study was subsequently performed enabling further interpretation of the test results. Good agreements were observed between the test results and finite element analysis predictions, and the stress conditions within the coped web panel at different loading stages were fully revealed. The numerical study also showed that the ultimate loads of some models were not sensitive to initial imperfection amplitudes, especially when the cope length was large (i.e. 450mm or longer). It was believed that the imperfection insensitivity characteristic was due to the presence of post-buckling mechanism. Summarising the available test data, including the current test results and those previously reported by other researchers, design comments were made through comparisons against the existing design method. Conservative test-to-predicted ratios were generally shown, but unsafe predictions were obtained for some cases. A modification to the existing design approach was finally proposed for safer design of such connections.

Numerical methods for the design of cylindrical steel shells with unreinforced or reinforced cutouts

The effectiveness of the numerical methods GMNIA and MNA/LBA proposed in EN1993-1.6 for the design of steel shells is studied for cylindrical steel shells with an unreinforced or reinforced rectangular cutout chamfered elliptically at the four ends and for the corresponding shells without cutout. Moreover, another design method proposed in the literature and denoted here as MNA/GNA, which is based on a modified slenderness, is also evaluated. GMNIA is considered as the most reliable analysis type, provided that a judicious choice of shape and amplitude of initial imperfections is made. Thus, GMNIA results are used as basis for comparison, except for shells without cutout where the EN1993-1.6 normative strengths could serve the same purpose as well. For shells without cutout it is found that the modified slenderness gives similar results to the corresponding results of the conventional slenderness definition. In the case of unreinforced cutout the modified slenderness gives better results, thus the use of MNA/GNA is recommended. However, in the case of reinforced cutout the GMNIA results are approximated better by employing the conventional slenderness, thus MNA/LBA is more appropriate.

Laboratory tests and thermal buckling analysis for pipes buried in Bohai soft clay

Upheaval buckling of submarine pipelines occurs due to relative movement of pipeline and surrounding soil and is often triggered by high operational temperature of the pipeline, initial imperfection of the pipeline, or a combination of both. Since buckling can jeopardize the structural integrity of a pipeline, it is a failure mode that should to be taken into account for the design and in-service assessment of trenched and buried offshore pipelines. In this study, a series of vertical (uplift) and axial pullout tests were carried out on model pipe segments buried in soft clay deposit similar to that present in Bohai Gulf, China. Pipe segments with three different diameters (= 30 mm, 50 mm and 80 mm) were buried in different depth-to-diameter ratios ranging from 1 to 8. Based on the results of laboratory tests, nonlinear force–displacement relations are proposed to model soil resistance mobilized during pipeline movement. The proposed nonlinear soil resistance models are employed in finite element analysis of buried pipelines with different amplitudes of initial geometric imperfections. Thermal upheaval buckling behavior of pipelines operating at different temperatures is studied. Results show that the capacity of pipeline against thermal buckling increases with the burial depth and decreases with the amplitude of initial imperfection.

Linearly tapered bridge girder panels with steel corrugated webs near intermediate supports of continuous bridges

Nowadays, girders with corrugated webs are used in bridges as an efficient alternative to conventional girders with flat stiffened webs. Particularly in bridge girders with corrugated webs (BGCWs), the corrugated webs are the main elements for bearing the shear forces. Instead of prismatic BGCWs, tapered BGCWs are currently used mainly due to their structural efficiency, providing at the same time aesthetical appearance. Available literature shows that tapered BGCWs may be classified into four typologies. Among these typologies, Case I is the most common case appearing commonly near to the intermediate supports of continuous bridges. Accordingly, in this paper, the finite element (FE) method is employed to investigate the inelastic behavior of tapered BGCWs of Case I, following to the fundamental behavior of such girders published recently by the current authors. Previously validated 3-D nonlinear FE models are developed and used in this study. The paper seeks, first, at finding the validity limit of the previously proposed design strengths for the tapered BGCWs with respect to the girder’s initial imperfection. This is made by considering different initial imperfection amplitudes. Accordingly, it is found that the proposed equation is valid with initial imperfections of hw1/200; hw1 is the height of the long vertical edge of the web panel. However, the accuracy increases for initial imperfections similar to the web thickness (tw) for cases of tw≥hw1/200. Then, it investigates the effect of the aspect ratio of the web panels, different flange inclination angles and flange slenderness ratios. Finally, the paper checks the authors’ previously proposed design model using the results of the generated parametric studies. Overall, the outcomes of this study are expected to provide more insight into the behavior of tapered BGCWs and enable accurate prediction of the shear capacity of this special type of BGCWs.

Thermal Postbuckling of Imperfect Circular Functionally Graded Material Plates: Examination of Voigt, Mori–Tanaka, and Self-Consistent Schemes

Thermal postbuckling of solid circular plates made of a through-the-thickness functionally graded material (FGM) is analyzed in this paper. Initial imperfection of the plate is also taken into account. Each thermomechanical property of the plate is assumed to be a function of the temperature and thickness coordinate. Equivalent properties of the FGM media are obtained based on three different homogenization schemes, namely, Voigt rule, Mori–Tanaka scheme, and self-consistent estimate. Temperature profile is assumed to be through-the-thickness direction only. The solution of the heat conduction equation is obtained using an iterative central finite difference scheme. Various types of thermal loadings, such as uniform temperature rise, temperature specified at surfaces, and heat flux, are considered. Nonlinear equilibrium equations of the plate are obtained by means of the conventional Ritz method. Solution of the resulting nonlinear equilibrium equations and temperature distribution are obtained simultaneously at each step of heating. It is shown that response of a perfect clamped FGM plate is of the bifurcation type of buckling with stable postbuckling equilibrium branch, whereas imperfect clamped and perfect/imperfect simply supported FGM plates do not reveal the bifurcation type of instability through the nonuniform heating process. Furthermore, amplitude of initial imperfection is an important factor on the equilibrium path of FGM circular plates, especially for simply supported ones.

Imperfection sensitivity of slender/stocky metal plates

Buckling and postbuckling behavior of metal plates is governed by their slenderness parameter. Using nonlinear finite element simulations, unstiffened mild carbon steel, stainless steel and aluminum plates under the action of axial compression are first classified into slender, moderate and stocky plates. Then the effects of initial imperfection amplitude on each plate type and material is studied via sensitivity analyses. The results show that the transition from slender to stocky plates, regardless of material type, occurs at the slenderness parameter of 2. Empirical equations for evaluating the buckling and postbuckling capacities of imperfect plates are drawn out. It is observed that the increase of imperfection amplitude decreases the buckling load of slender plates, but their postbuckling reserves and ultimate capacities are unaffected. In contrast, the ultimate strength of stocky plates is highly affected by initial imperfections.

Behavior of bridge girders with corrugated webs: (II) Shear strength and design

The current paper focuses on the shear strength of bridge girders with corrugated webs (BGCWs) using the realistic initial imperfection amplitudes. Firstly, the results of full-scale experimentally tested BGCWs, available in literature, are used to check the validity of the available design shear strengths. Secondly, they are checked using the same equations utilizing the interactive shear buckling strength formula, recently, proposed by the current authors to account for the realistic support condition at the juncture between the web and flanges which was found to be nearly fixed. However, the comparison indicated that the available design shear strengths in the literature are conservative and need to be improved. Hence, the ABAQUS software is used to construct a nonlinear finite element (FE) analysis, including geometric and material nonlinearities, on full-scale BGCWs failing by shear. To ensure the accuracy of the FE models, the models are verified using the available experimental results provided by other researchers. The available design shear strength formulae were in addition compared with the FE shear strengths of the corrugated webs. However, among the strengths using the proposed interactive shear buckling strength formula, the one adopting Sause and Braxtan (2011) [7] equation was found to be the most suitable. It was as well found that stocky corrugated webs cannot practically reach the yield shear strength. At the end, an illustrative example for the calculation of the shear strength of BGCWs using the currently proposed formula is provided.