Influence Of Initial Geometric Imperfections Research Articles

Equivalent sway imperfections and sway-member imperfection combinations for GMNIA-based steel design

Two types of geometric imperfection typically need to be considered in the analysis and design of structural systems: global frame out-of-plumbness, also referred to as sway imperfections, and member out-of-straightness, also known as bow imperfections; the effect of local cross-section imperfections is generally accounted for through cross-section resistance checks. For modelling convenience, equivalent geometric imperfections are often employed to allow for the combined influence of initial geometric imperfections and residual stresses. For design by geometrically and materially nonlinear analysis with imperfections (GMNIA), amplitudes for equivalent bow imperfections for members are provided in EN 1993–1-14; however, no provisions exist for global sway imperfections. Therefore, equivalent sway imperfections suitable for use in the design of steel structures by GMNIA ϕ0,GMNIA are established herein. Two proposals for calculating ϕ0,GMNIA are presented: (1) ϕ0,GMNIA=ϕ0,geom+α/100, with ϕ0,geom representing the pure geometric sway imperfection, and (2) ϕ0,GMNIA=α/50. In both proposals, the varying degree and influence of residual stresses for different cross-section geometries and axes of buckling is captured by the imperfection factor α, as defined in EN 1993–1-1 for carbon steel and EN 1993–1-4 for stainless steel, respectively. A flow chart that provides guidance on the appropriate selection of frame and member imperfections to avoid duplication of the effects of residual stresses in design by GMNIA is also presented.

Equivalent global sway imperfections for use in design by GMNIA

AbstractThree types of geometric imperfection need to be considered in the design of structural systems: global frame out‐of‐plumbness, also referred to as sway imperfections, member out‐of‐straightness, also known as bow imperfections, and local cross‐section imperfections. For modelling convenience, equivalent geometric imperfections are often employed to account for the combined influence of initial geometric imperfections and residual stresses. For design by geometrically and materially nonlinear analysis with imperfections (GMNIA), amplitudes for equivalent bow imperfections for members are provided in prEN 1993‐1‐14; however, no provisions exist for global sway imperfections. Therefore, equivalent sway imperfections suitable for use in the design of steel structures by GMNIA, expressed by the out‐of‐plumbness Φ0,GMNIA are established herein. Two proposals for calculating Φ0,GMNIA are presented: (1) Φ0,GMNIA = Φ0,geom + α/100 with Φ0,geom representing the amplitude of the pure geometric sway imperfection, and (2) Φ0,GMNIA = α/50. In both proposals, the varying influence of residual stresses from different cross‐section geometries and axes of bending is captured by the imperfection factor α, as defined by the buckling curves in EN 1993‐1‐1 for carbon steel and EN 1993‐1‐4 for stainless steel, respectively.

On the large amplitude vibration of shallow sandwich shells with FG-GNPRP core considering initial geometric imperfections

The present study investigates the influence of initial geometric imperfections on large amplitude vibration of shallow sandwich shells with functionally graded graphene nanoplatelets reinforced porous (FG-GNPRP) core embedded between two aluminium facets. The aluminium core is reinforced with graphene nano-platelets (GNP) and the effective properties such as elastic modulus, and mass density, etc. are estimated using Halpin-Tsai and Voigt models, respectively. The continuous functions are adopted to accomplish micro-structural gradation while creating pores which imparts the variation in material properties along thickness direction. The nonlinear governing equations based on higher order shear deformation theory and Sander’s approximation are derived using variational approach. The nonlinearity is introduced in von-Kármán sense and various imperfection modes such as sine, global and local types are considered in transverse direction. The nonlinear results are accessed using finite element method in conjunction with direct iterative technique. The influence of porosity, GNP weight fraction, imperfection amplitude, thickness, side, and radius ratios on the vibration response of the sandwich shells is explored in detail.

Nonlinear Stability of Natural-Fiber-Reinforced Composite Cylindrical Shells with Initial Geometric Imperfection Considering Moisture Absorption and Hygrothermal Aging.

In this paper, the nonlinear stability of a natural-fiber-reinforced composite cylindrical shell with initial geometric imperfection is investigated. The nonlinear governing equations are established by high-order shear deformation theory. The load-edge shortening curves for different imperfection amplitudes are obtained by the Galerkin method. Several numerical examples are presented to verify the accuracy of the proposed method and to investigate the influence of initial geometric imperfection, moisture absorption, and hygrothermal aging on the post-buckling behavior of natural-fiber-reinforced composite cylindrical shells.

Buckling behavior of double skin composite walls under axial compressive load

In this paper, the steel faceplate buckling of double skin composite walls stiffened with studs or steel-bar trusses is studied and analyzed by the axial compressive test, including ten specimens. According to the investigation, the buckling mode of steel faceplate, whose restraint situation is four points arranged in different shapes, is observed, and the calculated equation of buckling stress is proposed. Based on the test, the buckling strain monitored by strain gauges and maximum strength increases with the decline in welding spot spacing-to-thickness ratio and spacing aspect ratio. According to the finite element model (FEM) established by ABAQUS, the failure mode of the walls is simulated well. The buckling stress and load–displacement curve obtained by FEM corresponds well with these of the test. The parametric analysis is conducted to study the influence of initial geometric imperfection by considering the welding spot spacing-to-thickness ratio and spacing aspect ratio on faceplate buckling stress. When the initial geometric imperfection is larger than 1/1000 of the vertical welding spot spacing, the faceplate buckling stress drops more slowly with the increase of initial geometric imperfection. The relationship between the buckling stress and welding spot spacing-to-thickness ratio obeys the Euler curve. The buckling stress of the steel faceplate decreases linearly with the increase in the spacing aspect ratio. The results by using the buckling equations with the consideration of the initial geometric imperfection and spacing aspect ratio are approximately in accordance with the simulated results.

Equivalent imperfections for the out-of-plane stability design of steel beams by second-order inelastic analysis

In current structural design specifications, such as EN 1993-1-1 for steel and EN 1993-1-4 for stainless steel, the stability of members is typically assessed through the use of buckling curves, which consider the influence of initial geometric imperfections and residual stresses. An alternative, more direct, approach is to perform either an elastic or inelastic second-order analysis of the member or structure with imperfections. For modelling convenience, so-called ‘equivalent’ imperfections are typically utilised, which consider the combined influence of both geometric imperfections and residual stresses. Equivalent imperfections for the design of columns and beams by second-order elastic analysis, also referred to as geometrically nonlinear analysis with imperfection (GNIA), are provided in the current design specifications. For columns, equivalent imperfections for design by second-order inelastic analysis, also referred to as geometrically and materially nonlinear analysis with imperfections (GMNIA), were recently developed, but for beams that are susceptible to lateral-torsional buckling (LTB), there are currently no appropriate provisions. The aim of this study is therefore to develop equivalent imperfections for use in out-of-plane stability design of steel and stainless steel members by GMNIA. The proposals are calibrated against the results of benchmark finite element (FE) simulations performed on a large number of steel and stainless steel members with geometric imperfections and residual stresses subjected to major axis bending. Two proposals for equivalent imperfection amplitudes are developed: (1) e0,mod, for use with eigenmode-affine imperfections and (2) e0,bow, for use with sinusoidal bow imperfections. The latter is applied solely in the lateral direction and as a summation of a half-sine wave and a full-sine wave. Relative to the traditional Eurocode design calculations, employing the proposed LTB imperfections in GMNIA provides generally more accurate member resistance predictions, while remaining safe-sided relative to the benchmark FE results. The reliability of the design provisions is demonstrated through statistical analysis, where it is shown that partial safety factors of 1.0 for steel and 1.1 for stainless steel can be safely adopted.

Equivalent bow imperfections for design by second order inelastic analysis

AbstractThe stability of compression members is typically assessed through buckling curves, which include the influence of initial geometric imperfections and residual stresses. Alternatively, the capacity can be obtained more directly by carrying out a second order analysis using equivalent bow imperfections that account for both geometric imperfections and residual stresses. For design by second order elastic analysis, following EN 1993‐1‐1 recommendations, the magnitudes of the equivalent bow imperfections can either be back‐calculated for a given member to provide the same result as would be obtained from the member buckling curves or taken more simply as a fixed proportion of the member length. In both cases, a subsequent linear axial + bending cross‐section check is required. For design by second order inelastic analysis, there are currently no suitable recommendations for the magnitudes of equivalent bow imperfections and, as demonstrated herein, it is not generally appropriate to use equivalent bow imperfections developed on the basis of elastic analysis. Equivalent bow imperfections suitable for use in design by second order inelastic analysis are therefore established in the present paper and shown to yield reliable results when compared to benchmark results and current design guidance.

Influence of initial geometric imperfection on static and free vibration analyses of porous FG nanoplate using an isogeometric approach

In this paper, the size-dependent analysis of geometrically imperfect porous functionally graded (FG) nanoplates is studied by an isogeometric approach based on a new refined plate theory. Simultaneous effects of initial geometric imperfection and porosity on the natural frequency and deflection of the FG nanoplates are investigated. The initial geometric imperfection is considered as an initial curvature and modeled by an analytical function in the governing equations of the nanoplate. Material properties of porous FG nanoplate are defined by a modified power-law function, and two types of distribution for porosity are used. A four-variable refined plate theory with a new polynomial shape function is proposed. Based on Hamilton’s principle, a weak form of static and free vibration problem for nonlocal plate is derived. The discrete system of equations is solved by an isogeometric approach based on NURBS basis functions, and the accuracy of the present study is verified by comparing the results with solutions given in published papers. Present results indicate the importance of porosity parameter, porosity distributions, nonlocal parameter, material index, plate geometrical parameters, and specially imperfection amplitude on the static and free vibration behavior of FG nanoplates.

Numerical analysis of stability of the stiffened plates subjected aliquant critical loads

The aim of the work is to research the precritical and postcritical equilibrium of the stiffened plates subjected aliquant critical loads. Methods. The finiteelement complex MSC PATRAN - NASTRAN was used in the paper. To simulate the plates, flat four-node elements were used. Calculations taking into account geometric nonlinearity were carried out. The material of the shells was considered absolutely elastic. Results. A technique has been developed to study the stability of reinforced longitudinally compressed plates; the critical forces of the stiffened plates of various thicknesses had been calculated. Graphs of deflections dependences on the value of the compressive load had been constructed. The influence of initial geometric imperfections on the value of the critical loads for stiffened plates has been investigated.

Effect of Initial Geometric Imperfections on Nonlinear Vibration of Thin Plate by an Asymptotic Numerical Method

In this work, the influence of initial geometric imperfections on geometrically nonlinear free vibrations of thin elastic plates has been investigated by an asymptotic numerical method. The nonlinear strain displacement relationship of von Karman theory is adopted to calculate the elastic strain energy. The harmonic balance approach and Hamilton’s principle are used to convert the equation of motion into an operational formulation. The nonlinear problem is transformed into a sequence of linear ones having the same stiffness matrix, which can be solved by a classical finite-element method. To improve the validity range of the power series, Pade approximants are incorporated and a continuation technique is also used to get the whole solution. Numerical results are discussed and compared to those available in the literature and convergence of the solution is shown for various amplitudes of imperfection.

INFLUENCE OF BUCKLING FORMS INTERACTION ON STIFFENED PLATE BEARING CAPACITY

The work is devoted to studying the influence of initial geometric imperfections on a value of the peak load for the compressed stiffened plate with the two-fold buckling load. The finite-element set MSC PATRAN – NASTRAN was used for solving the set tasks. When modelling the stiffened plate, flat four-unit elements were used. Geometric non-linearity was assumed for calculations. The plate material was regarded as perfectly elastic. Buckling forces of stiffened plate at the two-fold buckling load were calculated (simultaneous buckling failure on the form of the plate total bending and on the local form of wave formation in stiffened ribs). Equilibrium state curves, peak load decline curves depending on initial imperfection values and the bifurcation surface were plotted.

Equivalent bow imperfections for use in design by second order inelastic analysis

The stability of compression members is typically assessed through buckling curves, which include the influence of initial geometric imperfections and residual stresses. Alternatively, the capacity may be obtained more directly by carrying out either an elastic or an inelastic second order analysis using equivalent bow imperfections that account for both geometric imperfections and residual stresses. For design by second order elastic analysis, following the recommendations of EN 1993-1-1, the magnitudes of the equivalent bow imperfections can either be back-calculated for a given member to provide the same result as would be obtained from the member buckling curves or can be taken more simply as a fixed proportion of the member length. In both cases, a subsequent M–N (bending + axial) cross-section check is also required, which can be either linear elastic or linear plastic. For design by second order inelastic analysis, also referred to as design by geometrically and materially nonlinear analysis with imperfections (GMNIA) there are currently no suitable recommendations for the magnitudes of equivalent bow imperfections and, as demonstrated herein, it is not generally appropriate to use equivalent bow imperfections developed on the basis of elastic analysis. Equivalent bow imperfections suitable for use in design by second order inelastic analysis are therefore established in the present paper. The equivalent bow imperfections are calibrated against benchmark FE results, generated using geometrically and materially nonlinear analysis with geometric imperfections of L/1000 (L being the member length) and residual stresses. Based on the results obtained, an equivalent bow imperfection amplitude e0 = αL/150 (α being the traditional imperfection factor set out in EC3), is proposed for both steel and stainless steel elements and shown to yield accurate results. The reliability of the proposed approach is assessed, using the first order reliability method set out in EN 1990, against the benchmark FE ultimate loads, where it is shown that partial safety factors of 1.0 for steel and 1.1 for stainless steel can be adopted.

Flexural behaviour of horizontally curved I-girders with round concrete-filled tubular flange

The flexural behaviour of the simply supported individual curved round concrete-filled tubular flange girders (CRCFTFGs) and the corresponding curved I-girder (CIG) under concentrated load at mid-span is investigated experimentally and analytically. Two CRCFTFG specimens and one CIG specimen are considered in this study. One of the CRCFTFG specimens is designed with a pair of transverse stiffeners at mid-span. The other one has uniformly arranged seven pairs of transverse stiffeners along the girder span. These specimens are denoted as CRCFTFG-1 and CRCFTFG-2, respectively. A special rolling track device is designed to ensure that the load is in the vertical direction during the test. In the experiment, the failure mechanism of three specimens and the development of strain and displacement with the vertical load at certain critical positions are measured and analysed in detail. Experimental results show that increasing the number of transverse stiffeners can effectively avoid web distortion and enhance the load carrying capacity of CRCFTFGs. CRCFTFGs have much larger load carrying capacity and smaller lateral displacement and cross-sectional rotation than CIG. The finite element (FE) analysis is used in the numerical analysis to model the test specimens. The comparison outcome between the FE models and the experimental results indicated that they are in reasonably good agreement. A parametric study is conducted based on the validated FE models to investigate the influence of initial geometric imperfections, web distortion, the ratio of span to curvature radius (L/R) and the infilled concrete on the load carrying capacity of CRCFTFGs.

Influence of initial geometric imperfections on the 1:1:1:1 internal resonances and nonlinear vibrations of thin-walled cylindrical shells

The analysis of internal resonances in continuous structural systems is one of the main research areas in the field of nonlinear dynamics. Internal resonances enable the transfer of energy between the related vibration modes, usually leading to new phenomena that have a profound influence on nonlinear oscillations, bifurcations and dynamic instabilities. Shells of revolution usually exhibit internal resonances due to their inherent circumferential symmetry and dense frequency spectrum in the lower frequency range, which may lead not only to m:n internal resonances but also to multiple internal resonances. In this work, the nonlinear response of an imperfect circular cylindrical shell, simply supported at the edges, to harmonic excitation is studied. Geometries that have two modes with n and n+1 circumferential waves, corresponding to the lowest natural frequency, are identified. These two modes are driven to resonance, with each being in one-to-one internal resonance with its companion mode, thus leading to a possible 1:1:1:1 internal resonance, a topic rarely investigated in the technical literature. The investigation of internal resonances in continuous systems is usually conducted using low-dimensional discrete models. Here, using a perturbation procedure, a consistent modal expansion is derived for an arbitrary number of interacting modes, leading to reliable low-dimensional models. Using the discrete models derived in this way, the shell nonlinear dynamics is explored by using bifurcation diagrams of the Poincaré map, continuation techniques and the Floquet stability criterion. The importance of internal resonances to the nonlinear vibrations and instabilities of the shell is clarified. It is well known that small geometric imperfections in the order of the shell thickness have a strong influence on the buckling and post buckling behavior of a thin-walled shell. However, their influence on internal resonances, dynamic instability and energy transfer is largely unknown. Thus, a detailed parametric analysis that considers different types of modal imperfection is conducted in the present work, and the influence of such imperfections on the activation of energy exchanges between the modes involved is analyzed. The results confirm that the form and magnitude of initial geometric imperfections have a profound influence on the results, enabling or preventing the transfer of energy among the resonant modes being considered. • Derivation of a consistent modal expansion by a perturbation procedure considering arbitrary number of interacting modes. • The influence of geometric imperfections on internal resonances, dynamic instability and energy transfer between modes. • Analysis of 1:1:1:1 internal resonance considering four vibration modes with the same natural frequency. • The dynamic bifurcations are sensitive to the form and magnitude of initial geometric imperfections.

Effect of residual stress and geometric imperfection on the strength of steel box girders

In the recent years, steel box girder bridges have been extensively used due to high bending stiffness, torsional rigidity, and rapid construction. Therefore, researches related to this girder bridge have been widely conducted. This paper investigates the effect of residual stresses and geometric imperfections on the load-carrying capacity of steel box girder bridges spanning 30 m and 50 m. A three – dimensional finite element model of the steel box girder with a closed section was developed and analyzed using ABAQUS software. Nonlinear inelastic analysis was used to capture the actual response of the girder bridge accurately. Based on the results of analyses, the superimposed mode of webs and flanges was recommended for considering the influence of initial geometric imperfections of the steel box model. In addition, 4% and 16% strength reduction rates on the load – carrying capacity of the perfect structural system were respectively recommended for the girders with compact and non-compact sections, whose designs satisfy the requirements specified in AASHTO LRFD standard. As a consequence, the research results would help designers eliminate the complexity in modeling residual stresses and geometric imperfections when designing the steel box girder bridge.

Stability Investigation of a Stiffened Plate by Using Numerical Methods

the influence of initial geometric imperfections of a stiffened plate under longitudinal compression on the double critical buckling loads had been studied in this paper. An appropriate bifurcation diagram and bifurcation set were plotted. The results obtained showed that sensitivity of critical load to any initial geometric imperfections is actually insignificant (max 22% loss of the critical load) with specific geometric plate parameters and stiffeners selected.

Hybrid Artificial Intelligence Approaches for Predicting Critical Buckling Load of Structural Members under Compression Considering the Influence of Initial Geometric Imperfections

The main aim of this study is to develop different hybrid artificial intelligence (AI) approaches, such as an adaptive neuro-fuzzy inference system (ANFIS) and two ANFISs optimized by metaheuristic techniques, namely simulated annealing (SA) and biogeography-based optimization (BBO) for predicting the critical buckling load of structural members under compression, taking into account the influence of initial geometric imperfections. With this aim, the existing results of compression tests on steel columns were collected and used as a dataset. Eleven input parameters, representing the slenderness ratios and initial geometric imperfections, were considered. The predicted target was the critical buckling load of columns. Statistical criteria, namely the correlation coefficient (R), the root mean squared error (RMSE), and the mean absolute error (MAE) were used to evaluate and validate the three proposed AI models. The results showed that SA and BBO were able to improve the prediction performance of the original ANFIS. Excellent results using the BBO optimization technique were achieved (i.e., an increase in R by 7.15%, RMSE by 40.48%, and MAE by 38.45%), and those using the SA technique were not much different (i.e., an increase in R by 5.03%, RMSE by 26.68%, and MAE by 20.40%). Finally, sensitivity analysis was performed, and the most important imperfections affecting column buckling capacity was found to be the initial in-plane loading eccentricity at the top and bottom ends of the columns. The methodology and the developed AI models herein could pave the way to establishing an advanced approach to forecasting damages of columns under compression.

Behaviour of large fabricated stainless steel beam-to-tubular column joints with extended endplates

This paper presents the flexural behaviour of stainless steel beam-to-tubular column joints with extended endplates subjected to static loading. Moment-rotation relationships were investigated numerically by using Abaqus software with geometric and material nonlinearity considered. The prediction of damages among components was achieved through ductile damage models, and the influence of initial geometric imperfections and residual stresses was evaluated in large fabricated stainless steel joints involving hollow columns and concrete-filled columns. Parametric analysis was subsequently conducted to assess critical factors that could affect the flexural performance significantly in terms of the initial stiffness and moment resistance. A comparison between codes of practice and numerical results was thereafter made, and design recommendations were proposed for further applications. Results suggest that the finite element model can predict the structural behaviour reasonably well with the component damage consistent with test outcomes. Initial geometric imperfections and residual stresses are shown to have little effect on the moment-rotation responses. A series of parameters that can influence the joint behaviour remarkably include the strain-hardening exponents, stainless steel strength, diameter of bolts, thickness of endplates, position of bolts, section of beams and columns. AS/NZS 2327 is more reliable to predict the joint performance regarding the initial stiffness and moment capacity compared to EN 1993-1-8.

Bending and buckling of internally-pressurized steel lined pipes

During offshore installation, steel lined pipes are subjected to severe plastic bending, resulting in detachment of the thin-walled liner pipe from the outer pipe and eventually, the formation of local buckling in the form of short-wave wrinkles that menace the structural integrity of the pipeline. The paper focuses on the mechanical behaviour of mechanically lined pipes subjected to monotonic bending, considering for the presence of low and moderate levels of internal pressure, aimed at preventing or delaying wrinkle formation, and improving structural performance. The problem is solved numerically, accounting for geometric non-linearities, local buckling phenomena and elastic-plastic material behaviour for both the liner and the outer pipe. Two types of lined pipes are examined, with and without mechanical bonding between liner and outer pipe referred to as tight-fit and snug-fit lined pipe, respectively. The results demonstrate that the bending performance of lined pipes, under low or moderate internal pressure levels, is significantly improved. The influence of initial geometric imperfections on liner pipe buckling is also examined, showing the imperfection sensitivity of bi-material pipe bending behaviour.

Influence of initial geometric imperfections and porosity on the stability of functionally graded material plates

ABSTRACTIn the present paper, the effect of initial geometric imperfections and porosity on the stability of functionally graded material (FGM) plates is investigated. The formulations are based on the recently developed nonpolynomial higher order shear and normal deformation theory by the authors. The present theory accounts for a nonlinear variation of in-plane and transverse displacement across the thickness. Accountability of thickness stretching effect using only four unknowns makes it distinct from the existing renowned theories. The generic imperfection function is used to model various possible initial geometrical imperfections such as sine-type, local-type, and global-type imperfections. An efficient C0 finite element is used for the model and the variational approach is utilized to derive the fundamental equations for the FGM plates. Extensive numerical studies have been conducted to bring out the influence of geometric imperfection, porosity, geometric configuration, and volume fraction index on the stability of FGM plates.