Geometric Imperfection Amplitude Research Articles

Comparative analysis of geometric imperfections and residual stresses on the global stability behavior of cantilever composite alveolar beams

Few studies addressed the influence of geometric and structural imperfections of steel alveolar I-sections on the stability behavior of composite beams under hogging moment. Therefore, this paper aims to study the sensitivity to geometric imperfection amplitude and residual stress distribution on their global stability. The research primarily focuses on comparing numerical results with experimental data in detail, which addresses four tests involving cantilever composite beams with castellated and cellular I-sections. It includes applying various residual stress patterns and geometric imperfection values to advanced numerical analyses as documented in the literature. Linear buckling analyses (LBA) and geometrically and materially nonlinear analyses with imperfections (GMNIA) are carried out using the ABAQUS software. Regarding the first positive eigenvalue from LBA analyses, the eigenvectors presented Web-Post Buckling (WPB) with a slight compressed flange lateral curvature, inserted as the initial geometric imperfection in the GMNIA analyses. However, when the residual stresses were implemented in the GMNIA analyses, some finite element models had different failure modes regarding the deformed configurations from LBA analyses, in which the failure modes were characterized by Lateral-Distortional Buckling (LDB), which was in agreement with the test results. As the beams reached LDB in an inelastic regime, residual stresses significantly affected their resistant capacity. This way, the distribution of compressive residual stresses in the flanges had the most critical influence on the global stability behavior of the analyzed beams, as these residual stresses favor the LDB occurrence. Finally, higher geometric imperfection amplitudes did not provide only lower ultimate loads, as when the instability phenomena are reached in an inelastic regime, the effect of global geometric imperfections becomes highly complex.

Design of press-braked stainless steel C-beams subjected to global-distortional interaction buckling

A detailed finite element (FE) model studying the global-distortional (G-D) interaction of press-braked stainless steel C-beams was reported herein. According to previous bearing capacity tests, the model incorporating measured material characteristics and precise geometric imperfections was validated by comparing to the failure mode, load-vertical displacement curve and bearing capacity. Following the calibration of the model, comprehensive parametric investigations were conducted to investigate the influence of the distribution and amplitude of geometric imperfections, material strain hardening coefficient and effect of cold working. It is found that the distribution of geometric imperfections has significant and complex impacts on the failure mode and ultimate capacity, while the amplitude of imperfection could have positive or negative effects on the ultimate capacity. The accuracy of the design methods provided by EN 1993–1-4, AS/NZS 4673 and ASCE 8–22 was assessed using the test data. All codes are found to account for distortional buckling by employing the Effective Width Method (EWM) to reduce the compression plate area. The calculation results were discrete. Therefore, based on the Direct Strength Method (DSM), a novel and accurate design method was developed for the G-D interaction of stainless steel C-beams. The strong correlation between the ratio of ultimate capacity to global buckling bearing capacity and the G-D interaction slenderness was verified by 260 numerical analyses prior to proposing the new design method. The proposed design method underwent a reliability analysis using first order reliability method to meet the requirement of ASCE 8–22.

Research on the local-distortional interaction buckling capacity of stainless steel lipped C-section columns

The plates of the specimens subjected to a large section width to thickness ratio are prone to multiple instances of mode interaction buckling failure under compression. Hence, to investigate the local-distortional interaction buckling capacity of stainless steel lipped C-section columns, the material properties test of 4 stainless steel plate specimens and the capacity tests of 19 stainless steel lipped C-section column specimens under axial compression were carried out. The development process and failure mode of the local-distortional interaction buckling of stainless steel columns were revealed, and the local-distortional interaction buckling capacities, load-axial shortening curves, load-lateral displacement curves and load–strain curves of the stainless steel columns were obtained. The numerical analysis model of the stainless steel lipped C-section column under compression was established based on ABAQUS finite element software. The finite element results were in agreement with the test results, which verified the accuracy of the finite element model. A parametric analysis was carried out on two key factors, the initial geometric imperfection amplitude and boundary conditions, which affect the local-distortional interaction buckling capacity of stainless steel lipped C-section columns. The results show that the initial geometric imperfection amplitude of specimen has a significant influence on the local-distortional interaction buckling capacity of stainless steel lipped C-section column, while the influence of boundary conditions is small.

Simplified Numerical Model Development of Lightweight‐concrete Encased Cold‐formed Steel Column‐end Joints and Panels

AbstractWith the increasing demand for using cost‐effective structures in the construction field, more and more novel structural systems have been developed. One of these new efficient systems is cold‐formed steel (CFS) members encased in polystyrene aggregate concrete (PAC). In this study, a simplified numerical model has been proposed, using ANSYS software, for PAC‐encased CFS column‐end joints and panels under compression. Each model has been validated with previous experimental results from the literature, where both ultimate axial load and failure mode were compared with tests. The main idea in this numerical model was to substitute the bracing effect of concrete on buckling with springs. A detailed imperfection sensitivity study was performed for column‐end connections to determine the effect of imperfection values on both ultimate capacities and failure modes. The necessary equivalent geometric imperfection amplitude was determined for each case of the available tests. Finally, an equivalent geometric imperfection amplitude was proposed for column‐end joints and panels to predict the design capacity according to the test failure mode.

Thermal Upheaval Buckling of Buried Pipelines: Experimental Behavior and Numerical Modeling

Pipelines transporting oil and natural gas may experience upheaval buckling due to substantial compressive forces induced by high temperature and pressure of the fluid content. Such upheaval buckling may pose a major threat to the structural integrity, safety, and operability of pipelines. This study presents results from a series of scaled physical model tests conducted to investigate the uplift behavior and upheaval buckling of buried pipelines. The first set of experiments investigated the resistance force during vertical pullout for different pipe geometries, embedment depths, and relative densities of sand. The second set of experiments investigated the development of global upheaval buckling due to high axial compression of a buried pipe. The study examined the effect of embedment depth on the buckling characteristics and the postbuckling behavior of the pipe. Numerical analyses simulated the experiments and validated the numerical models. A parametric investigation based on rigorous numerical simulations examined the effect of trench-base initial imperfection, internal pressure, and soil strength on the upheaval buckling resistance. The results showed that as the geometric imperfection amplitude increased and its distribution length decreased, the upheaval buckling resistance substantially decreased. Similarly, an increase of the internal pressure of the pipeline may significantly decrease upheaval buckling resistance.

Influence of Geometric Imperfections on Buckling Resistance of Reinforcing Bars during Inelastic Deformation.

This paper presents the results of numerical simulations on three main factors and their influence on the buckling resistance of reinforcing bars and on their behaviour in the range of postcritical deformations. These three factors are the shape of initial deformation, the amplitude of geometric imperfection and the slenderness of bars. The analysis was made of bars fixed on both sides for three initial shapes of deformation between adjacent stirrups, four amplitudes of geometric imperfections and eight bar slendernesses. The results of the numerical analyses carried out showed that the factors analysed have a very high influence on the inelastic buckling of the bars. The initial deformation shape, the radius of curvature and the slenderness of the bars have a significant influence on the buckling resistance of these bars and their longitudinal and transverse deformations. The research demonstrates that bars which are bent or compressed initially have a smaller resistance to buckling compared to straight bars, as the amplitude of geometric imperfections increases and the slenderness of the members increases. However, for the deformation shape of the bars, which is accompanied by shear forces, the drop in the buckling resistance of the members is small, and resistance to buckling for items with a small slenderness was higher than that of straight bars.

Nonlinear Parametric Vibration of the Geometrically Imperfect Pipe Conveying Pulsating Fluid

In this paper, the novel model of fluid-conveying imperfect pipe supported at both ends is established by considering the geometric imperfection and the geometric nonlinearity induced by mid-plane stretching. The integral-partial differential equation is discretized by the Galerkin method and solved by a fourth-order Runge–Kutta integration algorithm. Compared with the supercritical pitchfork bifurcation of the perfect pipe conveying fluid, the results show that the cusp bifurcation occurs in the imperfect pipe when increasing the flow velocity. Excellent agreement is observed between the numerical results and the analytical results. The two stable asymmetry bifurcation branches bring interesting phenomena in the post-buckling state. The global nonlinear dynamic behaviors of the imperfect pipe are studied by establishing the bifurcation diagrams. The influence of the geometric imperfection amplitude on the nonlinear response is leading to cusp bifurcation comparing with pitchfork bifurcation of the perfect pipe. When pulsation frequency is set as the bifurcation parameter, there are clear nonresonance ranges, low energy resonance ranges and high energy resonance ranges. In the high energy resonance ranges, the first mode vibration coexisting with the sub-harmonic resonance and combination resonance occurs. As the mean flow velocity and pulsation amplitude are set as bifurcation parameters, the vibration of the imperfect pipe becomes more and more complicated. The vibration exhibits far richer dynamic behaviors including periodic, multi-periodic, quasi-periodic, and chaotic motions. The viscoelastic damping can effectively suppress the vibration response and transfer the high energy resonance to the low energy resonance state. The improved model and corresponding results provide useful information for further studying the dynamic behaviors of fluid-conveying pipe with geometric imperfections.

Nonlinear thermo-mechanical response of temperature-dependent FG sandwich nanobeams with geometric imperfection

In this paper, the nonlinear dynamic response of functionally graded (FG) sandwich nanobeam associated with temperature-dependent material properties by considering the initial geometric imperfection is investigated. The size-dependent behavior of the FG sandwich nanobeam is simulated based on the nonlocal strain gradient theory, and Von Karman nonlinear hypothesis is used to model the geometrical nonlinearity. Moreover, the geometric imperfection is considered as a slight curvature satisfying the first mode shape, and four different FG sandwich patterns including two asymmetric configurations and two symmetric configurations are taken into account. The governing equation of the FG sandwich nanobeam subjected to thermal and harmonic external excitation loadings is derived on the basis of Hamilton’s principle. The numerical results are obtained by employing the multiple-scale method, which are also validated by comparison with two previous studies. Furthermore, comprehensive investigations into the influences of size-dependent parameters, external temperature variation, geometric imperfection amplitude, gradient index and sandwich configuration on the nonlinear characteristics of imperfect FG sandwich nanobeams are conducted through numerical results.

Nonlinear resonance of FG multilayer beam-type nanocomposites: Effects of graphene nanoplatelet-reinforcement and geometric imperfection

In this paper, the nonlinear dynamic response of a FG multilayer beam-type nanocomposite reinforced with graphene nanoplatelet (GNP) by considering the initial geometric imperfection is investigated on the basis of nonlocal strain gradient Euler-Bernoulli beam theory. Four patterns of GNP distribution incorporating the uniform distribution (UD) and O-, X-, and A- FG pattern distributions are taken into account and the effective elastic properties of the beam-type nanocomposite are evaluated in the framework of Halpin-Tsai scheme. The first-order vibrational mode is employed to represent the initial geometric imperfection of the nonlinear FG beam-type nanocomposite. Correspondingly, the nonlinear amplitude-frequency response of the imperfect FG multilayer beam-type nanostructures subjected to the excitation resonance is analyzed with the aid of multiple scale method. Firstly, the present model is validated with a comparison of two previous works. Then, a comprehensive investigation is conducted to evaluate the effects of GNP distributed pattern, weight fraction of GNPs, geometric imperfection amplitude, boundary condition, excitation amplitude, nonlocal and strain gradient size scale parameters on the nonlinear frequency-response of FG multilayer beam-type nanostructures. The current work is beneficial for the application of GNP as reinforcement to enhance mechanical performances of nanostructures.

Analyzing nonlinear mechanical-thermal buckling of imperfect micro-scale beam made of graded graphene reinforced composites

This research is devoted to analyzing mechanical-thermal post-buckling behavior of a micro-size beam reinforced with graphene platelets (GPLs) based on geometric imperfection effects. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. The micro-size beam is considered to be perfect (ideal) or imperfect. Buckling mode shape of the micro-size beam has been assumed as geometric imperfection. Modified couple stress theory has been used for describing scale-dependent character of the beam having micro dimension. Via an analytical procedure, post-buckling path of the micro-size beam has been derived. It will be demonstrated that nonlinear buckling characteristics of the micro-size beam are dependent on geometric imperfection amplitude, thermal loading, graphene distribution and couple stress effects.

Local–global mode interaction in thin-walled inelastic rectangular hollow section struts part 1: Nonlinear finite element analysis

Abstract Mass efficient thin-walled rectangular hollow section (RHS) struts have been shown to be susceptible to local–global mode interaction and exhibit sensitivity to imperfections. Material nonlinearity may increase the imperfection sensitivity of such members further and affect the final failure mode. Nonlinear finite element (FE) models for welded inelastic thin-walled RHS struts with pre-defined local and global geometric imperfections alongside residual stresses are developed within the commercial package Abaqus and validated against two independent experimental studies. Based on the validated FE model, the effects of material nonlinearity and residual stresses from welding on the ultimate load, mechanical behaviour and the imperfection sensitivity of struts are investigated. A simplified method to determine the initial geometric imperfection amplitude introduced in the FE model with residual stresses explicitly modelled within the ECCS framework is proposed for the first time. The experimental and numerical results in conjunction with existing experimental results from the literature are employed in the companion paper for the assessment of the Effective Width Method and Direct Strength Method, which also forms the basis for a new set of design recommendations.

Global stability analysis of spatial structures based on Eigen-stiffness and structural Eigen-curve

The global stability of a spatial structure is usually analysed via a nodal load-displacement curve (NLDC). However, the global mechanical properties of a structure can hardly be reflected comprehensively by specific NLDCs, and no criterion is available to select the representative node for getting the most reasonable NLDC. In this paper, a scalar parameter derived from the incremental equilibrium equation of nonlinear stability analysis, named Eigen-stiffness, is defined to characterize the global structural stiffness. The Structural Eigen-curve (SEC), based on Eigen-stiffness, is proposed to depict the equilibrium path. Two types of extreme points on SEC are defined to determine the critical state of the structure, including the structural limit state and the structural snap-back. Firstly, the stability of a hinge-supported planar arch is analysed to introduce the SEC concept. Then a K6 reticulated shell is designed to give further understanding. Subsequently, practical application of the SEC is illustrated in the stability analysis of a roof structure, namely, Shanghai International Conference Centre. In addition, a parametric study on a K6 reticulated shell is carried out, based on the Eigen-stiffness and the SEC, to investigate the effects of the rise to span ratio and the geometric imperfection amplitude on the structural stiffness and the structural load-carrying capacity. The results demonstrate that the ultimate load-carrying capacity obtained from the SEC is equal to that from NLDC. More importantly, unlike NLDC, the SEC — free from node selection — can efficiently capture the features of global structural behaviour and the evolution of structural stiffness.

Numerical modelling of steel plate girders at normal and elevated temperatures

The main goal of this study is to increase the knowledge on the behaviour of steel plate girders subjected to shear buckling at both normal and elevated temperatures. Hence, numerical models were duly validated with experimental tests from the literature. Experimental tests on steel plate girders with different configurations were numerically reproduced, showing a good agreement between numerical and experimental results. Afterwards, applying the validated numerical models, sensitivity analyses on the influence of initial imperfections were performed. Different values for the maximum amplitude of geometric imperfections were considered and residual stresses were also taken into account. Finally, the effect of the end supports configuration was also studied aiming to understand the strength enhancement given by the rigid end support at normal temperature and evaluating if that strength enhancement is maintained in case of fire.

The Temporal Evolution of Buckling in a Dynamically Impacted Column

The time-dependent progressive evolution of transverse displacements of an axially impacted, slender, geometrically imperfect, column is studied here. The analysis is concerned with evaluating the time-history associated with the evolution of the buckling response as a function of the initial geometric imperfection amplitude. The exact solution of the axial stress wave propagation is employed to study the physics of the buckling response with the nonuniform axial strain distribution varying in time and space. The responses of axially impacted columns are examined in light of past experimental results and associated numerical solutions. Results in the present paper are limited to elastic column behavior.

Vibration of geometrically imperfect panels subjected to thermal and mechanical loads

The results of a study of the vibration response of transversely isotropic flat and curved panels subjected to temperature fields and to mechanical loads into the postbuckling load range are presented. The results were obtained using a higher-order transverse-shear-deformation theory of shallow shells that includes the effects of geometric nonlinearities and initial geometric imperfections. The results focus on the interaction between the temperature field, the applied mechanical load, and the fundamental frequency associated with small vibrations about the prebuckling and postbuckling equilibrium states. Results are presented for a wide range of temperatures and mechanical load magnitudes and of geometric parameters. The results show that transverse-shear flexibility has a significant effect on the analytical prediction of panel response and that the fundamental frequency of a panel may be substantially overestimated in the prebuckling load range and underestimated in the postbuckling load range. Results are also presented that indicate that the fundamental frequency of flat panels generally increases as the initial geometric imperfection amplitude increases for both the prebuckling and postbuckling load ranges. The results, however, also indicate that the fundamental frequency of curved panels generally decreases in the prebuckling load range and increases in the postbuckling load ranges.