Effects Of Initial Geometric Imperfections Research Articles

Investigation on internal resonance of fluid conveying pipes with initial geometric imperfection

This paper shows numerical research on the 1:2 internal resonance and chaotic bifurcation phenomena of the graphene platelets reinforced metal foams (GPLRMF) pipes, with emphasis on the effect of initial geometric imperfection. To this end, combining the high order shear deformation beam theory and Kelvin-Voigt viscoelasticity, a mathematical model that considers geometric imperfection is established. The fluid in pipeline is supposed to be incompressible and inviscid. Subsequently, the Galerkin discretization and multiscale method are utilized for solving the nonlinear governing equations in the case of 1:2 internal resonance. And the nonlinear dynamic behavior of the fluid conveying pipes can be analyzed through the frequency amplitude diagrams, bifurcation curves, time course curves, phase trajectories, and Poincaré maps. The double jump phenomena are excited to demonstrate the dynamic characteristics of the pipes with 1:2 internal resonance. In the case of small disturbance coefficients, various internal resonance and chaos phenomena can be captured in the pipeline system. Research shows that the coupled effects between initial geometric imperfection and nonlinear geometric relationships is non-monotonic. That is to say, for bimodal internal resonance, when the initial geometric imperfection increase, the unstable region will be compressed, and the response amplitude will increase.

Nonlinear aero-thermo-elastic flutter analysis of stiffened graphene platelets reinforced metal foams plates with initial geometric imperfection

Due to its lightweight design and high load-bearing capacity, the stiffened plate structure is extensively applied in the passive control of aircraft flutter. However, the evolution mechanism of the nonlinear response of stiffened plates within the unstable region remains unclear. In particular, there is a lack of research on the nonlinear aero-thermo-elastic properties of stiffened plates with initial geometric imperfection. Inspired by this, this article investigates the stability and post-instability behavior of stiffened geometrical imperfect graphene platelets reinforced metal foams (GPLRMF) plates under combined thermal load and aerodynamic pressure. Graphene platelets (GPLs) and foam are distributed evenly or unevenly in the plates, while the material properties are calculated by modified Halpin-Tsai model and rule of mixture. Considering initial geometric imperfection, the models of plates and stiffeners are established by first-order shear deformation (FOSD) plate and Timoshenko beam theories, respectively. Using the linear piston theory to simulate supersonic aerodynamic pressure. The stability boundary of stiffened plates is determined by eigenvalue analysis. The Newton-Raphson approach is used to simulate the aero-thermo-elastic static response of stiffened plates, and the dynamic post-flutter behavior of the stiffened plate is determined through the Runge-Kutta method. Finally, the effects of initial geometric imperfection, material parameters (foam distribution type, porosity coefficient, GPLs weight fraction and GPLs distribution type), and stiffeners (size, position, and stiffening scheme) on the thermal aeroelastic behavior of stiffened GPLRMF plates are revealed. It can be found that the presence of initial geometric imperfection will significantly change the nonlinear flutter behavior of the stiffened plates.

Flexural–torsional buckling of steel circular arches with I-section under central concentrated load in elevated-temperature environment

This article reports the fire resistance experiments conducted on I-section circular steel arches, as well as the observed out-of-plane flexural–torsional buckling (FTB) behavior and in-depth finite element numerical simulation results. The test was carried out using a large fire test furnace to provide a real fire environment with a nonuniform temperature field. A specially designed loading device allowed for unconstrained out-of-plane deformation of the specimens inside the furnace, thereby achieving effective load conditions and noncoupled response of the components. Numerical analyses were performed using a combination of the general codes Fluent and Abaqus, with the former used for heat transfer analyses, and a structural FE model including the loading device and complex geometric imperfections was established based on the measured data. Thus, accurate simulation of the out-of-plane behavior of the steel arches at elevated temperature was achieved. On this basis, an in-depth parametric study was carried out to investigate the effects of temperature field variations, load ratio (LR), and geometric imperfection. The analysis results show that FTB occurs at nonuniform temperatures for the arches under concentrated load, and the difference in temperature distribution in fire has a minimal effect on the FTB behavior. LR is negatively correlated with critical temperature; the smaller the LR, the more significant the weakening of critical loads by fire. The effect of initial geometrical imperfections on FTB at elevated temperatures is similar to that at ambient temperatures, and the effect on the critical temperature of FTB can almost be ignored when the imperfection amplitude is less than S/400.

The method for calculating the bearing capacity of cold-formed C-Section axial compression member using Direct Strength Method

The paper carried out numerical analysis using experimental and finite element analysis methods to determine the bearing capacity of cold-formed C-section axial compression member. Finite element analysis was performed using the application ABAQUS and the results were compared with experimental measurements. This paper also made out the reason for the error between the experimental results and the results of the finite element analysis, and the ultimate bearing capacity is determined by finite element analysis with C-section axial compression member of various sizes. At the same time, the effect of initial geometric imperfection on the bearing capacity of the member is analyzed in detail. Based on finding out that the supporting capacity of the member is directly related to local buckling, distortional buckling, and lateral-bending buckling critical stress, the formula for calculating the bearing capacity of the cold-formed C-section axial compression member by analyzing the research results on the direct strength method.

The Ultimate Strength of Fully Transparent Pressure-Resistant Spherical Cabins

The fully transparent cabin used in a manned submersible is typically made of the viscoelastic material polymethyl methacrylate (PMMA). The pressure-bearing capacity of a PMMA-manned cabin was investigated considering the effects of initial geometrical imperfections and large openings. Three types of cabins were studied within the failure mode of nonlinear buckling, including an intact spherical cabin, a spherical cabin with a single opening, and a spherical cabin with double openings. The initial geometrical imperfection ranges from 0.1% to 0.5% of the inner diameter. The ultimate strength decreasing tendency for the different types of cabins with increasing initial imperfection was obtained and the thickness of the hatch cover determined based on the principle of equivalence differed its effects on the strength of the cabin. The influence of the hatch cover stiffness was not linear and indicated the necessity of exploring the coordinated design between the PMMA shell and the metal hatch cover for the transparent cabin.

Novel Imperfection Method for Post-Buckling Strength of C-Sectioned CFS Members

The overall behavior of cold-formed steel (CFS) members is significantly affected from existing geometric imperfections. In this work, a mode shape-based imperfection coefficient computation method is developed to investigate the effects of initial geometric imperfections on member behavior. The point clouds of CFS members are collected and used to extract imperfection distributions and coefficients. The computed coefficients are integrated into the numerical model for analysis. Finally, axial loading tests are conducted to compare the numerical and experimental results. The results obtained using mode shape-based imperfection coefficients are generally closer to the experimental results than the common method used in practice.

Large scale fire resistance tests of prestressed continuous steel–concrete composite beams to evaluate the effects of geometric imperfections

Little attention has been devoted to exploring the effect of geometric imperfections under fire conditions. To bridge this knowledge gap, this paper presents findings from five large scale fire tests on prestressed continuous steel–concrete composite beams (PCCBs) designed to investigate the effect of initial geometric imperfection (IGI) on the fire resistance of PCCBs. The examined parameters include several IGI modes, load levels, and prestress levels. Various fire responses were monitored and recorded during these tests, such as cross-sectional temperature rise, mid-span deflection, prestress in the cable strands, and side-support reactions. The results of these fire tests indicate that PCCBs with the initial mode of flexural–torsional buckling at the middle support applied as an IGI had larger mid-span deflection and lower critical temperature relative to that of the beams without IGI. The same beams also underwent a larger degree of relaxation in prestress levels, thus reaching failure at a faster pace. Our findings also indicate that while the end-support reactions were redistributed when exposed to fire, the side-support reactions decreased at the first stage of fire exposure and then gradually increased toward the final stage of the fire exposure. Evidently, for PCCBs with IGI, the side-support reaction towards the end of the fire tests is larger than the initial reaction. To complement the conducted fire tests, a series of finite element (FE) models were developed to further study the effect of IGIs in terms of the fire response of PCCBs.

Dynamic stability of single-layer spherical reticulated shell structures under earthquake action

In past decade, earthquake disasters have seriously damaged nonstructural components, so it is very important to study their dynamic stability. However, the existing researches mainly focus on the dynamic stability of multistory and high-rise buildings, and there are still deficiencies in the analysis of dynamic stability of reticulated shell structures under earthquake action. This paper takes the 40 m span K8 single-layer spherical reticulated shell structure with practical engineering significance as the research object, we study its dynamic instability characteristics under earthquake action, and propose a dynamic stability judgment method. The influence of various parameters on the critical loads of emotional stability of reticulated shell structures is systematically analyzed, including the impact of horizontal seismic action, the vertical seismic activity, and the three-dimensional seismic movement, considering the influence of material elastoplasticity; the result of different seismic inputs, the effects of initial geometric imperfections; the effects of varying rise span-ratio. In this paper, to investigate the nonlinear time-history response analysis, we uses the finite-element package ABAQUS. We first analyze the rise-span ratio as the dynamic stability of 1/3 single-layer reticulated shell structure under the action of the El Centro (1940) earthquake to reveal the dynamic loss of reticulated shell structure under earthquake action stable feature. The practical method for determining the proposed dynamic stability has a clear physical meaning and a range of applications. Our findings highlight that the critical load for dynamic stability under horizontal earthquake action is significantly lower than vertical earthquake action, and the critical load is the lowest under three-dimensional earthquake action. Material elastoplasticity influences the critical loads for dynamic stability of reticulated shell structures under different ground motions. The critical load of dynamic stability of single-layer structures with a larger rise-span ratio is lower, while those with a smaller one is higher. The initial geometric defects of the structure should be considered in practical engineering applications. The reticulated shell structure with a larger rise-span ratio needs to consider the dynamic stability problem in the strong earthquake area.

Effect of initial geometric imperfections on dynamic ultimate strength of stiffened plate under axial compression for ship structures

Compared with static loading condition, the initial geometric imperfection has a significant influence on dynamic ultimate strength, which can greatly change the failure mode and also ultimate capacity. In previous studies, only the 1st buckling mode of plate is usually considered as the initial geometric imperfection. However, it might not trigger the dangerous failure mode and also cannot give the lowest estimation of dynamic ultimate strength. In this paper, the stiffened plates used in ship structures are chosen as the study object. The dynamic action is assumed as a load with impact velocity at the plate short edge along axial direction. The effect of initial geometric imperfection with higher buckling modes is analyzed. Based on validation of the experiment results, a general procedure is offered for considering initial geometric imperfection in dynamic ultimate strength analysis. Then, the influence factors, including imperfection shape, plate slenderness ratio and impact velocity are discussed detailly. At last, a simple formula for dynamic ultimate strength evaluation of stiffened plate is proposed. The conclusions in this paper can provide a guidance for dynamic ultimate strength calculation and ship rules modification.

Investigation on buckling behavior of T-shaped box-T section columns under axial load

Special-shaped columns (i.e., L-shaped, T-shaped, and cross-shaped) present the main advantages of avoiding column protrusion and enlarging the indoor space, and they also have large stiffness and strength in the direction of their longer sections. However, there is a lack of systematic research of the buckling performance of T-shaped column. In this paper, T-shaped box-T section columns, composed of one cold-formed box section and several T-sections, were concerned. The elastic buckling analysis of T-shaped box-T section columns was firstly conducted, and it is recommended to set stiffeners to restrain the distortional buckling of the first order buckling modes of the columns. Based on the elastic buckling analysis, 10 T-shaped box-T section columns with one stiffener were tested under axial load. The measured material properties, geometries, initial imperfections, failure modes, ultimate capacities, and loading histories of the specimens were reported and employed to validate the finite element (FE) models. The plane section assumption was confirmed for T-shaped box-T section columns based on the records of the strain gauges and the FE results. FE analysis was carried out to investigate the effects of initial geometric imperfections, residual stress, and stiffeners on the buckling performances of T-shaped box-T section columns. Totally 880 FE results of the pin-ended columns were employed to evaluate the design curves of the current specifications GB 50017-2017, EN 1993-1-1, and ANSI/AISC 360-16, and new design curves were also proposed.

The Effect of Initial Geometric Imperfections in Steel Frame on Performance

Çelik yapılar, eleman ya da sistem bazında kusurlu olabilmektedirler. Yapısal stabilite ve imalat açısından kusurların geometrik tolerans aralığında kalması gerekir. Çalışmada düzlem çelik çerçeve için üç farklı geometrik ön kusur durumu incelenmiştir. Doğrusal olmayan dinamik analiz yapılarak çerçevelerin performans eğrileri oluşturulmuştur. Çerçeveler, maksimum çatı deplasmanına ulaşılıncaya kadar analiz edilmişlerdir. Plastik mafsal noktalarındaki hasar performans düzeyleri ve performans eğrileri üzerinden karşılaştırma yapılmıştır. Senaryo 1 ve 2’ deki göçme durumu, kiriş mekanizması şeklinde gerçekleşmiştir. Senaryo 3 ve 4’ deki göçme durumu, çerçeve mekanizması şeklinde gerçekleşmiştir. Senaryo 1 ve 2 çerçevelerindeki hasar performans düzeylerinin aynı olduğu belirlenmiştir. Senaryo 3 ve 4 çerçevelerindeki hasar performans düzeylerinin aynı olduğu belirlenmiştir. Kusurların, çerçeve performansını minör olarak olumsuz etkilediği ve tolere edilebilir olduğu tespit edilmiştir.

Investigation of dynamic buckling of fiber metal laminate thin-walled columns under axial compression

This paper presents an investigation of the dynamic buckling phenomenon in thin-walled Fiber Metal Laminate short columns subjected to axial compressive loading. The numerical analysis is performed with the FEM ANSYS software for three profiles differentiate in the laminate stacking sequence. Two groups of criteria were implemented to assess the structure resistance to dynamic pulse loading: the dynamic buckling criteria and strength failure criteria. Parametric analysis was performed to determine the effect of initial geometric imperfection, laminate stacking sequence, and the pulse load's shape on the dynamic stability. The value of the amplitude of initial geometric imperfection and the shape of pulse load influence the value of critical Dynamic Load Factor strongly. Aluminium yielding was observed as the primary failure source developed in the FML structure subjected to the pulse loading.

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.

Nonlinear Buckling Strength of Steel H-Beam under Localized Fire and Pure Bending

This paper presents a numerical simulation to assess lateral-torsional buckling (LTB) behavior of steel H-beams exposed to localized fire. The nonlinear buckling analysis was conducted using a finite element program, ABAQUS, to assess LTB of the beams. The steel beams were subjected to pure bending and localized fire. The location of the localized fire was applied below at a one-eighth point, a quarter-point and a half of the beam from the support. The combined effects of initial geometric imperfection and residual stress were also considered. The buckling strength of the beam under localized fire and ISO-834 standard fire were generated and compared. The results showed that the LTB strength degradation of the beam under localized fire was slower than that in ISO-834 standard fire. The fire source location and the length-to-height ratio of the beam have a significant effect on the LTB strength of the beam. The LTB capacity of beams using Eurocode 3 with the uniform heating assumption can give over-conservative results when the real fire scenario is localized fire. The buckling strength of steel beams using Eurocode 3 can give unconservative results when the fire scenario is ISO-834 standard fire.

Fabrication and mechanical characterization of CFRP X-core sandwich panels

A hot-press molding technique is developed to design and manufacture carbon fiber reinforced polymer (CFRP) X-core sandwich panels that allowed both the composite face sheets and its X-core to be simultaneously molded together. Compression tests were performed on the sandwich panels to assess the effects of relative density on its compressive properties and the failure mode that it develops. Analytical models were developed to predict the panel stiffness and strength; and a failure map of its deformation mode is generated based on the geometric parameters of the unit cell. Linear and nonlinear finite element analyses were performed to further investigate the effects of initial geometric imperfection and progressive damage on the response of the sandwich panels with different cell wall slenderness. Predictions from analytical and numerical models will be shown to be in good agreement with the experiments. The CFRP X-core sandwich panels will be shown to attain good compressive properties that are comparable to typical high strength cellular materials, which will be potentially useful for lightweighting applications.

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.

A mixed-field Timoshenko beam-column element for direct analysis of tapered I-sections members

ABSTRACT Tapered members produced by robotic fabrication techniques offer architectural and structural advantages and have the potential to become more prevalent than prismatic members. However, the conventional analysis and design methods based on simplified assumptions such as equivalent stiffness cannot be used to accurately evaluate a member's performance. To provide a reliable and practicable stability design method, a direct analysis method of tapered I sections is proposed. A mixed-field tapered beam-column element is derived for use within the modeling of structural frames. The effects of initial geometric imperfection and additional shear stress are directly considered in the element formulation. A polynomial describing the member's critical initial out-of-plumbness is adopted, and an arbitrarily located internal hinge is incorporated in the element to enhance the element's deformation capacity and capture the behaviors of the most critical section. Displacement and force interpolation matrices incorporating the shear deformation are utilized, and the Gauss quadrature method is employed to evaluate the element stiffness matrix. Finally, verification examples demonstrate that the proposed method can be used to accurately and efficiently evaluate the performance of tapered members, indicating that the element can be conveniently employed in member and frame analysis and design.

Numerical modelling of engineered cementitious composites-concrete encased steel composite columns

Recently, a new section form of concrete encased steel composite columns with Engineered Cementitious Composites (ECC) confinement (ECC-CES), which outperforms conventional CES columns in terms of failure behaviour, ductility and toughness has been introduced. Numerical modelling of the post-peak behaviours of such encased composite columns is a challenging task due to brittle failure of concrete, interface bond failure and buckling of steel section. This study presents a finite element modelling procedure for the ECC-CES columns. Both material and geometric nonlinearities are incorporated in the model and inelastic behaviour of ECC, concrete and steel were described by using appropriate material constitutive laws. Moreover, effects of initial geometric imperfections, contact interactions and confinement by steel and ECC encasement on concrete core were considered. Concrete damaged plasticity model was employed to describe the failure of ECC and concrete. The FE model was validated against experimental results and found to give good predictions of compressive behaviour of ECC-CES columns compared with the test results. Finally, a small scale parametric study was conducted using the validated numerical model to study the effect of the materials' strength on the column compressive behaviour.

Vibration and nonlinear dynamic analysis of variable thickness sandwich laminated composite panel in thermal environment

Based on the first-order shear deformation theory taking into account geometrical nonlinearity, initial geometrical imperfection, vibration and nonlinear dynamic analysis of the sandwich laminated composite panel characterized by a continuous thickness variation in thermal environment and resting on an elastic foundation are considered in this paper. Variable thickness could affect the design of composite panel since it allows to tailor the stiffness features in the most stressed areas within the domain, keeping the weight constant. As a consequence, an improved dynamic behavior of the structure may be exhibited. The motion equations of dynamic analysis are determined due to Galerkin method and the obtained equation is numerically solved by using Runge–Kutta method. In numerical results, the effects of initial geometrical imperfections and geometrical parameters, material properties, coefficients of foundation, mechanical loads, temperature and the variable thickness on the nonlinear dynamic response and vibration of the laminated composite panel are investigated.

Stability performance of steel liner domes of nuclear reactor containment during construction

The steel liner dome of containment structures has a large span and small thickness, and is attached to the concrete with welded studs and angle steel section anchorages. It acts as the interior formwork during pouring of the concrete, but there is no support or brace for the steel liner dome owing to the construction difficulty, which makes the issue of stability during construction very important. A pressurized water reactor containment was used as an example to investigate the stability of a steel liner dome during construction. In the first key construction phase, stability analysis of the steel liner dome was carried out systematically to obtain the buckling modes and plasticity development. The effect of initial geometrical imperfections on the stability of the steel liner dome was investigated, and a prediction equation for the stability bearing capacity was proposed. In the second key construction phase, the functional failure of the steel liner–concrete composite dome was investigated, and the effects on the buckling loads of composite domes were examined. The results show that the transition area of the dome at which the radius of curvature changes is the weak area in the first key construction phase. Dents occur at this transition area, and the plasticity development at the transition area results in the buckling of the whole structure. The effect of initial geometrical imperfections on the ultimate bearing capacity is not significant. The functional failure is cracking in the ring beam during the second key construction phase.