Symmetric Buckling Mode Research Articles

Study on symmetric buckling mode triggered by dual distributed buoyancy sections for subsea pipelines

In order to control lateral buckling, buckle initiation techniques, such as distributed buoyancy section (DBS) are employed to trigger lateral buckles at planned locations. Dual DBSs with a gap between are sometimes employed as a buckled initiation method, which may trigger either a symmetric or antisymmetric mode. In this study, analytical models for symmetric mode triggered by dual DBSs are proposed, which are validated by comparing with test data. First, the buckled configuration and the post-buckling behaviour are analysed. Then, a detailed analysis is carried out to present the effect of dual DBSs on the characteristics of the buckling behaviour. Comparisons between symmetric and antisymmetric buckling mode triggered by the same dual DBSs are discussed. The results show that when dual DBSs are utilised as the buckle initiation technique, both the symmetric and antisymmetric mode can be triggered. Symmetric mode is prone to be triggered for relative small spacing between dual DBSs. The symmetric mode is more dangerous than antisymmetric mode except that the weight ratio coefficient is small enough. Therefore, during the design process, it's better to check the maximum stress of both symmetric and antisymmetric mode to ensure the integrity of the buckled pipeline.

Antisymmetric thermal buckling triggered by dual distributed buoyancy sections

Rogue buckles may occur for unburied subsea pipelines operating under high temperature and high pressure conditions. Distributed buoyancy section (DBS) is often installed to trigger pipeline lateral buckling. Single distributed buoyancy section (SDBS) is normally adopted to trigger a symmetric lateral buckling mode. But in some cases, dual distributed buoyancy sections (DDBS) with a gap between them are utilised to trigger an antisymmetric lateral buckling mode. This paper concerns the behaviour of antisymmetric lateral buckling triggered by DDBS. First, the locations of the maxima of the deflection and bending stress are determined. Then, comparisons of the post-buckling behaviour between antisymmetric buckling mode, triggered by DDBS, and symmetric buckling mode, triggered by SDBS, are presented and discussed. The influences of the spacing between dual buoyancy sections and the parameters of the DBS on the buckled configuration and post-buckling behaviour are presented. Finally, the effects of the DBS on the minimum critical temperature difference, the maxima of the deflection and stress are discussed. The results show that the maxima of the deflection and stress of the antisymmetric mode are much smaller than that of the symmetric mode under the same operating conditions. During the design process, the spacing between dual buoyancy sections, the length and the weight ratio coefficient of the DBS should be determined in sequence.

Experimental test and hysteretic behavior of single cross-arm PCS-BRBs

An innovative buckling-restrained brace (BRB) is devised by imposing a cable stayed system (CSS) on a common BRB, namely single cross-arm pre-tensioned cable-stayed buckling-restrained brace (SPCS-BRB). Its overall external stiffness thus load-bearing capacity can be dramatically enhanced over the common BRB. A previous study conducted by the authors investigated comprehensively the elastic buckling behavior of the brace, yet experimental investigations and detailed design suggestions were not provided. Two SPCS-BRB specimens have been devised and tested. Test results revealed that both specimens possessed excellent hysteretic response with stable hysteretic curves, which fulfilled the ductility requirement specified in the AISC seismic provisions. The adopted simplified Finite Element (FE) model for experimental simulations corresponds well with the obtained test results. Moreover, additional FE analysis (FEA) has been conducted on the SPCS-BRBs subjected to monotonic and cyclic axial loads, respectively as to validate the test results further. In addition, threshold values of restraining ratios are obtained by guaranteeing the cables to remain tensioned prior to attaining ultimate failures, and ensuring maximum load resistance of the SPCS-BRBs is obtained. It is observed from the FEA that global instability failures of the SPCS-BRBs are caused by expansion of yielding at the extreme fibers of the external tube. Finally, FEA has been conducted on the load resistance of the SPCS-BRBs by considering the effect of interactive buckling and prestressing force of cables. It is found that interactive buckling could become critical in dominating the load resistance of the SPCS-BRBs when single-wave symmetric buckling mode is considered.

On the mechanical stability and buckling analysis of carbon nanotubes filled with ice nanotubes in the aqueous environment: A molecular dynamics simulation approach

In this article, molecular dynamics (MD) simulations are utilized to investigate the buckling behavior of carbon nanotubes (CNTs) containing ice nanotubes in the vacuum and aqueous environment. The obtained results show that unlike the critical strain, the critical buckling load of CNT containing ice nanotube is higher than that of pure CNT in the vacuum. It is also indicated that the sensitivity of critical buckling load and the critical strain of CNT containing ice nanotube to the variation of length decreases when the nanostructure is subjected to the aqueous environment. Additionally, it is observed that the calculated critical buckling load and the critical strain of CNTs filled with ice nanotubes in the aqueous environment are respectively larger and smaller than those obtained in the vacuum. It is further observed that CNTs lose their symmetric buckling mode shape as they are filled with ice nanotubes in the vacuum. The results of these simulations can be used as a benchmark for further studies in designing novel potential applications such as proton electronic-based nanoelectromechanical systems (NEMS).

04.09: Cylindrically curved steel panels in bridge design: Buckling and post‐buckling behaviour under shear stresses

ABSTRACTThe main goal of this work is to investigate the behaviour of the cylindrically curved steel panels subjected to pure in‐plane shear stresses. The most relevant works regarding the simply supported curved panels under shear stresses were firstly revised and based on these studies the numerical models were calibrated. As one of the main objectives of this study, the influnce of aspect ratio and curvature parameter on both elastic buckling and post‐buckling behavior of curved panels was analysed. Regarding the curvature parameter, it was concluded that the higher curvatures in general lead to the increased critical buckling load and moreover to the shell‐like behaviour, which result in rather unstable post‐critical behaviour. As for the aspect ratio effect, due to the reduction of the initial stiffness, the higher aspect ratios lead to the drop in buckling load, and thus also lower post‐buckling reserves. On the other hand, the curved panels with low aspect ratio, showed a behaviour similar to the panels with the high curvatures parameters, which is characterized by sudden drop in bearing capacity and huge deflections after the critical load is reached. Furthermore, using the fully non‐linear numerical simulations, the imperfection sensitivity of the curved panels was examined, where, in particular, shape, amplitude and sign of the imperfections were varied. It was concluded that the panels with the higher curvatures as well as the non‐squared panels are more sensitive to the imperfections. Concerning the shape effect, it is more emphasized in case of the panels with the smaller radii, where it may have an impact on the post‐buckling behaviour. Finally, regarding the sign of the imperfections, it was proven that both directions of imperfections have to be verified in order to obtain the most unfavourable behaviour. The sign sensitivity is particularly noticed for the panels which buckle in symmetric buckling mode.

Buckling of an annular plate under tensile point loading

In this paper, we address the stability of an elastic thin annular plate stretched by two point loads that are located on the outer boundary. A roller support is considered on the outer boundary while the inner edge of the plate is free. Muskhelishvili’s theory of complex potentials has been applied to obtain a solution of the plane problem in the form of a power series. The buckling problem has been solved using the Rayleigh–Ritz method, based on the energy criterion. The critical Euler force and the respective buckling mode have been computed. Dependence between the critical force and the relative orifice size has been illustrated. Analysis of the results has shown that a symmetric buckling mode takes place for a sufficiently large hole, with the greatest deflection observed around the hole along the force line. However, an antisymmetric buckling mode occurs for relatively small holes, with the greatest deflection being along a line that is orthogonal to the force line.

The symmetric buckling mode in laminated elastoplastic micro-structures under plane strain

The present work considers lamellar (micro) structures of thin, elastic lamellae embedded in a yielding matrix as a stability problem in the context of the theory of stability and uniqueness of path-dependent systems. The volume ratio of the stiff lamellae to the relatively soft matrix is assumed low enough to initiate a symmetric buckling mode, which is investigated by analytical and numerical means. Using a highly abstracted, incompatible model, a first approach is made, and the principal features of the problem are highlighted. Assuming plane strain deformation, an analytic expression for the bifurcation load of a refined, compatible model is derived for the special case of ideal plasticity and verified by numerical results. The effect of lamella spacing and matrix hardening on the bifurcation load is studied by a finite element unit cell model. Some of the findings for the ideal plastic matrix are shown to also apply for a mildly hardening matrix material. Furthermore, the postbuckling behaviour and the limit load are investigated by simulating a bulk lamella array.

A relationship between progressive collapse and initial buckling for tubular structures under axial loading

The progressive collapse of tubular structures under axial loading is a challenging problem in mechanics. Due to the nonlinearities in large plastic deformation, such a problem can only be solved case by case under the assumption of an appropriate collapse mechanism. In this paper, a relationship between the progressive collapse of an axially loaded tube and the initial buckling of its windowed counterpart is presented. Numerical investigation was performed on the axial crushing of triangular, square and pentagonal tubes and the initial buckling modes of the corresponding windowed tubes. Results show that at the critical symmetric buckling mode, the theoretical mean crushing force of the angle-shaped column in the windowed tube matches very well with the actual mean crushing force of the conventional one. This relationship is crucial to the development of a generalized method for progressive collapse without assuming collapse mechanism. Based on it, an empirical equation on the mean crushing force of axially loaded square tubes is presented. The mean crushing forces predicted by this equation are in good agreement with the experimental results and theoretical values.

Initial Compressive Buckling of Clamped Plates Resting on Tensionless Elastic or Rigid Foundations

The unilateral contact buckling problem of thin plates resting on tensionless foundations is investigated. Three different plate models are considered. For a plate of limited length on a tensionless elastic foundation, the plate is first simplified to a one-dimensional mechanical model by assuming a buckling mode in terms of transverse coordinates, after which a new method is employed to determine the initially unknown boundaries of the areas in contact. Based on the continuity condition on the borderline between contact and noncontact regions, the buckling mode displacements of the whole plate may be expressed through the critical load coefficient and the first half-wavelength, reducing the buckling problem to two nonlinear algebraic equations with two unknowns. This procedure has been named the transfer function method. For a very long plate with a symmetric buckling mode, an infinite plate model with two half-waves is presented. For a plate on a rigid foundation, a single half-wave buckling model is shown to be appropriate. Comparison of limiting cases with exact solutions and with ABAQUS results showed good agreement. Finally, the influences of aspect ratio and foundation stiffness are presented.

Formulation and application of a three-dimensional structural model for upper internal structures

A finite element structural model is developed for the upper internals which is capable of treating material nonlinearities and geometric nonlinearities arising from large displacements when subjected to dynamic loads. This structural model can be used either by itself or in an interactive mode with a hydrodynamics code. The upper internal structures which are located above the core and below the head cover may play a significant role in the hydrodynamics of an energy excursion by mitigating its response. The upper internal structure (UIS) is essentially a massive, perforated rigid body which is connected to the reactor head by support columns with a cylindrical cross section. The major response of interest is the buckling of these support columns which results from the compressive forces they sustain when the upper internals are loaded vertically upward by dynamic loads. In addition to buckling, these columns sustain plastic deformations and changes in cross section making geometric and material nonlinearities accountable. For the case of substantial change in the shape of the column cross section, it will be more convenient to treat the behaviour of the elements stiffness in terms of moment-curvature relations which account for the changes in flexural rigidity with change in cross section. Two factors considered of importance in developing the model are: (1) whether an imperfection is necessary in the initial mesh of the columns to trigger buckling and to what extent does the magnitude of the imperfection effect the results; (2) whether the buckling pattern is symmetric or asymmetric. It was established by these studies that elastic buckling is not affected by the magnitude of the imperfection; for plastic buckling, the results are more sensitive to the magnitude. The studies also showed that the UIS mass is sufficiently large so that it cannot be laterally displaced. By checking the deformed shape, it was observed that the column always attempts to reach the symmetric buckling mode. Even if the asymmetric shape is triggered, it is always at a load higher than that required to trigger a symmetric response. The behavior of the model has also been compared with the SRI tests simulating highly energetic CDAs. The model predicts the magnitude of the axial deflection quite well.

The Effect Of Induced Imperfections On TheFormation Of The First Lobe Of SymmetricProgressive Buckling Of Thin- Walled SquareTubes

An experimental investigation showing the effect of induced imperfections on the symmetric progressive buckling of thin-walled square mild steel tubes is presented. The imperfections include: a circular hole; indentations of various shapes; and combinations of a hole positioned centrally in an indentation. In all cases identical imperfections were induced symmetrically in opposite walls of the tube. The results indicate that the ultimate buckling load of the tube decreases with an increase in the severity of the imperfection. The distance between the plastic hinges that form the first lobe of buckling decreases with two opposing holes, but increases with large indentations. The change in the size of the first lobe leads to instabilities in the symmetric buckling mode which in turn leads to a decrease in the stroke of the tube. The results further indicate that combining a hole with an indentation has a cumulative effect on both the ultimate buckling load and the size of the first lobe. The stability of the symmetric progressive buckling of the tube is retained while decreasing the ultimate buckling load significantly for a range of indentation sizes and hole diameters.