Buckling Instability Research Articles

Static and dynamic instability of functionally graded graphene origami-enabled auxetic metamaterial beams with variable thickness in fluid

Functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) structures have shown great potential for various engineering applications due to their exceptional mechanical and physical properties such as high strength-to-weight ratio, tuneable stiffness and strength, and negative Poisson's ratio (NPR). This paper aims to investigate the buckling and dynamic instability behaviours of FG-GOEAM beams with variable thickness immersed in a fluid, with a particular focus on the influence of NPR. The material properties such as Young's modulus and Poisson's ratio of the GOEAM are determined by using a genetic programming (GP)-based micromechanics model. Within the framework of the first-order shear deformation theory and by employing Hamilton's principle and modelling the fluid effect as added mass, the governing equations of motion are established and are then discretised by means of differential quadrature (DQ) method to obtain a linear system of Mathieu-Hill equations from which the principal instability regions of the FG-GOEAM beam are determined by Bolotin's method. A comprehensive parametric study is conducted to reveal the effects of GOri's folding degree, distribution, weight fraction, as well as fluid density and beam dimensions on the static and dynamic instability behaviours of the FG-GOEAM beam immersed in fluid. Numerical results show that the FG-GOEAM beam with NPR considerably outperforms its pristine metallic counterpart in terms of resistance against static buckling and dynamic stability.

Stability analysis of hybrid laminated cylindrical shells reinforced with shape memory fibers

Laminated composite structures are widely used in various industries. Body and cape of high-speed flight vehicles are exposed to aerodynamic heating so that causes thermal buckling and dynamic instability. Shape memory alloys (SMAs) have extraordinary mechanical and physical properties which made them suitable for application in laminated structures. In this paper, stability analysis of hybrid laminated cylindrical shells reinforced with SMA fibers is investigated. Utilizing the principle of virtual displacement, governing equations and associated boundary conditions are determined based on the first-order shear deformation theory of shells considering Von- Kármán form of geometrical non-linearity and Love's first approximation. Material properties of SMA fibers and composite vary due to temperature. Variation of thermo-mechanical properties for SMA fibers due to uniform change of temperature are determined through the one-dimensional form of Brinson's constitutive law. Also, different types of loading conditions consist of axial load, pure lateral pressure and hydrostatic pressure are considered. Eventually, the effect of material properties, boundary supports and temperature on the critical buckling axial load, pure lateral pressure and hydrostatic pressure of the laminated cylindrical shells are studied. Investigations indicate that volume fraction and pre-strain of SMA fibers have significant effect on the stability of the laminated cylindrical shells.

Study on the Behavior of Assembled T-Shaped Aluminum Alloy Specimens under Axial Compression

Assembled T-shaped aluminum alloy components represent a new type of structural member in aluminum alloy structures with broad application prospects. In this study, axial compression tests were carried out on 32 aluminum alloy components, considering parameters such as the cross-sectional type and slenderness ratio of the components, to obtain the ultimate bearing capacity and failure mode of the members. The test results show that, for the equilateral assembled T-shaped aluminum alloy components with obvious strong and weak axes, bending instability was most common, and local buckling of the plate occurred when the slenderness ratio of the component was relatively small. For the unequal T-shaped aluminum alloy structures without an obvious strong or weak axis, torsional buckling instability occurred, accompanied by local deformation of the connecting limbs due to mutual compression. A verified finite element model was also established. Based on this model, a parametric analysis was conducted to study the influence of parameters such as initial defects, slenderness ratio, and cross-sectional type on the axial compressive bearing capacity of the assembled T-shaped aluminum alloy components. The experimental and numerical results were then compared with Chinese and European standards, revealing that the standard calculation methods tend to be unsafe. Finally, the calculation parameters for component defects in Chinese and European standards were revised.

A rigid–flexible coupling finite element model of coupler for analyzing train instability behavior during collision

AbstractRail vehicles generate huge longitudinal impact loads in collisions. If unreasonable matching exists between the compressive strength of the intermediate coupler and the structural strength of the car body, the risk of car body structure damage and train derailment will increase. Herein, a four-stage rigid–flexible coupling finite element model of the coupler is established considering the coupler buckling load. The influence of the coupler buckling load on the train longitudinal–vertical–horizontal buckling behavior was studied, and the mechanism of the train horizontal buckling instability in train collisions was revealed. Analysis results show that an intermediate coupler should be designed to ensure that the actual buckling load is less than the compressive load when the car body structure begins to deform plastically. The actual buckling load of the coupler and the asymmetry of the structural strength of the car body in the lateral direction are two important influencing factors for the lateral buckling of a train collision. If the strength of the two sides of the car body structure in the lateral direction is asymmetrical, the deformation on the weaker side will be larger, and the end of the car body will begin to deflect under the action of the coupler force, which in turn causes the train to undergo sawtooth buckling.

Research on stability of deepwater drilling riser system in freestanding mode

If a floating drilling platform encounters sudden bad sea conditions during deepwater operation, it is necessary to disconnect the drilling riser and the floating platform in an emergency. A buoyancy can structure is required to be installed at the top of the riser to ensure that the disconnected drilling riser can stand alone without instability accidents. According to the main structural characteristics and environmental conditions of the freestanding riser and the buoyancy can at the top of the riser, the compressive buckling stability of deepwater drilling riser in freestanding mode under the condition of insufficient top tension is studied in this paper, and the main problem is simplified to the buckling problem of an equal section beam under uniformly distributed axial load and top concentrated force. Firstly, the elastic stability control equation of the riser is established according to the mechanical balance, geometry and constitutive relationship of the riser's micro-element, and the equation as well as the corresponding top and bottom boundary conditions are made dimensionless. Secondly, the elastic stability equation of the micro-bending riser is linearized, the power series solution is obtained according to the perturbation theory, and the influence of different parameters on linear buckling is analyzed. Finally, we convert the elastic stability equation with large deflection into a two-point boundary value problem of the first-order differential equation system under the boundary conditions and two other given conditions. The shooting method program of the two-point boundary value problem including the changes of the top concentrated load and the distributed axial load parameters is developed by using MATLAB, and the calculation analysis is carried out, which reveals the rules of the buckling load and buckling shape after the buckling. The research results of this paper can provide scientific basis and technical guidance for the structure and size design of drilling riser and buoyancy can.

Topology optimization of multiscale structures considering local and global buckling response

Much work has been done in topology optimization of multiscale structures for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based work by Bendsøe and Kikuchi from 1988, which lately has been revived due to advances in manufacturing methods like additive manufacturing. Orthotropic microstructures locally oriented in principal stress directions provide for highly efficient stiffness optimal designs, whereas for the pure stiffness objective, porous isotropic microstructures are sub-optimal and hence not useful. It has, however, been postulated and exemplified that isotropic microstructures (infill) may enhance structural buckling stability but this has yet to be directly proven and optimized. In this work, we optimize buckling stability of multiscale structures with isotropic porous infill. To do this, we establish local density dependent Willam–Warnke yield surfaces based on local buckling estimates from Bloch–Floquet-based cell analysis to predict local instability of the homogenized materials. These local buckling-based stress constraints are combined with a global buckling criterion to obtain topology optimized designs that take both local and global buckling stability into account. De-homogenized structures with small and large cell sizes confirm validity of the approach and demonstrate huge structural gains as well as time savings compared to standard singlescale approaches.

Numerical study on the instabilities of hard-magnetic soft materials with viscoelastic effects

As a type of soft composite material, the hard-magnetic soft materials (HMSM) can retain high residual magnetization due to the high-coercivity of hard-magnetic particles. Meanwhile, the inherent viscoelasticity of the soft polymer matrix usually causes the rate dependent behavior and affects the stability of HMSM. The effects of viscoelasticity on the finite deformation and instability of HMSM are studied in this paper. A numerical model is developed for magneto-mechanical coupled problems of the viscoelastic HMSM. With this model, the instabilities of two typical HMSM structures (i.e. beam and spherical shell) with viscoelastic effects are investigated, including the buckling and snap-through instability. The results show that the viscoelastic effects delay the onset of instability and suppress the snap-back phenomenon during the unloading process. In addition, three different buckling behaviors (i.e. fully relaxed immediate buckling, elastic immediate buckling and the delayed buckling) at different loading rate ranges are observed in both beam and spherical shell. This work provides an effective numerical model to analyze the finite deformation and instabilities of viscoelastic HMSM and may guide the design of HMSM devices.

Kirchhoff’s Analogy between the Kapitza Pendulum Stability and Buckling of a Wavy Beam under Tensile Loading

The Kirchhoff analogy between the oscillation of a pendulum (in the time domain) and the static bending of an elastic beam (in the spatial domain) is applied to the stability analysis of an inverted pendulum on a vibrating foundation (the Kapitza pendulum). The inverted pendulum is stabilized if the frequency and amplitude of the vibrating foundation exceed certain critical values. The system is analogous to static bending a wavy (patterned) beam subjected to a tensile load with appropriate boundary conditions. We analyze the buckling stability of such a wavy beam, which is governed by the Mathieu equation. Micro/nanopatterned structures and surfaces have various applications including the control of adhesion, friction, wettability, and surface-pattern-induced phase control.

Self-buckling and self-writhing of semi-flexible microorganisms.

The twisting and writhing of a cell body and associated mechanical stresses is an underappreciated constraint on microbial self-propulsion. Multi-flagellated bacteria can even buckle and writhe under their own activity as they swim through a viscous fluid. New equilibrium configurations and steady-state dynamics then emerge which depend on the organism's mechanical properties and on the oriented distribution of flagella along its surface. Modeling the cell body as a semi-flexible Kirchhoff rod and coupling the mechanics to a flagellar orientation field, we derive the Euler-Poincaré equations governing the dynamics of the system, and rationalize experimental observations of buckling and writhing of elongated swarmer cells of the bacterium Proteus mirabilis. A sequence of bifurcations is identified as the body is made more compliant, due to both buckling and torsional instabilities. These studies highlight a practical requirement for the stiffness of bacteria below which self-buckling occurs and cell motility becomes ineffective.

A study on the effect of thickness and spherical diagonal for LYP Infill Plate of shear walls

One of the most significant parameters which should be considered by all engineers is improving structures’ strength subjected to lateral load. Steel shear wall whose duty is to affect lateral load (wind and earthquake) is a wall which consists of shear part. Application of low yield point (LYP) steel in shear walls allows the employment of moderate and/or stocky infill plates with low yielding and high buckling capacities, which can result in enhanced buckling stability, serviceability, and energy dissipation capacity of such systems. Infill LYP plate is used to improve shear wall behavior which leads to enhancement of stiffness. In the present research, infill plate with spherical appendages is applied, and its impact on plate stiffness, cyclic behavior and energy absorption are investigated. The spherical diameter has been chosen respectively 10 and 20 cm distributed with two patterns (diagonal and plus form). The best performance is for a LYP plate with a 10 cm spherical diagonal pattern.

Omission of intermediate stiffeners in box link beams using trapezoidal corrugated webs

In box link beams, intermediate stiffeners are often used to delay local shear bucklings, but welding operations in order to connect the intermediate stiffeners to the web of box link beams lead to increased construction costs, reduced execution speed, creating residual stresses and geometric imperfections, and weakening of materials at the junction of stiffeners to the web. The present study investigated corrugating webs of box link beams as an alternative to flat webs with intermediate stiffeners using Abaqus finite element software. First, equations were presented to determine the slenderness ratio and critical inelastic buckling stress of trapezoidal corrugated plates used as the web of box link beams. A comparison between box link beams with corrugated webs and box link beams with flat webs and intermediate stiffeners showed that box link beams with corrugated webs experienced more buckling stability, ductility, and energy dissipation due to the intrinsic geometrical characteristics of this type of web plate. The results of this study revealed that the use of trapezoidal corrugated webs in box link beams, if the geometric parameters of the corrugated webs are appropriately selected, can increase the maximum permissible compactness ratio of the web up to about 12% and 200% more compared to box link beams with flat webs and with or without intermediate stiffeners, respectively; Also, the energy dissipation of the box link specimens can be increased by about 20%.

Dynamic Instability of Functionally Graded Graphene Platelet-Reinforced Porous Beams on an Elastic Foundation in a Thermal Environment.

Under thermal environment and axial forces, the dynamic instability of functionally graded graphene platelet (GPLs)-reinforced porous beams on an elastic foundation is investigated. Three modes of porosity distributions and GPL patterns are considered. The governing equations are given by the Hamilton principle. On the basis of the differential quadrature method (DQM), the governing equations are changed into Mathieu-Hill equations, and the main unstable regions of the porous composite beams are studied by the Bolotin method. Thermal buckling and thermo-mechanical vibration problems are also studied. The effects of porosity coefficients and GPL weight fraction, dispersion pattern, initial thermal loading, slenderness ratio, geometry and size, boundary conditions, and foundation stiffness are discussed. The conclusions show that an elastic foundation has an obvious enhancement effect on thermal buckling, free vibration, and dynamic instability, which improves the stiffness of the beam.

Nonlinear thermal buckling instability analysis of a rotating nanocomposite beam reinforced with graphene platelet via the Chebyshev–Ritz scheme

Resorting to the Chebyshev–Ritz scheme instability as well as post-instability response as a consequence of the buckling occurrence for a rotating nanocomposite beam in a uniform thermal environment is studied. The beam has been reinforced with graphene platelet. The Halpin–Tsai theory is utilized for the sake of specifying the elasticity modulus of the reinforced nanocomposite beam. The Chebyshev set of polynomial functions has been used to serve as a required independent set for the Ritz method. The static displacement field owing to the rotation of the beam and the thermal load is acquired by employing a potent algorithm. The outcomes indicate that for nanocomposite beams with the graphene platelet patterns in the model of O- and U-patterns rotating, respectively, below 9,326, and 7,420 rpm, the graphene reinforcing phase should not be used since it leads to a thermal buckling stiffness for the nanocomposite rotating beam smaller than the thermal buckling stiffness of the associated original rotating beam that just made of a host matrix. Moreover, developing the weight fraction of the graphene platelet for a U-type beam rotating below 9,628 rpm lessens the corresponding thermal buckling stiffness while an X-type beam always strengthens in a similar conditions.

Thermal buckling and post-buckling analyses of rotating Timoshenko microbeams reinforced with graphene platelet

A comprehensive study is established to investigate on the thermal buckling instability and the subsequent post-critical deflection of a rotating nanocomposite microbeam reinforced with graphene platelet. The main scope of the current research is shedding light on the effectiveness of reinforcing a rotating microbeam with graphene platelet subjected to a constant temperature development. The Timoshenko beam theory comes along the von-Karman strain displacement relations to extract the governing equations of motion in accordance with the modified couple stress theory. The modified Halpin–Tsai micromechanical model is implemented to determine the practical elasticity modulus of the nanocomposite beam. The Ritz technique is accompanied by the Chebyshev orthonormal polynomial set to discretize the weak form of the nonlinear equations of motion. The Newton–Raphson technique is applied to the discretized static nonlinear equations of motion to compute the static deformation due to the centrifugal force. On the basis of two effective algorithms the nonlinear equations of motion are attacked to find out the critical buckling temperature change as well as the succeeding post-critical deflection. It is observed that adjoining the graphene phase in the form of an X-pattern promotes the static strength of a rotating microbeam against the buckling instability. However, in contrast, for stationary microbeams and microbeams that rotate with a velocity below a threshold speed adjoining the graphene platelet reinforcement in the form of an O-Pattern not only does not strengthen the microbeam but also weakens it against the buckling instability. Moreover, the buckling modeshape of rotating simply-clamped microbeams is more impressed by the graphene phase.

Mechanism of Mechanical Analysis on Torsional Buckling of U-Shaped Bellows in FLNG Cryogenic Hoses

Floating liquefied natural gas (FLNG) cryogenic hoses can be employed for the transmission of liquefied natural gas (LNG). Usually, U-shaped metal bellows can be applied as the inner lining of FLNG cryogenic hoses. In installation, positioning and other working conditions, torsion is one of the main loads, and torsional buckling instability is a major failure mode of U-shaped metal bellows of FLNG cryogenic hoses. In the current research, the buckling instability of bellows under torsional loads has been investigated in detail, the mechanical mechanism of deformation in torsional buckling mode of bellows has been analyzed and the influence of the structural design parameters on the stability performance has been summarized. It was seen that the axis of the bellows was presented as a spiral line shape during the torsional buckling stage. At the same time, the torsional buckling properties of toroid and spiral bellows were analyzed. The obtained results showed that the torsional buckling stability of the spiral bellows was weaker than that of the toroid bellows and increase of the spiral angle of the spiral bellows intensified this trend. In addition, the post-buckling analysis of U-shaped bellows under torsional loads was carried out by means of experiments and finite element simulation. It was shown that the results obtained from finite element (FE) analysis in this research presented a relatively accurate critical torque value and a consistent buckling instability mode, compared with the experimental results. On this basis, the effects of common defects such as thickness thinning on the torsional stability of bellows were investigated. Considering the geometric defect of thickness thinning, the error of FE analysis was reduced further, and it was found that the defect could significantly decrease the stability of the bellows. The above analysis results could provide a reference for structural design and post-buckling analysis of bellows.

Investigations on the lateral-torsional buckling of an innovative U-shaped steel beam

An innovative solution of a steel-concrete composite beam was developed for buildings with beam spans between 6 and 12 m, taking into consideration the fire situation and the construction stage. The beam is composed of an U-shaped steel part, connected to a reinforced concrete part. In the construction phase, the beam is supporting the slab and constitutes a formwork for the reinforced concrete part. When casting concrete, the steel beam is filled at the same time as the slab, this allows considerable time savings on site. In the exploitation stage, the beam behaves as a steel-concrete composite beam.The developed U-shaped section is composed of three steel parts; a hot rolled steel plate (180x8x6300 mm, and two cold-formed steel plates (470x4x6300 mm) before folding. The section was assembled together with four self-drilling screws longitudinally spaced of 150 mm.In the construction stage, the U-shaped steel beam without restraints is prone to lateral torsional buckling instability. In this paper, the mechanical behaviour of the steel beam at the construction stage, in particular its lateral-torsional buckling stability, was studied. In order to characterize this instability without lateral support, a four-point bending test was carried out on a life-size specimen. The load introduction system was developed especially for the test to allow for all displacements due to LTB. The test clearly showed the lateral torsional buckling behaviour of the steel beam. The test results are compared with numerical simulations and analytical studies. A parametrical study, covering 200 geometrical configurations of the U-shaped beam, is carried out to validate the use of the curve “b” for the design of the steel beam for lateral torsional buckling according to Eurocodes 3.

The role of surface adhesion on the macroscopic wrinkling of biofilms.

Biofilms, bacterial communities of cells encased by a self-produced matrix, exhibit a variety of three-dimensional structures. Specifically, channel networks formed within the bulk of the biofilm have been identified to play an important role in the colonies' viability by promoting the transport of nutrients and chemicals. Here, we study channel formation and focus on the role of the adhesion of the biofilm matrix to the substrate in Pseudomonas aeruginosa biofilms grown under constant flow in microfluidic channels. We perform phase contrast and confocal laser scanning microscopy to examine the development of the biofilm structure as a function of the substrates' surface energy. The formation of the wrinkles and folds is triggered by a mechanical buckling instability, controlled by biofilm growth rate and the film's adhesion to the substrate. The three-dimensional folding gives rise to hollow channels that rapidly increase the effective volume occupied by the biofilm and facilitate bacterial movement inside them. The experiments and analysis on mechanical instabilities for the relevant case of a bacterial biofilm grown during flow enable us to predict and control the biofilm morphology.

Topology optimization of trusses incorporating practical local buckling stability considerations

For the practical application of optimized truss structures, the local stability of the bar must be considered to obtain stable and realistic structures. However, in the practical design of structures, the initial crookedness of the bars and residual stresses that remain in the bar after the manufacturing process should be taken into account, which makes the buckling strength highly non-connected and non-convex in terms of the cross-sectional properties. Therefore, most conventional truss optimization formulations include only local buckling constraints based on the Euler buckling criterion, while local buckling constraints based on design specifications are rarely incorporated. To treat these problems, a novel topology optimization model for trusses is proposed, where the critical buckling strength is calculated according to the practical design code GB5007-2017. In addition, a linearized iterative allowable stress method is used to solve the optimization model. Since the allowable stresses are calculated at each iteration based on the critical buckling strength, other types of design codes can also be incorporated into the proposed truss topology optimization model. The proposed computational model shows, through several numerical examples, the remarkable effect of including local buckling stability in the optimal design of trusses, while demonstrating that the optimized topology depends on whether the local buckling constraints are derived from the Euler buckling criterion or from actual structural design codes.

Necking limit analysis of thin wall aerosol can

Abstract Because of thin wall thicknesses and closed bottom ends of the extruded aerosol can, the necking limit analysis needs intensive investigation. The numerical analysis of the necking process of 0.45 mm thickness pure aluminum aerosol can was carried out. The result indicated that the length of the aerosol can wall, which is not fixed by the bottom die and the angle of inclination of necking tools are important factors that affect the development of deformation boundary limits due to plastic instability of local buckling. The fraction of taper angle of tool becomes more series parameter while necking at larger free length and it needs more concentration. Instead, the ratio of necking tool displacement to the total free length to initiate buckling was increased while increasing free length.

Topology optimization of truss structure considering nodal stability and local buckling stability

In order to obtain stable and realistic truss structures in practical applications, it is essential to include nodal and local buckling stability in truss topology optimization. There have been several approaches to address the challenges including nodal stability or local buckling stability. However, these approaches often lead to ill-conditioned optimization problems, such as convergence problems due to the concavity of the problem or high computational costs. In this study, two novel but conceptually simple methodologies, the nominal perturbing force (NPF) approach, and the allowable stress iteration (ASI) approach, are proposed to address nodal instability and local buckling instability problems in truss topology optimization, respectively. Initially, in the NPF approach, an infinite number of disturbing forces that a node may suffer are incorporated into the truss topology optimization problem in the form of nominal perturbing force conditions, whose magnitude and direction are discussed to capture the worst case. In the ASI approach, the allowable stress for each compressive bar is redefined in each iteration to ensure that the Euler critical buckling constraint is active. In this way, the concave local buckling instability problem is linearized in each iteration and can be solved efficiently by a linear programming solver. Finally, based on the finite element limit analysis (FELA) method, a truss topology optimization formulation incorporating the NPF and ASI approaches is proposed to solve the nodal stability and local buckling stability problems simultaneously. The proposed formulation is demonstrated through several numerical examples showing significant effects of including nodal stability and local buckling stability in the optimized designs, while at the same time demonstrating the validity and potential of the proposed approaches.