Buckling Model Research Articles

Multiple-generation folding and non-coaxial strain of lava crusts

Viscoelastic strain in lava flows is commonly expressed as gravity-driven buckling of the lava crust. This surface folding process creates the well-known ropy pāhoehoe texture of basaltic lavas and the ogives and surface ridges of more compositionally evolved lava flows. Previous work has shown that surface fold wavelengths are proportional to the viscosity contrast between the lava crust and core, and to the thickness of the crust. Thus, fold analysis can be an important tool for understanding lava flow rheology. We analyze fold wavelength patterns of solidified natural lava flows from the Myvatn lava fields (Iceland), Piton de La Fournaise (La Reunion), and experimental lava flows from the Syracuse University Lava Project. In each case, lava flows exhibited two dominant wavelengths, consistent with multiple generations of coaxial folding. The ratio of the two dominant wavelengths for basalt (Iceland, La Reunion) is ~ 5:1 whereas the wavelength ratio for basaltic andesite (Syracuse) is ~ 3:1, suggesting a compositional control on deformation, as proposed by previous studies. Video analysis of incrementally folded Syracuse lava crusts reveals significant non-coaxial strain, which violates the assumptions of plane strain used in crustal buckling models. These results show that interpreting lava rheology from finite strain requires careful consideration of complex three-dimensional strain fields. Despite these complexities, the correlation between fold wavelength ratios and lava flow composition persists and may provide important insight into flow characterization.

A refined model for local buckling of rectangular CFST columns with binding bars

This paper presents a refined model for local buckling of rectangular concrete-filled steel tubular (CFST) columns with binding bars under axial compression due to a deficiency in the previous model i.e. the influences of horizontal spacing and diameter of binding bars were not considered. The influences of longitudinal spacing, horizontal spacing and diameter of binding bars on the critical local buckling stress can be reasonably considered in the proposed model, which is applicable to both elasto-plastic phase and elastic phase. The refined model is verified against the experimental results, showing better agreement than the previous model. Then, the proposed model is employed to investigate the influences of longitudinal spacing, horizontal spacing, diameter of binding bars and cross-sectional aspect ratios on the critical local buckling stress. It is found that the critical local buckling stress increases considerably with the decrease of the spacing of binding bars. Furthermore, the influence of longitudinal spacing of binding bars on the critical local buckling stress is more significant than that of horizontal spacing. It is also found that the critical local buckling stress increase modestly with the increase of diameter of binding bars in the case of small spacing of binding bars. In addition, the cross-sectional aspect ratio have little influence on the critical local buckling stress, which can be ignored. Aiming at delaying the occurrence of local buckling of steel plates in rectangular CFST columns with binding bars, it is suggested that decreasing longitudinal spacing as an efficient measure has priority over other measures.

Mechanical responses of titanium 3D kagome lattice structure manufactured by selective laser melting

Three dimensional (3D) kagome lattice structure incorporates excellent mechanical and actuation performances. Thus, here, 3D kagome lattice structures were fabricated by selective laser melting with titanium alloy. The mechanical responses under compression and three point bending were experimentally tested and compared with the theoretical predictions. With the increased relative density from 2.8% to 5.5% and 9.1%, the average compressive strength significantly enlarges from 2.0 MPa to 8.0 and 17.5 MPa, and the average bending load capacity increases from 260.0 N to 850.0 and 1750.0 N. We reveal that different from other lattice structures which usually present sole buckling or fracture failure, kagome lattice structure exclusively presents mixed failure model of both buckling and fracture. The buckling failure always arises first, and follows by the subsequent fracture. Thus, the experimental strength and load capacity are close to but a little higher than the theoretical predictions under buckling. Moreover, critical relative densities between the buckling and fracture failure models are analytically established. It is revealed that in order to significantly raise the strength and load capacity, the failure model should be respectively designed as fracture and buckling corresponding to the condition that the relative densities are respectively lower and higher than the critical relative densities. The results obtained here provide potential application of the lightweight structures for aerospace, civil and transportation engineering.

Buckling of cylindrical stainless-steel tubes subjected to external pressure at extremely high temperatures

Abstract This study aims to experimentally investigate the buckling behaviors of stainless steel cylindrical tubes subjected to external pressure at extremely high temperatures. Buckling experiments were conducted on specimens of two different buckling modes for a wide range of pressures, specifically, from 200 to 1000 kPa in gauge pressure. The buckling temperature was measured as a function of the external pressure to examine the relationship between the buckling temperature and the external pressure. Moreover, the effect of the tube dimension (radius-to-thickness ratio) on the buckling temperature was investigated for a wide range of radius-to-thickness ratios, specifically, from 10 to 56. The buckling temperature was proportional to the external pressure and to the radius-to-thickness ratio. The measured buckling temperatures were compared with the theoretical predictions obtained from several conventional buckling models. The difference in the buckling temperatures between the experimental results and the theoretical predictions was discussed by considering the creep effect, geometrical imperfections, and a temperature dependent material property. Additionally, the buckling deformation of the stainless steel tube columns was recorded with a high-speed camera.

Thermal-induced upheaval buckling of concrete pavements incorporating the effects of temperature gradient

Thermal upheaval buckling of continuously reinforced concrete pavements is widely reported around the world in conjunction with the evolution of global warming trends and increasing numbers of prolonged heatwaves, and which may lead to catastrophic scenarios. Such heatwaves may produce a large temperature gradient through the thickness of the pavement, and there is a need to examine the effects of a temperature gradient on pavement buckling. This paper proposes an analytical closed-form model for the thermal upheaval buckling of pavements, with a temperature gradient being embedded in the formulation. The principle of stationary total potential is employed to develop the non-linear equations of equilibrium for the postbuckling response of the pavement, and these equations are solved analytically by considering both the lift-off region and the adjoining region. It is found that the temperature gradient has no influence on a continuous lengthwise-symmetric pavement, so two pavement types are analysed in this investigation, one is a continuous pavement with a joint and the other is a continuous pavement adjoining a rigid structure. The paper demonstrates that a positive temperature gradient will lower the safe temperature of a concrete pavement with a joint, while it raises the safe temperature of a pavement adjoining a rigid structure. The buckling and postbuckling responses of pavements with different characteristics are analysed by considering the temperature gradient; the parameters being the pavement thickness, pavement base and effective weight.

A simplified flange–lip model for distortional buckling of cold-formed steel channel-sections with stiffened web

This paper presents a simplified analytical model for determining the critical stress of distortional buckling of lipped channel-sections with stiffened web made from cold-form steel (CFS). Lipped channel-section with stiffened web have been shown to have a distinct advantage in resisting local buckling and are associated with the higher distortional buckling stress, when compared to the channel-section without stiffeners. It is widely used as a substitution for standard channel-section in cold form steel construction applications. In the current work, CFS channel-sections with stiffened web are investigated based on the flange–lip model. In order to determine the stiffness of rotational springs representing the restraining effect of the web to the flange–lip system, the web with different type of stiffeners is modeled as an orthopedic plate. Using the total potential energy principle, the formula for calculating the local buckling stress of the stiffened web considering loading scenarios including a pure compression and a pure bending moment are derived. The stiffness of rotational spring can be obtained. Finally, the prediction of distortional buckling critical stress of lipped channel-section with different type of stiffened webs is carried out, which is shown to be in good agreement with those calculated by the finite strip method (FSM).

Model analysis of feedstock behavior in fused filament fabrication: Enabling rapid materials screening

This research presents a rapid screening process for analyzing the extrudability of polymeric materials for filament extrusion based additive manufacturing (AM) by predicting extrusion failure. This rapid screening process can further suggest optimal Fused Filament Fabrication (FFF) processing conditions for a specific material. Annular backflow and filament buckling, which are the two primary failure modes during extrusion in FFF, are considered in this study. The screening method focuses on model analysis of annular backflow while simultaneously considering a previously developed model for filament buckling and includes the introduction of a non-dimensional number (Flow Identification Number, or FIN) that predicts a material's propensity to backflow based on a rheological analysis and the system geometry. Annular backflow was modeled by calculating velocity profiles and determining the normalized net flow magnitude. The backflow and buckling models were experimentally verified with acrylonitrile butadiene styrene, low density polyethylene, and sodium sulfonated poly(ethylene) glycol. We empirically validated that the FIN was able to accurately predict backflow and that the potential to backflow and, by extension, propensity to fail during extrusion, is most sensitive to fluctuations in filament diameter and the material's shear thinning behavior. Our results demonstrate the importance of printing in the shear thinning regime to reduce the effect of processing conditions on the extrudability of a polymer.

Nonlocal strain gradient shell model for axial buckling and postbuckling analysis of magneto-electro-elastic composite nanoshells

Abstract The present study deals with the size-dependent nonlinear buckling and postbuckling characteristics of magneto-electro-elastic cylindrical composite nanoshells incorporating simultaneously the both of hardening-stiffness and softening-stiffness size effects. To accomplish this purpose, the nonlocal strain gradient elasticity theory is applied to the classical shell theory. Via the virtual work's principle, the size-dependent governing differential equations are constructed including the coupling terms between the axial mechanical compressive load, external magnetic potential and external electrical potential. The nonlinear prebuckling deformations and the large postbuckling deflections are taken into consideration based upon the boundary layer theory of shell buckling. Finally, an improved perturbation technique is employed to achieve explicit analytical expressions for nonlocal strain gradient stability curves of magneto-electro-elastic nanoshells under various surface electric and magnetic voltages. It is seen that a positive electric potential and a negative magnetic potential cause to increase both of the nonlocality and strain gradient size dependencies in the nonlinear instability behavior of axially loaded magneto-electro-elastic composite nanoshells, while a negative electric potential and a positive magnetic potential play an opposite role.

Hencky bar-net model for plate buckling

This paper presents the Hencky bar-net model (HBM) for elastic buckling analysis of rectangular plates with any combination of edge conditions. HBM comprises a grid (or net) of rigid bar segments joined by rotational springs as well as a torsional spring system in each grid panel. The HBM is developed from the finite difference plate model that allows researchers to perform plate buckling analysis via solving a set of algebraic equations instead of solving a fourth order partial differential equation. The elastic spring stiffnesses for the HBM that provides the flexibility for deformation are established for the first time for elastic rotationally restrained edges and free edges. Some plate buckling problems were solved by using the developed HBM and the solutions shown to converge to those of the continuum plate counterparts when the grid size becomes very small; thereby verifying the validity of the model.

Nonlinear buckling analysis of magneto-electro-elastic CNT-MT hybrid nanoshells based on the nonlocal continuum mechanics

This study presents a size-dependent continuum model for the nonlinear buckling of magneto-electro-elastic (MEE) hybrid nanoshells in thermal environment. The nanocomposite cylindrical shell is composed of a carbon nanotube (CNT), a microtubule (MT) and a MEE nanoscale layer which are coupled by polymer or filament matrix. The hybrid nanostructure is subjected to thermo-electro-magnetic loads. The small scale effect is taken into consideration based on the nonlocal elasticity theory. The Pasternak model is used to simulate the normal and shear behavior of the coupling elastic medium. Using the principle of virtual work and von Karman’s strain-displacement relations, the nonlinear governing differential equations are derived. The non-dimensional postbuckling loads of the hybrid nanoshells are obtained using the Galerkin’s approach. The validity of the present model and method of solution is verified by comparing the results with available experimental data and the molecular dynamics simulation results from the literature. It is found that the nonlinear buckling loads of MEE hybrid nanoshells are strongly sensitive to the small scale coefficient. In addition, the non-dimensional buckling loads decrease with increasing the external electric voltage, while the applied magnetic potential has an increasing effects on the critical buckling loads.

Analytical buckling model for slender FRP-reinforced concrete columns

Research is limited with respect to load-deflection behavior of slender concrete columns internally reinforced with Fiber Reinforced Polymer (FRP) spirals and longitudinal bars. An analytical buckling model based on numerical integration is presented to predict the load versus deflection performance of slender concrete columns reinforced with FRP spirals and longitudinal bars, subjected to eccentric loads. The model can be used to predict the behavior of slender concrete columns with various configurations including FRP and/or steel reinforcement, single or double spiral, and number of longitudinal bars. The longitudinal bars considered include steel, FRP, or hybrid reinforcement consisting of steel and FRP bars. The model is found to predict the experimental performance of slender concrete columns reinforced with Glass FRP longitudinal bars and spirals with satisfactory accuracy. The model is used to create interaction diagrams for FRP spiral-confined circular concrete columns with various slenderness ratios, reinforced with steel, FRP or hybrid reinforcement.

Failure of flight feathers under uniaxial compression

Flight feathers are light weight engineering structures. They have a central shaft divided in two parts: the calamus and the rachis. The rachis is a thinly walled conical shell filled with foam, while the calamus is a hollow tube-like structure. Due to the fact that bending loads are produced during birds' flight, the resistance to bending of feathers has been reported in different studies. However, the analysis of bent feathers has shown that compression could induce failure by buckling. Here, we have studied the compression of feathers in order to assess the failure mechanisms involved. Axial compression tests were carried out on the rachis and the calamus of dove and pelican feathers. The failure mechanisms and folding structures that resulted from the compression tests were observed from images obtained by scanning electron microscopy (SEM). The rachis and calamus fail due to structural instability. In the case of the calamus, this instability leads to a progressive folding process. In contrast, the rachis undergoes a typical Euler column-type buckling failure. The study of failed specimens showed that delamination buckling, cell collapse and cell densification are the primary failure mechanisms of the rachis structure. The role of the foam is also discussed with regard to the mechanical response of the samples and the energy dissipated during the compression tests. Critical stress values were calculated using delamination buckling models and were found to be in very good agreement with the experimental values measured. Failure analysis and mechanical testing have confirmed that flight feathers are complex thin walled structures with mechanical adaptations that allow them to fulfil their functions.

Distortional buckling of perforated cold-formed steel channel-section beams with circular holes in web

This paper presents the numerical and analytical investigations on the distortional buckling of perforated cold-formed steel channel-section beams with circular holes in web. The numerical investigation involves the use of finite element methods. In the analytical analysis the distortional buckling model recommended in EN1993-1-3 is employed. The influence of the web holes on the distortional buckling behaviour and corresponding critical stress and moment of perforated cold-formed steel channel-section beams are discussed. Finally, a simple analytical formulation is proposed for evaluating the effect of hole size on the reduction of critical stress and critical moment of the channel-section beams with circular holes in web.

An analytical investigation on the wrinkling of aluminium alloys during stamping using macro-scale structural tooling surfaces

Structural surface texturing is believed to be a promising approach to modify tribological and thermal performances of tooling for sheet-stamping processes. However, a fundamental study on the surface-texturing design and resulting material deformation is currently lacking. In this paper, an advanced analytical buckling model specifically for the utilisation of textured tools at macro-scale, comprising dislocation-driven material model, isotropic yield criteria, bifurcation theory and Donnell-Mushtari-Vlasov (DMV) shell structure theory, was established. The developed analytical buckling model was validated by cylindrical deep-drawing experiments. Further finite element (FE) simulations with the implementation of material model via user-defined subroutine were also used to validate the bucking model for large surface texture designs. Effects of theoretical assumptions, such as yield criterion, boundary condition and test-piece geometry, on the accuracy of model prediction for wrinkling were investigated. It was found that the von Mises yield criterion and hinged boundary condition exhibited more accurate predictions. In addition, the DMV shell theory made this model most representative for large structural texturing designs. Furthermore, the implementation of induced shear strain component has an important effect on precisely predicting the wrinkling occurrence. The advanced analytical models developed in this study combine various classical mechanics, structure stability and material modelling together, which provides a useful tool for tooling engineers to analyse structural designs.

Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory

Abstract This paper presents a finite element model based on the first-order shear deformation theory for free vibration and buckling of functionally graded beams. The present element has five nodes and ten degrees-of-freedom. Material properties vary continuously through the beam thickness according to the power-law form. Governing equations are derived with the aid of Lagrange's equations. Natural frequencies and buckling loads are calculated numerically for different end conditions, power-law indices, and span-to-depth ratios. Accuracy of the present element is demonstrated by comparisons with the available results.

An Analytical and Numerical Investigation on Flange Wrinkling Behavior in Warm Forming Process of AA5754 Using Macro-Textured Tool Design

In this paper, an analytical buckling model is established to predict the flange wrinkling behavior of deep drawn cylindrical cups of aluminium alloy sheet in warm forming conditions using macro-textured blankholders for the first time. A continuum damage mechanism (CDM) based material model was utilized to reflect the visco-plastic feature of material at elevated temperatures. Forming speed and temperature effects were investigated, and texture ratio and draw ratio effects were also discussed. The developed analytical buckling model was validated by finite element simulations. The increase of forming temperature and forming speed is prone to cause wrinkling for AA5754, but the effects are not as significant as the texture geometry and draw ratio. The analytical model presented in this paper can be used as a design guide to determine tool texture geometry necessary to avoid wrinkling defects in the warm forming processes of aluminium alloy.

Out-of-Plane Buckling of Ductile Reinforced Structural Walls due to In-Plane Loads

AbstractReinforced structural walls are often implemented as a lateral force resisting system in multistory buildings, designed to deform elastically under wind loads and form plastic hinges at their base under seismic excitation. Past research suggests plastic tensile demands and subsequent load reversals can cause a plastic, localized lateral instability in walls. Although lateral stability is addressed by some building codes, plastic buckling is rarely directly addressed. In 2010 and 2011, New Zealand experienced earthquakes that damaged many structural wall buildings, and plastic buckling was observed. This paper re-examines two existing local buckling models using a range of data sources. A review of prior experimental work assesses the models’ accuracy at predicting plastic buckling capacities. A parametric study on a range of walls examines the variables most influential to affect plastic buckling capacities. Additionally, three nonlinear time history analyses of buildings subjected to the 2010 and...

The Effects of Boundary Conditions and Friction on the Helical Buckling of Coiled Tubing in an Inclined Wellbore.

Analytical buckling models are important for down-hole operations to ensure the structural integrity of the drill string. A literature survey shows that most published analytical buckling models do not address the effects of inclination angle, boundary conditions or friction. The objective of this paper is to study the effects of boundary conditions, friction and angular inclination on the helical buckling of coiled tubing in an inclined wellbore. In this paper, a new theoretical model is established to describe the buckling behavior of coiled tubing. The buckling equations are derived by applying the principles of virtual work and minimum potential energy. The proper solution for the post-buckling configuration is determined based on geometric and natural boundary conditions. The effects of angular inclination and boundary conditions on the helical buckling of coiled tubing are considered. Many significant conclusions are obtained from this study. When the dimensionless length of the coiled tubing is greater than 40, the effects of the boundary conditions can be ignored. The critical load required for helical buckling increases as the angle of inclination and the friction coefficient increase. The post-buckling behavior of coiled tubing in different configurations and for different axial loads is determined using the proposed analytical method. Practical examples are provided that illustrate the influence of the angular inclination on the axial force. The rate of change of the axial force decreases with increasing angular inclination. Moreover, the total axial friction also decreases with an increasing inclination angle. These results will help researchers to better understand helical buckling in coiled tubing. Using this knowledge, measures can be taken to prevent buckling in coiled tubing during down-hole operations.

On boundary conditions for buckling and vibration of nonlocal beams

In this paper, we argue that the boundary conditions for Eringen's nonlocal beam theory have to take on the discrete forms similar to those for the first order central finite difference beam model for beam buckling and vibration problems. The latter finite difference beam model has been found to be analogous to the physical Hencky bar-chain and therefore these two models can be regarded as one discrete beam model. Based on the phenomenological similarities between this discrete beam model and the Eringen's nonlocal beam theory, one may calibrate the Eringen's small length scale coefficient e0 which is expected to be a constant appropriate to each material. When using the classical continuous nonlocal boundary conditions, we find that e0 is not a constant but it depends on the cases of boundary conditions (such as pinned-pinned, clamped-clamped, clamped-pinned ends). However, this conundrum may be resolved if we use the discrete boundary conditions instead. By adopting the discrete boundary conditions, analytical solutions for e0 may be obtained and the e0 values finally converge to 0.289 for buckling problems and 0.408 for free vibration problems regardless of the cases of boundary conditions.

Abrupt out-of-plane edge folding of a circular thin plate: Implication for a mature Victoria regia leaf.

Inspired by the observation of the configurations of Victoria regia leaves, we establish a phenomenological buckling model for the abrupt out-of-plane edge folding of a circular thin sheet. A reduced model is first developed, and further refined by a more sophisticated growth strain field so that the resulting buckling morphology resembles that of a mature Victoria regia leaf. Parametric studies are carried out to investigate the effects of geometric, material, and strain field parameters on the buckling morphology. Several main characteristics discovered through numerical studies are verified by theoretical analysis of a simple geometry-based model. Besides, the roles of the thickness variation and cracks are examined. This work may not only shed some light on the morphogenesis of certain plants, but also provide some useful insights on three-dimensional fabrications using mechanical self-assembly.