Mechanical Buckling Research Articles

Mechanical buckling of functionally graded polyethylene/clay nanocomposites columns based on the Engesser-Timoshenko beam theory

This paper deals with mechanical buckling of polyethylene/clay nanocomposite beams of functionally graded and uniformly distributed of nanoclay subjected to axial compressive load with simply supported conditions at both ends. The Young moduli of functionally graded and uniformly distributed nanocomposites are calculated using a genetic algorithm procedure and then compared with experimental results. The formulation is modified to include the effect of nanoparticles weight fractions in the calculation of the Young modulus for uniform distribution. Also, it is modified to take into account the Young modulus as a function of the thickness coordinate. The displacement field of the beam is assumed ba- sed on the Engesser-Timoshenko beam theory. Applying the Hamilton principle, governing equations are derived. The influence of nanoparticles on the buckling load of the beam is presented. To investigate the accuracy of the present analysis, a compression study with the experimental results is carried out.

Buckling Analysis of Embedded Nanosize FG Beams Based on a Refined Hyperbolic Shear Deformation Theory

In this study, the mechanical buckling response of refined hyperbolic shear deformable (FG) functionally graded nanobeams embedded in an elastic foundation is investigated based on the refined hyperbolic shear deformation theory. Material properties of the FG nanobeam change continuously in the thickness direction based on the power-law model. To capture small size effects, Eringen’s nonlocal elasticity theory is adopted. Employing Hamilton’s principle, the nonlocal governing equations of FG nanobeams embedded in the elastic foundation are obtained. To predict the buckling behavior of embedded FG nanobeams, the Navier-type analytical solution is applied to solve the governing equations. Numerical results demonstrate the influences of various parameters such as elastic foundation, power-law index, nonlocal parameter, and slenderness ratio on the critical buckling loads of size dependent FG nanobeams.

Metamaterials with relative displacements in their microstructure: technological challenges in 3D printing, experiments and numerical predictions

3D printing technology has opened application perspectives which were difficult to imagine only few years ago. In this paper, we show how it is possible to design and print some microstructures in which relative displacements are allowed at micro-level. Some structural elements have been built in the aforementioned structures which can be confidently modeled as perfect pivots or as soft elastic connections. The obtained specimens can be regarded as constituted by very exotic materials, as forecast theoretically. We numerically study the behavior of pantographic structures including soft or nearly perfect pivots in large deformations, and we experimentally observe an enlarged elastic range and peculiar buckling mechanisms. The presented results are extremely promising: We consider now as proven that higher gradient metamaterials can be realized by using microstructures having micro-characteristic lengths of the order on tenth of millimeters.

Mechanical buckling analysis of functionally graded power-based and carbon nanotubes-reinforced composite plates and curved panels

The main aim of this paper is to investigate the mechanical buckling behavior of functionally graded materials and carbon nanotubes-reinforced composite plates and curved panels. The governing equations are established using a double directors finite element shell model which induces a high-order distribution of the displacement field and takes into account the effect of transverse shear deformations. The effective material properties of functionally graded materials are estimated using a power law distribution and those of nanocomposites by an extended rule of mixture with some efficiency parameters. Uniform and four profiles of carbon nanotubes are considered to describe the distribution of these reinforcements through the thickness of the nanocomposite shell structure. A comparison study of the present results with those available in the literature is carried out for the isotropic case in order to prove the validity as well as the accuracy of the present model. Then, the results are extended to functionally graded materials and nanocomposites. The results reveal that the critical buckling load of plates and curved panels can be significantly increased as a result of a functionally graded reinforcement. They also show that the mechanical buckling behavior of such structures is significantly influenced by the plate aspect ratio, the length-to-thickness ratio, radius-to-thickness ratio, boundary conditions, power law index as well as the carbon nanotubes profiles and their volume fractions.

Axial buckling behavior of single-walled carbon nanotubes: Atomistic structural instability analysis

To reveal the atomistic scale mechanism of buckling of single-walled carbon nanotubes (SWCNTs) under axial compression, we carried out molecular dynamics (MD) simulation and atomistic structural instability (ASI) analysis. The ASI analysis enables us to reveal the development of ‘latent’ instability modes until buckling of structure, which cannot be clarified with MD alone. Euler-type buckling was found in relatively thin and long nanotube models, while buckling triggered by change of cross-sectional shape (i.e., radial buckling) was found in thick and short models. With growing radius, a crossover between the Euler-type and radial buckling modes was clearly found in the ASI analysis. Even when the deformation behavior was apparently the same, the buckling can be triggered by different instability modes. We also analyzed the structural instability using the Flügge theory based on linear continuum mechanics (LCM) to compare the results with the ASI analysis. Initial eigenvalues and development of instability modes were different between the ASI and LCM results, leading to a significant deviation of buckling strain and instability crossover points. We investigated the effect of chirality of CNT which is difficult to explain by LCM.

Resistance from agar medium impacts the helical growth of Arabidopsis primary roots.

Agar is widely used in studies of root growth since it can be mixed at different concentrations to impact mechanical impedance. At high concentrations (1.2-1.5%), growth of Arabidopsis roots has been found to be wavy, but little research has explored this behavior based on a quantitative understanding of mechanical behavior. To this end, agar media with concentration ranging from 0.5% to 1.2% were prepared to produce gradient resistance during root penetration, and Young's moduli and penetrometer resistance were tested. Arabidopsis roots were then cultivated in these agar media with gradient stiffness. The result showed that Young's modulus increased linearly with the increase of concentration of agar media. For Arabidopsis primary roots, it was preferred to develop a helical pattern in agar media with concentration from 0.5% to 1.0%. As stiffness of agar increased, the percentage of helical roots and helix diameters in each agar medium declined; root lengths and auxin distributions showed variety. We demonstrate that the size of helical deformation decreases with agar stiffness as expected by theoretical analysis based on a combination of growth-induced mechanical buckling. In conclusion, the resistance from agar media impacts the properties of root helix, and helical roots growth is driven by growth force. Growth force and external mechanical forces contribute to root phenotypes in Arabidopsis.

Probing buckling and post-buckling deformation of hollow amorphous carbon nanospheres: In-situ experiment and theoretical analysis

Amorphous carbon probably is the most-known and widely used carbon allotrope. However, unlike crystalline carbon such as graphene or carbon nanotubes, amorphous carbon generally is brittle and unable to sustain large mechanical deformation due to the inherent lack of long-rang order. In this work, we demonstrate a significant delay of failure on an amorphous carbon hollow nanosphere due to the buckling and post-buckling deformation of the spherical shell. Both in situ experiments and finite element analyses are conducted to probe deformation mechanism of buckling and post-buckling, suggesting a strong dependence of the shell thickness on the buckling process. A unified deformation energy-based mechanics model is developed to extract the critical buckling and post-buckling force, and shows good agreement with in situ experiments and finite element analyses. Extension of the model to inhomogeneous hollow nanospheres is also discussed and confirmed with finite element analyses.

The Internal Buckling Behavior Induced by Growth Self-restriction in Vertical Multi-walled Carbon Nanotube Arrays

ABSTRACTThe internal buckling is a common phenomenon in the as-grown carbon nanotube arrays. It makes the physical properties of carbon nanotube array in experiment lower than that in theory. In this work, we analyzed the formation and evolution mechanism of the internal buckling based on quasi-static compression model, which is different from collective effect of the van der Waals interactions. The self-restriction effect and the different growth rate of carbon nanotubes verify the possibility of the quasi-static compression model to explain the morphology evolution of vertical carbon nanotube arrays, especially the phenomenon of the quasi-straight and bent carbon nanotubes coexisted in the array. We generalized the Euler beam to wave-like beam and explained the mechanism of high-mode buckling combined with the van der Waals interaction. The calculated result about the link between compressive stress and strain confirms with the stage of collective buckling in the quasi-static compression test of carbon nanotube array. Preparation of well-organized carbon nanotube arrays was strong evidence verified the effect of self-restriction in experiment.

Avoiding/inducing dynamic buckling in a thermomechanically coupled plate: a local and global analysis of slow/fast response.

The nonlinear response of a reduced model of an orthotropic single-layered plate with thermomechanical coupling is investigated in the presence of thermal excitations, in addition to mechanical ones. Different issues are addressed via accurate and extended local and global analyses. (i) Assessing the possible occurrence, disappearance or modification of mechanical buckling as a result of thermal aspects; (ii) exploiting global dynamics to unveil the effects of coupling; (iii) highlighting the crucial role played by the slow thermal transient evolution in modifying the fast steady mechanical response; (iv) framing the influence of coupling and underlining the need to use a thermomechanical model to grasp the actual plate dynamics; and (v)getting hints of technical interest as to the outcome robustness with respect to variations in the external/internal thermal parameters.

Floating ice plate failure due to its thermal expansion at the surface

The problem of a floating ice sheet failure caused by stresses induced in ice by temperature changes at its top surface is investigated. The ice cover is modelled as a plate of uniform thickness, which is laterally constrained at its edges by rigid walls, and is assumed to deform, and ultimately fail, by the mechanism of creep buckling. The floating plate is subjected to in-plane compressive stresses developing in ice to prevent its lateral expansion due to heating, and is transversely (vertically) bent by the forces acting at its base and caused by the reaction of underlying water. The sea ice is treated as a material whose elastic and viscous properties depend on its porosity and current temperature, and therefore vary with the depth of ice. The results of simulations, carried out for a variety of ice plate spans, thicknesses and temperature-change scenarios, illustrate the evolution of creep buckles in the plate prior to its failure, and show the time variation of the magnitudes of forces exerted by ice on the constraining walls.

Room‐Temperature Carbon Nanotube Single‐Electron Transistors with Mechanical Buckling–Defined Quantum Dots

AbstractSingle‐electron transistors (SETs) have been proposed as a future alternative to conventional Si‐based electronics. However, their practical applications are strongly limited because most SETs operate at cryogenic temperatures. In this work, room temperature operating SETs are successfully fabricated with the realization of a mechanical buckling–defined quantum dot within a suspended and strained single‐walled carbon nanotube. Clear Coulomb oscillations are observed at room temperature due to the Coulomb blockade effect. The Coulomb charging energy is calculated to be 160 meV, which substantially exceeds the thermal energy. At 10 K, the Coulomb staircases are observed in the current–voltage characteristics with an energy level separation ≈29 meV, confirming that the island behaves as a well‐defined quantum dot for the electrons. This device fabrication method may also help future investigations into the electromechanical properties of nanotube quantum systems.

Stability analysis of steel compression members under shock loads

This paper presents the results of a numerical analysis of the elastic-plastic behaviour of steel compression members subjected to compression with a permanent pre-deformation in the longitudinal axis by a longitudinal indispensable shock load. A differential load intensity was considered up to the loss of stability. A finite difference method was applied, with an explicit integration schema for the time of the dynamic stability equations. It was assumed that the precursor to the unstable behaviour of a steel compression member was a continuous deformation of the rod axis, which was defined according to current industry-standard design procedures. Cases of flexible and stiff rods, varying in slenderness, were considered. It was demonstrated that a significant load on the performance of the steel compression members and their buckling mechanisms is attributable to longitudinal wave effects. These longitudinal wave effects cause high-frequency changes in the axial forces with a significant stress concentration due to the effect of reflection from a pinned support. This is critical for the dissipation of internal energy by plastic deformation. The applied research method facilitated an estimation of the dynamic critical forces and their relationships with static values. Keywords: steel rods with pre-deformation of axis, elastic-plastic behaviour, dynamic stability of rods, differential approximation, effects of axial wave response

Mechanical and thermal buckling of exponentially graded sandwich plates

ABSTRACTThis article presents an analytical solution for the mechanical and thermal buckling of exponentially graded material (EGM) sandwich plates. The solution is obtained using a four-variable refined plate theory. Two types of sandwich plates are investigated: one with EGM face sheets and homogeneous core; the other with EGM core and homogeneous face sheets. The governing equations are derived based on the principle of virtual work and then solved through Navier method. The results on critical buckling load and temperature change of simply supported EGM sandwich plates are obtained. The influences of several parameters on buckling behaviors are discussed.

Investigation on Application of Semiloof Shell Element for Isotropic, Composite and Functionally Graded Material

In this research article, semiloof shell element was used to study the behaviour of plate and shells under mechanical and thermal load for stress, free vibration, initially stressed vibration, mechanical buckling, and non-linear vibration. In the above cases, the material properties: Isotropic, Composite and Functionally Graded Material (FGM) were considered. Wherein, the material property for the FGM shells was assumed to vary through the thickness of the shell by varying the volume fraction of the constituent, whereas, for composites, classical laminated theory was used. Utilizing the semiloof shell element, and the above material properties, the package COMSAP was developed. From the obtained results, we have observed that with coarse meshes, semiloof shell elements present better results, and it is especially effective in the case of thin plates and shells.

Bending of boron nitride nanotubes: An atomistic study

ABSTRACTThe present work investigates through molecular dynamics finite element method with Tersoff potential the buckling behavior of boron nitride (BN) armchair and zigzag nanotubes under bending. The critical bending buckling angle, moment, and curvature are studied and discussed with respect to the tube length-diameter ratios from 10 to 50. Effects of a Stone-Wales defect in the middle tube on the bending behavior are also examined. The bending buckling mechanism is governed by the local instabilities and bond breaking in the compressive zone of the tubes. Results are useful for the design of nanocomposites and nano-devices with BN nanotubes.

Self-organizing periodicity in development: organ positioning in plants.

Periodic patterns during development often occur spontaneously through a process of self-organization. While reaction-diffusion mechanisms are often invoked, other types of mechanisms that involve cell-cell interactions and mechanical buckling have also been identified. Phyllotaxis, or the positioning of plant organs, has emerged as an excellent model system to study the self-organization of periodic patterns. At the macro scale, the regular spacing of organs on the growing plant shoot gives rise to the typical spiral and whorled arrangements of plant organs found in nature. In turn, this spacing relies on complex patterns of cell polarity that involve feedback between a signaling molecule - the plant hormone auxin - and its polar, cell-to-cell transport. Here, we review recent progress in understanding phyllotaxis and plant cell polarity and highlight the development of new tools that can help address the remaining gaps in our understanding.

Morphable 3D mesostructures and microelectronic devices by multistable buckling mechanics.

Three-dimensional (3D) structures capable of reversible transformations in their geometrical layouts have important applications across a broad range of areas. Most morphable 3D systems rely on concepts inspired by origami/kirigami or techniques of 3D printing with responsive materials. The development of schemes that can simultaneously apply across a wide range of size scales and with classes of advanced materials found in state-of-the-art microsystem technologies remains challenging. Here, we introduce a set of concepts for morphable 3D mesostructures in diverse materials and fully formed planar devices spanning length scales from micrometers to millimeters. The approaches rely on elastomer platforms deformed in different time sequences to elastically alter the 3D geometries of supported mesostructures via non-linear mechanical buckling. Over 20 examples have been experimentally and theoretically investigated, including mesostructures that can be reshaped between different geometries as well as those that can morph into three or more distinct states. An adaptive radio frequency circuit and a concealable electromagnetic device provide examples of functionally reconfigurable microelectronic devices.

Thermal buckling analysis of stiffened FGM truncated conical shells resting on elastic foundations using FSDT

This work presents an analytical approach to investigate the mechanical and thermal buckling of functionally graded material truncated conical shells resting on Pasternak elastic foundations, subjected to thermal load and axial compressive load. The shells are reinforced by closely spaced stringers and rings. The change in spacing between the stringers in the meridional direction is also taken into account. Two cases on uniform temperature rise and linear temperature distribution through the thickness of the shell are considered. Using the first-order shear deformation theory, Lekhnitskii smeared stiffener technique and the adjacent equilibrium criterion, the linearization stability equations are established. An approximate solution satisfies simply supported boundary conditions, and the Galerkin method is applied to obtain a closed-form expression for determining the critical compression buckling load and thermal buckling load in cases of uniform temperature rise and linear temperature distribution across the shell thickness. The effects of temperature, foundation, stiffeners, material properties, dimensional parameters and semi-vertex angle on the buckling behaviors of shell are shown.

Strain control of oxygen kinetics in the Ruddlesden-Popper oxide La1.85Sr0.15CuO4

Oxygen defect control has long been considered an important route to functionalizing complex oxide films. However, the nature of oxygen defects in thin films is often not investigated beyond basic redox chemistry. One of the model examples for oxygen-defect studies is the layered Ruddlesden–Popper phase La2−xSrxCuO4−δ (LSCO), in which the superconducting transition temperature is highly sensitive to epitaxial strain. However, previous observations of strain-superconductivity coupling in LSCO thin films were mainly understood in terms of elastic contributions to mechanical buckling, with minimal consideration of kinetic or thermodynamic factors. Here, we report that the oxygen nonstoichiometry commonly reported for strained cuprates is mediated by the strain-modified surface exchange kinetics, rather than reduced thermodynamic oxygen formation energies. Remarkably, tensile-strained LSCO shows nearly an order of magnitude faster oxygen exchange rate than a compressively strained film, providing a strategy for developing high-performance energy materials.

Capillary flow and mechanical buckling in a growing annular bacterial colony.

A growing bacterial colony is a dense suspension of an increasing number of cells capable of individual as well as collective motion. After inoculating Pseudomonas aeruginosa over an annular area on an agar plate, we observe the growth and spread of the bacterial population, and model the process by considering the physical effects that account for the features observed. Over a course of 10-12 hours, the majority of bacteria migrate to and accumulate at the edges. We model the capillary flow induced by imbalanced evaporation flux as the cause for the accumulation, much like the well-known coffee stain phenomenon. Simultaneously, periodic buckles or protrusions occur at the inner edge. These buckles indicate that the crowding bacteria produce a jam, transforming the densely packed population at the inner edge to a solid state. The continued bacterial growth produces buckles. Subsequently, a ring of packed bacteria behind the inner edge detach from it and break into pieces, forming bacterial droplets. These droplets slowly coalesce while they continually grow and collectively surf on the agar surface in the region where the colony had previously spread over. Our study shows a clear example of how fluid dynamics and elasto-mechanics together govern the bacterial colony pattern evolution.