Buckled Shape Research Articles

Ultrasensitive Ultrasoft Buckled Crack‐Based Sensor for Respiration Measurement and Enhanced Human–Machine Interface

Wearable strain sensors have transformed the real‐time monitoring of health conditions and human–machine interactions. However, recently developed wearable strain sensors exhibit several limitations. For example, when a sensor is designed with high sensitivity to detect strain, it struggles to accurately measuring the deformation of low‐stiffness materials like skin. Additionally, finding the optimal balance between sensitivity, durability, hysteresis, and strain range in sensor design is challenging. To address these challenges, a Buckled, Ultrasoft, Crack‐based, Large strain, EpiDermal (BUCKLED) sensor is developed. This sensor integrates the benefits of soft structure engineering with high sensitivity of crack‐based sensing mechanisms to ensure optimal skin deformation measurements. The BUCKLED sensor exhibits significant improvements in compliance (18 500 mm N−1), stretchability (100%), hysteresis (2%), durability (10 000 cycles with 100% strain), and force sensitivity () owing to its buckled shape, confirming its ability to detect subtle movements with enhanced accuracy. The sensor's high compliance allows it to accurately measure low‐stiffness objects, ensuring reliable performance. Furthermore, the sensor's tunability is demonstrating its effectiveness in applications such as respiratory monitoring, facial expression recognition, and silent speech interfaces. Consequently, the proposed sensor is versatile and holds great potential for a wide range of sensing applications.

On the mechanical, thermoelectric, and excitonic properties of Tetragraphene monolayer

Two-dimensional carbon allotropes have attracted much attention due to their extraordinary optoelectronic and mechanical properties, which can be exploited for energy conversion and storage applications. In this work, we use density functional theory simulations and semi-empirical methods to investigate the mechanical, thermoelectric, and excitonic properties of Tetrahexcarbon (also known as Tetragraphene). This quasi-2D carbon allotrope exhibits a combination of squared and hexagonal rings in a buckled shape. Our findings reveal that tetragraphene is a semiconductor material with a direct electronic bandgap of 2.66eV. Despite the direct nature of the electronic band structure, this material has an indirect exciton ground state of 2.30eV, which results in an exciton binding energy of 0.36eV. At ambient temperature, we obtain that the lattice thermal conductivity (κL) for tetragraphene is approximately 118 W/mK. Young’s modulus and the shear modulus of tetragraphene are almost isotropic, with maximum values of 286.0N/m and 133.7N/m, respectively, while exhibiting a very low anisotropic Poisson ratio value of 0.09.

Post-Buckling Analysis of E-Glass Fiber Reinforced Thin-Walled Cylindrical Composite

Post buckling analysis of E-glass fiber reinforced cylindrical composite under axial compression using both experimental and numerical method is presented. Using the Eigen value buckling analysis, the studies employ a mixture ratio of E-glass fiber composite of chopped strand mat. Five molds of each E-glass fiber mixture were reinforced with polyester resin to produce cylindrical shells of equal dimensions. Various cylindrical specimens’ predicted critical buckling load were tested and recorded using a compressive loading machine. Comparisons were made to ascertain the cylindrical shells buckling and post buckling behavior at certain load levels between the experimental and analytical results. A one-way Anova was used to compare the outcome of the theoretical, experimental and numerical methods of analysis and the result showed that there is no evidence to suggest difference between the three methods applied in the buckling load analysis. The post buckled shapes of the samples were obtained and recorded as bulge diamond shape of a buckled cylindrical structure. The effective mechanical properties of the chopped strand mat (CSM) reinforced composite cylinder were recorded from the experiment which has modulus of Elasticity 197.707 N/mm2, Poisson’s ratio of 0.22 and density of 1250 Kg/m3.

Spectral analysis for elastica dynamics in a shear flow

We present the spectral analysis of three-dimensional dynamics of an elastic filament in a shear flow of a viscous fluid at a low Reynolds number in the absence of Brownian motion. The elastica model is used. The fiber initially is almost straight at an arbitrary orientation, with small perpendicular perturbations in the shear plane and out-of-plane. To analyze the stability of both perturbations, equations for the eigenvalues and eigenfunctions are derived and solved by the Chebyshev spectral collocation method. It is shown that their crucial features are the same as in the case of the two-dimensional elastica dynamics in shear flow [Becker and Shelley, ] and the three-dimensional elastica dynamics in the compressional flow [Chakrabarti , ]. We find a similar dependence of the buckled shapes on the ratio of bending to hydrodynamic forces as in the simulations for elastic fibers of a nonzero thickness [Słowicka , ]. Published by the American Physical Society 2024

The compression-only behavior of coated microbubbles in a wall restricted flow.

The impact that the onset of the compression-only behavior of lipid shelled contrast agents bears on their dynamic interaction with a rigid wall under acoustic disturbances is investigated numerically in the context of axisymmetry. Wall presence is seen to not significantly affect the onset of compression-only since it only reduces the time frame required to trigger the effect. The standoff distance from the wall bears no significant effect on the amplitude threshold except that as it is reduced, it favors asymmetry by altering the compressed buckled shape around which the bubble oscillates. Above the amplitude threshold for parametric shape mode excitation, the onset of compression-only in the vicinity of a rigid wall typically interrupts the process of entrapment by reversing the direction of motion via the positive pressure drug that is generated as a result of the emerging concave upwards buckled shapes. Below this amplitude threshold, symmetric shapes or asymmetric shapes that are concave downwards continue to translate towards the wall where they perform saturated trapped pulsations around nearly spherical flattened or concave downwards buckled shapes. The latter shapes perform compression-only type pulsations and arise on the longer time scale required for the destabilization of the nearly spherical initially trapped shapes. Phase diagrams are constructed identifying regions of trapped pulsations, compression-only response, and microbubble collapse, in the parameter space defined by sound amplitude and shell viscoelastic properties.

2d Models of Steel Beams under Patch Loading for Buckling Coefficient Assessment

This paper proposes an equivalent 2d model incorporating translational and rotational springs to simulate constraints in the stability analysis of steel plates under in-plane patch loading. The main objective is to develop an equivalent stability analysis of these plates by accurately calibrating the level of constraint provided by the stiffeners and flanges. The calibration involves determining the spring constants of a 2d equivalent plate model to achieve the same linear elastic critical load and buckled shape as a 3d model. The paper uses the buckling coefficient as the objective function to calibrate the translational and rotational springs. The ultimate goal is to effectively replicate the constraint conditions imposed by the flanges and vertical stiffeners within the structure. The proposed simplified method yields results that closely align with those obtained from the original 3d model, incorporating finite-rigidity restraints.

Isolated disclination in an orthotropic von Kármán elastic plate

We investigate geometry and mechanics of the buckled orthotropic von Kármán elastic plate, with free boundary condition, in the presence of an isolated positive, or negative, disclination. The buckled shape of an isotropic elastic plate is cone-like for a positive disclination and saddle-like for a negative disclination. In either case, with increasing orthotropy, the shape of the buckled plate becomes more tent-like. The Gaussian curvature accordingly spreads along the ridge of the tent. The stress fields too remain focused in the neighbourhood of the defect point and the ridge, indicating that most of the stretching energy is accommodated in these singular regions.

Machine learning‐based predictions of buckling behaviour of cold‐formed steel structural elements

AbstractDesigning thin‐walled structural members is a complex process due to the possibility of multiple instabilities. This study aimed to develop machine learning algorithms to predict the buckling behavior of thin‐walled channel elements under axial compression or bending. The algorithms were trained using feed‐forward multi‐layer Artificial Neural Networks (ANNs), with the input variables including the cross‐sectional dimensions, the thickness, the presence and location of intermediate stiffeners, and the element length. The output data included the elastic critical buckling load or moment, as well as a modal decomposition of the buckled shape into the pure buckling mode categories: local, distortional and global buckling. The Finite Strip Method (FSM) and the Equivalent Nodal Force Method (ENFM) were used to prepare the sample output for training. To ensure the accuracy of the developed algorithms, the ANN models were subjected to a K‐fold cross‐validation technique and featured optimized hyperparameters. The results showed that the trained algorithms had a remarkable accuracy of 98% in predicting the elastic critical buckling loads and modal decomposition of the critical buckled shapes.

Compression performance of composite plates after multi-site impacts: A combined experimental and finite element study

This paper reports on a study of the damage tolerance of carbon fibre reinforced polymer plates, used in aircraft fuselage, subjected to multi-site impacts. A new fixture was designed to perform sequential low-velocity impacts at different locations on plates with two different thicknesses, representing upper and lower fuselage panels. The residual strength in compression was measured using a new compression-after-impact rig designed to prevent global buckling of thin plates. Experimental results indicated that compared to single impacts, multi-site impacts can reduce the residual strength of the thin plates, but not the thick plates. To explain this difference, a detailed finite element model was developed, which enabled modelling of multi-site impacts and compression after impact in one simulation. Simulations suggested that the second impact damage changes the buckled shape prior to failure for the thin plates. A parametric analysis on key material parameters showed that they have a small effect on the residual compressive strength. This work can help to improve the design of aircraft panels with respect to threats posed by multi-site impacts.

Interrogating the Configuration Space of Postbuckled Beams

This paper considers the global configuration space of postbuckled structures. Initially, a slender buckled beam is considered. The boundary conditions are pinned at one end and fully fixed at the other. The pin-end of the initially flat beam is moved toward the other end by a small amount. This causes the beam to buckle laterally (the beam is axially inextensional) with a characteristic shape. Since this is the outcome of a stable-symmetric pitchfork bifurcation, the buckled shape possesses a near mirror-image shape on the other side. Which of the two available equilibrium configurations is taken up depends on the usual, often small, symmetry-breaking effects commonly encountered in axially loaded systems. Given fixed conditions to maintain this initial buckled shape we then apply a moment at the pinned end. The relation between the applied moment and the change in shape is the primary focus of this study. The extent of the buckling (end shortening) is varied, with the magnitude of the moment, as a function of the angle, providing considerable information about the potential energy landscape in which the axially loaded system operates. The applied moment can be thought of as a probing mechanism whereby various equilibrium configurations are revealed, together with information regarding their stability and robustness. A similar approach is then used where the structure consists of two nominally identical beams attached at a right angle. In both cases, the opposite end from the actuation is clamped. An experimental study is conducted on 3D-printed specimens, and this is compared with a finite element analysis using ANSYS, and a large-deflection elastica analysis.

Lateral Buckling of an Elastic Pipe on a Frictional Seabed

Abstract Pipelines tend to buckle laterally under thermal expansion. In existing analytical solutions by Kerr and Hobbs, it is assumed that the seabed resistance q0 to lateral pipe movements is constant in magnitude and opposite in direction to the total displacement. Here, it is opposite to the velocity instead, i.e., the seabed is taken to be frictional rather than nonlinear elastic with a V-shaped potential function. A three-lobe (“mode 3f”) analytical solution is provided for the frictional case, using the same approximate end-of-buckle condition v = v′ = v″ = 0 used by Hobbs in his “mode 3” solution for the nonlinear elastic case. For both modes 3 and 3f solutions, the shape of the buckle does not change as it grows with increasing thermal expansion, though the scaling factors in the axial and lateral directions are different, i.e., the solutions are self-similar. A single finite element solution for the frictional case with an initial imperfection imposed by a bumper can be scaled to cover all such cases. It shows that the shape of the buckle depends on the amplitude of the initial triggering imperfection and is close to the mode 3f solution for very small initial imperfections. The difference between modes 3 and 3f is significant in regard to buckle shape and the relative size of the buckle lobes, but small in regard to the maximum bending moment for a given amount of thermal expansion accommodated by the buckle.

Predicting the buckling behaviour of thin-walled structural elements using machine learning methods

The design process of thin-walled structural members is highly complex due to the possible occurrence of multiple instabilities. This research therefore aimed to develop machine learning algorithms to predict the buckling behaviour of thin-walled channel elements subjected to axial compression or bending. Feed-forward multi-layer Artificial Neural Networks (ANNs) were trained, in which the input variables comprised the cross-sectional dimensions and thickness, the presence/location of intermediate stiffeners, and the element length. The output data consisted of the elastic critical buckling load or moment, while also providing an immediate modal decomposition of the buckled shape into the traditionally defined ‘pure’ buckling mode categories (i.e. local, distortional and global buckling). The sample output for training was prepared using a combination of the Finite Strip Method (FSM) and the Equivalent Nodal Force Method (ENFM). The ANN models were subjected to a K-fold cross-validation technique and the hyperparameters were tuned using a grid search technique. The results indicated that the trained algorithms were capable of predicting the elastic critical buckling loads and carrying out the modal decomposition of the critical buckled shapes with an average accuracy (R2-value) of 98%. The influence of the various channel parameters on the output was assessed using the SHapley Additive exPlanations (SHAP) method.

Formation of post-buckling shear mechanisms in stiffened web panels of slender steel plate girders

A series of validated finite element models are used to investigate the formation of mechanisms in stiffened slender web panels of steel plate girders under pure shear. The prototype girder is based on the seminal tests by Basler and has a web slenderness of 267. Six model cases are analyzed with variations in web panel aspect ratio (1, 1.5, and 3), steel yield strength (Grades 36 and 50), initial imperfection magnitude, and flange thickness. When loaded in shear, the web panels exhibit a 3-stage response: (1) elastic behavior, (2) web mechanism formation, and (3) panel mechanism. In Stage 1, the web initially exhibits an elastic in-plane shear response with no distinct buckling bifurcation. During this stage, the web’s initial out-of-plane imperfections become engaged in second-order bending along its compression diagonal. Concurrently, tension develops in the opposite diagonal as a non-uniform membrane stress field, with highest intensities at locations where second-order bending is low. In Stage 2, a web mechanism is formed when connected bands of thru-thickness von Mises yielding develop across the tension diagonal. These bands emerge at locations where tension membrane stresses interact with locations of maximum second-order bending stress in the buckled shape. The shear load at the end of web mechanism formation is recommended as a target for plastic limit state design because it marks a significant decrease in shear stiffness. In Stage 3, von Mises yielding continues to saturate the web panel, and the bounding flanges and transverse stiffeners become increasingly engaged in load redistribution from the plastified web. Any hardening increase in shear resistance during the panel mechanism stage is modest in magnitude (up to ∼10% for some cases in this study) and is heavily dependent on the sizing of the flanges and stiffeners to carry redistributed forces.

Robust fabrication of ultra-soft tunable PDMS microcapsules as a biomimetic model for red blood cells.

Microcapsules with liquid cores encapsulated by thin membranes have many applications in science, medicine and industry. In this paper, we design a suspension of microcapsules which can flow and deform like red blood cells (RBCs), as a valuable tool to investigate microhaemodynamics. A reconfigurable and easy-to-assemble 3D nested glass capillary device is used to robustly fabricate water-oil-water double emulsions which are then converted into spherical microcapsules with hyperelastic membranes by cross-linking the polydimethylsiloxane (PDMS) layer coating the droplets. The resulting capsules are monodisperse to within 1% and can be made in a wide range of size and membrane thickness. We use osmosis to deflate by 36% initially spherical capsules of diameter 350 μm and a membrane thickness of 4% of their radius. Hence, we can match the reduced volume of RBCs but not their biconcave shape, since our capsules adopt a buckled shape. We compare the propagation of initially spherical and deflated capsules under constant volumetric flow in cylindrical capillaries of different confinements. We find that only deflated capsules deform broadly like RBCs over a similar range of capillary numbers Ca - the ratio of viscous to elastic forces. Similarly to the RBCs, the microcapsules transition from a symmetric 'parachute' to an asymmetric 'slipper'-like shape as Ca increases within the physiological range, demonstrating intriguing confinement-dependent dynamics. In addition to biomimetic RBC properties, high-throughput fabrication of tunable ultra-soft microcapsules could be further functionalized and find applications in other areas of science and engineering.

Buckling shape control in metal plates via material distribution

The aim of this study is to explain from a fundamental perspective, how distributing the material thickness of a metal plate in different ways can be used to control the shape of the elastic buckling mode. The Evolutionary Structural Optimisation (ESO) method is modified to control the buckled shape of plates simply supported on three sides with the remaining longitudinal edge free. The bucking objectives are considered both from a fundamental perspective, and for the application of kinetic façade design, that is, façade panels that undergo shape changes to facilitate ventilation or shading control. A series of buckling experiments of optimised aluminium plates validates the optimised designs. It is shown that in order to achieve a maximum opening in a buckled plate, the buckled shape should be controlled in such a manner as to create a relatively flat zone of maximum transverse displacement over much of the displaced free edge, a shape that differs from the fundamental mode of a uniform thickness plate. Notably, such a shape may be achieved via optimisation with objectives that relate either to the shape itself, or to the objective of maximising the opening. The design methods and experiments demonstrate that redistribution of plate material can efficiently control the buckling characteristics of metal plates for desired functions, and provide significant performance enhancements over uniform thickness plates.

In-situ CLSM characterization of deformation and fracture behavior of (Cu, Cr) metal thin films on flexible substrates

Magnetron sputter deposited Cu thin films on an insulating polymer substrate such as polyimide are frequently used as flexible printed circuits. Understanding the tensile behavior of films deposited on polymer substrates is critical to optimize them for applications requiring flexibility. In this study, single layer copper, chromium (Cu, Cr) films, and Cu/Cr bilayer films were deposited on flexible polyimide substrates by magnetron sputtering. The mechanical behavior of these systems was investigated under tensile loading using the advanced in situ confocal laser scanning microscope (CLSM) technique. The results demonstrate that the buckled shapes, crack density and crack spacing are closely related to the film material and film thickness. The Cr interlayer greatly influences the cracking behavior of the overlying ductile Cu film. Moreover, the in situ tensile experiments indicate that the crack density of the film is obviously related to the loading rate. The findings in this work provide a qualitative guidance for the material selection and structural optimization of metal-based single layer and bilayer flexible electronics.

Research on a Buckling Detection Technique for Rectangular Concrete-filled Steel Tubular Columns based on Grating Projection

<p>The surface buckling of concrete-filled steel tubular (CFST) columns under axial compression was observed in real time by using fringe projection, and pre-set fringes with phase information were projected onto the surface of the member. The buckling information (the size and shape of drum buckling) and its evolution were obtained by analysing the buckling images during the loading process. Nine images of key moments during the experiment were obtained by a technique of obtaining the actual measurements synchronously, and the position of the bulge on the whole side of the steel pipe was obtained by unwrapping. The shape and evolution of the drum buckling of the steel pipe developed symmetrically before point C (the ultimate bearing capacity) and evolved from 2 to 3 peaks. After passing through point C, the buckling deformation was asymmetrical. The deformation near the loading end increased gradually, and the buckling deformation increased with loading. The fastest growth stage was between points C and F, and the load displacement curve showed a rapid reduction in the load. These experimental results show that this noncontact measurement method based on fringe projection is effective in detecting the buckling of rectangular CFST column surfaces.</p> <p> </p>

Dynamic instability of fiber composite cylindrical shell with metal liner subjected to internal pulse loading

Thin-walled cylindrical shells are commonly used structures in explosion containment vessels. When subjected to internal blast loading, these cylindrical shells are prone to dynamic buckling failure.In this work the dynamic stability of cylindrical fiber composite shells with metal liner subjected to uniform internal pressure pulse was investigated through both finite element simulations and theoretical modelling. In particular, pulse buckling of the inner metal liner and vibrational buckling of the outer fiber composite shell were observed and studied. Dynamic, Implicit analysis in ABAQUS Standard considering the initial geometric imperfections were conducted to study the mechanisms for the dynamic buckling of the inner metal liner and outer fiber composite shell. The simulated buckled shape using a simplified two-dimensional model could successfully reproduce the previous experimental results. The dynamic pulse buckling of the metal liner was found to occur during the plastic compression process. The effect of the buckling amplitude of the inner metal liner on the dynamic stability of the outer fiber composite shell was also revealed using numerical simulations. Instead of preventing the outer fiber composite shell from buckling instability, severely buckled metal liner with large buckling amplitude may even accelerate the growth of unstable mode of the fiber composite shell. The theoretical solution for the radial deformation of the metal liner was established by modelling the growth of the buckling mode as the amplification of the initial geometric or velocity imperfection. The most amplified mode and corresponding amplification were determined by the derived amplification function. The solutions for the radial deformation of the outer fiber composite shell were represented by a set of Mathieu differential equations. The dynamic instability of the fiber composite shells was determined from the Mathieu stability charts. The dependence of the dynamic instability of the bilayer composite shells on various parameters such as composite layup, thickness-to-radius ratio and impulse of pressure pulse loading was theoretically predicted and compared with the finite element simulation results.

Innovative Look at the ‘General Method’ of Assessing Buckling Resistance of Steel Structures

Abstract Stability checking is an essential element of the dimensioning of steel frame structures. One of the stability checking methods allowed by EN 1993-1-1 is the so-called general method of assessing structural stability, based on buckling curves and relative structure slenderness λ ¯ op {\bar \lambda _{op}} usually determined through numerical analyses. But this method is not widely used because of the limited computing capabilities of the engineering programs dedicated to static load analyses and difficulties in interpreting the results of the computations. The commonly used computer programs enable one to determine the shape of buckling and critical load amplifier αcr , from which one cannot directly determine the risk of buckling of a real structure. This paper presents a modified and innovative approach to the general method of assessing structural stability, which uses only three parameters, that is, the type of cross section, cross-section strength utilisation and αcr , to determine a member’s/structure’s bearing capacity mobilisation from the stability condition. The problem solution is presented in the form of simple formulas and legible diagrams. Finally, synthetic conclusions are formulated.

Experimental program on the flexural response of steel joist top chord extensions

This article describes an experimental program performed to investigate the stability response of the top chord member of open web steel joists extending as cantilevered members to support floor or roof extensions. The program included 15 full-scale specimens. Four different cross-sections were examined: single-C's, double C's back-to-back, double angle back-to-back, and cross-sections formed by a C-shape and an angle placed back-to-back. C and angle cross-section profiles were varied as well as the boundary conditions used for the top chord extension. The buckled shapes were examined using digitally scanned 3D renderings and monitored image correlation data. The ultimate strength, strains and the displacements of the extensions were measured to characterize their behaviours and be able to reproduce the test results with numerical simulations. Tensile tests and 4-point bending tests were performed to characterize the material properties. The influence of the restraint conditions and the type of section on flexural strength is presented. In all extension tests, failure took place at, or near the support by a combination of flexural yielding, lateral-torsional buckling (LTB) and local buckling. Extensions built with single C shapes without top flange lateral bracing failed by LTB and could not reach their plastic flexural strength. All specimens with top flange bracing could attain their plastic flexural capacity, although local buckling was observed near the bearing seats in most cases. For the deeper 2-C cross-sections, LTB of the individual C shapes also occurred near the support. Design methods for joist top chord extensions must account for these instability mechanisms.