Buckled State Research Articles

Buckled behavior of a pipe conveying fluid subjected to unilateral point constraint

In this work, the buckled behavior of a pipe conveying fluid subjected to unilateral point constraint is investigated. The essentially nonlinear governing equation of the post-buckled state of a clamped-clamped pipe conveying fluid is formulated through the Euler–Bernoulli beam theory and the Hamilton principle, in which the essentially nonlinear natural of the governing equation is induced by unilateral point constraint. The first two critical velocities of fluid in pipe have been analytically determined. The contact force between the pipe and constrained point, and the constrained post-buckled state are obtained by using numerical method. Effects of the constraint point location, gap and the velocity of fluid on contact force and constrained post-buckled state of pipe are investigated. Results show that there are critical departure gap of constraint point and the velocity of fluid, and the snap-through of pipe can be observed for some given parameters, i.e. the pipe jumps from a constrained buckled state to a remote buckled state without constraint when the gap of constrained point or the velocity of fluid is in excess of it’s critical departure gap or velocity.

Universal moiré buckling of freestanding 2D bilayers

The physics of membranes, a classic subject, acquires new momentum from two-dimensional (2D) materials multilayers. This work reports the surprising results emerged during a theoretical study of equilibrium geometry of bilayers as freestanding membranes. While ordinary membranes are prone to buckle around compressive impurities, we predict that all 2D material freestanding bilayers universally undergo, even if impurity-free, a spontaneous out-of-plane buckling. The moiré network nodes here play the role of internal impurities, the dislocations that join them giving rise to a stress pattern, purely shear in homobilayers and mixed compressive/shear in heterobilayers. That intrinsic stress is, theory and simulations show, generally capable to cause all freestanding 2D bilayers to undergo distortive bucklings with large amplitudes and a rich predicted phase transition scenario. Realistic simulations predict quantitative parameters expected for these phenomena as expected in heterobilayers such as graphene/hBN, [Formula: see text] heterobilayers, and for twisted homobilayers such as graphene, hBN, [Formula: see text]. Buckling then entails a variety of predicted consequences. Mechanically, a critical drop of bending stiffness is expected at all buckling transitions. Thermally, the average buckling corrugation decreases with temperature, with buckling-unbuckling phase transitions expected in some cases, and the buckled state often persisting even above room temperature. Buckling will be suppressed by deposition on hard attractive substrates, and survives in reduced form on soft ones. Frictional, electronic, and other associated phenomena are also highlighted. The universality and richness of these predicted phenomena strongly encourages an experimental search, which is possible but still missing.

Evaluation of Secondary Buckling and Ultimate Strength Behaviour According to Boundary Conditions of Curved Plate Subjected to Compressive Load

This paper analyzed the buckling and ultimate strength characteristics of plate members with curvature, which are essentially used in ships and marine structures, through numerical analysis. Major structural members are affected by rotational velocity depending on the rigidity of structures placed around them, and it is very important to check how this affects buckling and ultimate strength. The aspect ratio of the curved plate was adopted as 2.5, 3.0, and 3.5 to reflect the plate thickness range and high-strength steel characteristics actually used. In the case of no curvature, and in the case of curvature, 5 degrees, 10 degrees, 15 degrees, 20 degrees, 30 degrees, and 45 degrees were considered. Under certain thickness and curvature conditions, secondary buckling occurs and the buckling state of the plate changes rapidly. Therefore, the final strength is evaluated lower than in the case where there is no curvature. Buckling and ultimate strength were high in a clamped condition around the curved plate, and there was no specificity in behavior depending on the aspect ratio change. In the four-side simply supported condition, the in-plane stiffness gradient changes depending on the aspect ratio due to the secondary buckling effect, and this characteristic is a phenomenon that is not considered at all in the existing classification method.

3D height-alternant island arrays for stretchable OLEDs with high active area ratio and maximum strain

Stretchable optoelectronic devices are typically realized through a 2D integration of rigid components and elastic interconnectors to maintain device performance under stretching deformation. However, such configurations inevitably sacrifice the area ratio of active components to enhance the maximum interconnector strain. We herein propose a 3D buckled height-alternant architecture for stretchable OLEDs that enables the high active-area ratio and the enhanced maximum strain simultaneously. Along with the optimal dual serpentine structure leading to a low critical buckling strain, a pop-up assisting adhesion blocking layer is proposed based on an array of micro concave structures for spatially selective adhesion control, enabling a reliable transition to a 3D buckled state with OLED-compatible processes. Consequently, we demonstrate stretchable OLEDs with both the high initial active-area ratio of 85% and the system strain of up to 40%, which would require a lateral interconnector strain of up to 512% if it were attained with conventional 2D rigid-island approaches. These OLEDs are shown to exhibit reliable performance under 2,000 biaxial cycles of 40% system strain. 7 × 7 passive-matrix OLED displays with the similar level of the initial active-area ratio and maximum system strain are also demonstrated.

Analysis and Verification on Buckling Mechanism of Spatial Tow Steering in Automated Fiber Placement

Automated fiber placement (AFP) enables the efficient and precise fabrication of complex-shaped aerospace composite structures with lightweight and high-performance properties. However, due to the excessive compression on the inner edge of the tow placed along the curved trajectory, the resulting defects represented by buckling and wrinkles in spatial tow steering can induce poor manufacturing accuracy and quality degradation of products. In this paper, a theoretical model of tow buckling based on the first-order shear deformation laminate theory, linear elastic adhesion interface and Hertz compaction contact theory is proposed to analyze the formation mechanism of the wrinkles and predict the formation of defects by solving the critical radius of the trajectory, and finite element analysis involving the cohesive zone modeling (CZM) is innovated to simulate the local buckling state of the steered tow in AFP. Additionally, numerical parametric studies and experimental results indicate that mechanical properties and geometric parameters of the prepreg, the curvature of the placement trajectory and critical process parameters have a significant impact on buckling formation, and optimization of process parameters can achieve effective suppression of placement defects. This research proposes a theoretical modeling method for tow buckling, and conducts in-depth research on defect formation and suppression methods based on finite element simulation and placement experiments.

3D-Printed Hydrogels as Photothermal Actuators.

Thermoresponsive hydrogels were 3D-printed with embedded gold nanorods (GNRs), which enable shape change through photothermal heating. GNRs were functionalized with bovine serum albumin and mixed with a photosensitizer and poly(N-isopropylacrylamide) (PNIPAAm) macromer, forming an ink for 3D printing by direct ink writing. A macromer-based approach was chosen to provide good microstructural homogeneity and optical transparency of the unloaded hydrogel in its swollen state. The ink was printed into an acetylated gelatin hydrogel support matrix to prevent the spreading of the low-viscosity ink and provide mechanical stability during printing and concurrent photocrosslinking. Acetylated gelatin hydrogel was introduced because it allows for melting and removal of the support structure below the transition temperature of the crosslinked PNIPAAm structure. Convective and photothermal heating were compared, which both triggered the phase transition of PNIPAAm and induced reversible shrinkage of the hydrogel-GNR composite for a range of GNR loadings. During reswelling after photothermal heating, some structures formed an internally buckled state, where minor mechanical agitation recovered the unbuckled structure. The BSA-GNRs did not leach out of the structure during multiple cycles of shrinkage and reswelling. This work demonstrates the promise of 3D-printed, photoresponsive structures as hydrogel actuators.

Improving Stability, Crystallinity, and Photo‐Responsiveness of Supramolecular Frameworks by Surface Polymerization

AbstractMetal–organic cage‐based photo‐responsive supramolecular frameworks (PSMFs) with permanent porosity have gained attention for their modular properties, controllable functionality, and light‐induced reversible responsiveness. However, their high porosity and photo‐responsive efficiency are often compromised due to poor structural stability upon solvent removal, limiting their potential applications. Here, a solution to overcome this challenge by employing a surface polymerization strategy using isophorone diisocyanate (IDI) to stabilize PSMF (PCC‐20t) is presented. This approach results in the composite of PCC‐20t@PolyIDI, which preserves crystallinity and permanent high‐porosity while avoiding structural collapse commonly observed in highly porous supramolecular frameworks. Moreover, compared to activated PCC‐20t, PCC‐20t@PolyIDI exhibits an 18.6‐fold increase in specific surface area. Remarkably, the structural variability of PCC‐20t@PolyIDI can be observed in the photo‐regulation behavior of CO2 capacity under the irradiation of vis‐ and UV‐light, showing a 27.9% change in adsorption amount for CO2 which is significantly higher than that of the activated PCC‐20t with 7.0% for CO2. Grand Canonical Monte Carlo simulations demonstrate the light‐regulated adsorption performance is attributed to the configuration transformation of azobenzene from trans‐ to buckling state. The findings may pave the way for stabilizing high‐porosity materials to simultaneously meet demands for high‐porosity and photo‐responsive efficiency.

Numerical and Experimental Analysis of Buckling and Post-Buckling Behaviour of TWCFS Lipped Channel Section Members Subjected to Eccentric Compression.

The paper presents a static analysis of the buckling and post-buckling state of thin-walled cold-formed steel (TWCFS) lipped channel section beam-columns subjected to eccentric compression. Eccentricity is taken into consideration relative to both major and minor principal axes. An analytical-numerical solution to the buckling and post-buckling problems is described. The solution is based on the theory of thin plates. Equations of equilibrium of section walls are derived from the principle of stationary energy. Then, to solve the problem, the finite difference (FDM) and Newton-Raphson methods are applied. Linear (buckling) and nonlinear (post-buckling) analyses are performed. As a result, pre- and post-buckling equilibrium paths are determined. Comparisons of the obtained numerical results, FE simulation results, and experimental test results are carried out and presented in comparative load-shortening diagrams. Additionally, a comparison of the buckling forces and buckling modes obtained from theoretical analysis and experiments is presented.

Magnetization reversal and stability of vortex state in convex shaped cylindrical nanodisks

Cylindrical nanodisks typically exhibit in-plane magnetization reversal comprising of nucleation and propagation of a vortex closure state. Present work investigates the magnetization reversal process in a cylindrical disk of radius ranging from 20 nm to 100 nm in which the flat surfaces at top and bottom are modified to convex shaped surfaces. It is found that the nucleation of vortex state no longer occurs as a result of this surface modification. Instead, a buckled magnetization state is nucleated which transforms to reverse buckled state yielding a square hysteresis loop. However, the out-of-plane hysteresis loop exhibits a vortex state at remanence. Analytical calculation of total free energy of both vortex as well as buckled state and the comparison thereof shows that the vortex state is ground state if radius of nanodisk is above 60 nm . Below this critical radius, buckled state is the ground state. But the non-appearance of vortex state at remanence in in-plane hysteresis loop of all of the nanodisks indicates a presence of energy barrier between vortex and buckled state. Height of the energy barrier is estimated using nudged elastic band method (NEBM) in all cases which proves that the energy barrier for vortex state weakens and the barrier for buckled state intensifies with the reduction of nanodisk size. At the critical radius of 60 nm , crossover of the two barrier heights occurs. Eventually, at the radius of 30 nm , the vortex state becomes totally unstable which can be toppled to buckled state with the slightest of perturbation.

Ultimate bearing behavior in the post-buckling stage of composite pressure hulls based on new detection methods

This study employs novel testing methods and analysis techniques to investigate the ultimate load-bearing characteristics and failure mechanisms of composite thin-walled pressure hulls. An analytical model based on the classical laminated plate theory, incorporating the Hashin damage failure criterion, is developed to determine their ultimate bearing capacity. Five carbon fiber cylindrical shells are manufactured to validate the failure mechanism and evaluate the model's predictions. Deep-sea pressure testing and ultrasonic testing are conducted on these shells. The resulting data is analyzed using both macroscopic and microscopic approaches to gain insights into their load-bearing behavior and failure mechanisms. The study demonstrates the significant influence of the thickness (t) to radius (R) ratio on the ultimate load-bearing capacity of these composite thin-walled pressure hulls. Failure primarily arises from compression failure in both the matrix and fibers. The load-bearing process encompasses uniform shrinkage, critical buckling, and post-buckling states. Material failure primarily occurs during the post-buckling stage, while no damage occurs during the initial buckling. On a microscale, failure at the interface between the fibers and matrix is identified as the primary contributor to overall structural failure. Enhancing the fracture energy of the interface is recommended to enhance the ultimate load-bearing capacity of the hulls.

Comprehensive Distortion Analysis of a Laser Direct Metal Deposition (DMD)-Manufactured Large Prototype Made of Soft Martensitic Steel 1.4313

Additive manufacturing (AM) by using direct metal deposition (DMD) often causes erratic distortion patterns, especially on large parts. This study presents a systematic distortion analysis by employing numerical approaches using transient–thermal and structural simulations, experimental approaches using tomography, X-ray diffraction (XRD), and an analytical approach calculating the buckling distortion of a piston. The most essential geometrical features are thin walls situated between massive rings. An eigenvalue buckling analysis, a DMD process, and heat treatment simulation are presented. The eigenvalue buckling simulation shows that it is highly dependent on the mesh size. The computational effort of the DMD and heat treatment simulation was reduced through simplifications. Moreover, artificial imperfections were imposed in the heat treatment simulation, which moved the part into the buckling state inspired by the experiment. Although the numerical results of both simulations are successful, the eigenvalue and DMD simulation cannot be validated through tomography and XRD. This is because tomography is unable to measure small elastic strain fields, the simulated residual stresses were overestimated, and the part removal disturbed the residual stress equilibrium. Nevertheless, the heat treatment simulation can predict the distortion pattern caused by an inhomogeneous temperature field during ambient cooling in an oven. The massive piston skirt cools down and shrinks faster than the massive core. The reduced yield strength at elevated temperatures and critical buckling load leads to plastic deformation of the thin walls.

Frequency Design of a Vertical Cantilever Beam Carrying Tip Mass

Previous research has revealed that vertical cantilever beam structures, after considering the effects of gravity, can exhibit a 1:3 internal resonance between two transverse modes. However, whether a similar phenomenon would still occur in the system when a proof body is attached to the free end of cantilever beams, and how to perform parameter design to deliberately induce internal resonance are still open issues. The present study conducts research on the natural frequencies of a vertical cantilever beam with a tip mass. Within the framework of the Euler–Bernoulli beam theory, Hamilton’s principle is utilized to derive the integral-partial differential equation of free vibration of the system. The corresponding frequency equation is then solved using the Chebyshev pseudospectral method, with an algebraic equation of the natural frequency obtained. Moreover, an explicit analytical expression for the fundamental frequency is obtained using parameter fitting, which is then used to reveal the relationship among parameters under the critical state of buckling and evaluate the extent of gravity’s impact on the fundamental frequency. The study finally investigates the ratio of the first two natural frequencies. A parameter design method is proposed, which derives a parametric curve in terms of the fundamental frequency, ensuring a 1:3 ratio between the first two natural frequencies. The free vibration time history at the midpoint of the beam is acquired by directly solving the system’s partial differential equation through the finite element method. Fourier transformation of this time history verifies that the fundamental frequency aligns with a predetermined value, and the ratio between the first two natural frequencies is 1:3, thus confirming the efficacy of the proposed method. It is found that the addition of a tip mass provides more flexibility in adjusting parameters to achieve internal resonance, which facilitates the miniaturization of actual structures.

Forced resonance of a buckled beam flexibly restrained at the inner point

Restraints along slender structures, such as pipes conveying fluid and beams, play important roles in enhancing their bending stiffness. The current work investigates the influence of the midpoint restraint on the buckled axial force and dynamic characteristics for the first time. A continuous model is introduced by treating the midpoint restraint force as a concentrated force using Dirac function. The influence of the midpoint restraint is discussed based on modal expansion, and a partitioned model is proposed for validation. The conclusion is that the continuous model has good accuracy. Based on this model, it finds out two stable buckled states changing with the midpoint stiffness. The first stable buckled state occurs under weak midpoint restraint and has a cambered shape. The zero- and double frequency components occur in symmetric modal shapes and the response is softened along the whole beam. However, in the second stable buckled state, it turns into a whole sine function shape. The zero- and double frequency components just occur in the second modal shape, and the soften phenomenon doesn’t occur at the midpoint. With increasing excitation amplitude, a bubble appears on the primary resonance peak while another resonance peak emerges nearby it. This work explains the influence of midpoint stiffness on nonlinear resonance and enhances the study of the nonlinear behavior of buckled slender structures.

Subharmonic resonance of phospholipid coated ultrasound contrast agent microbubbles

Phospholipid encapsulated ultrasound contrast agents have proven to be a powerful addition in diagnostic imaging and show emerging applications in targeted therapy due to their resonant and nonlinear scattering. Microbubble response is affected by their intrinsic (e.g. bubble size, encapsulation physics) and extrinsic (e.g. boundaries) factors. One of the major intrinsic factors at play affecting microbubble vibration dynamics is the initial phospholipid packing of the lipid encapsulation. Here, we examine how the initial phospholipid packing affects the subharmonic response of either individual or a system of two closely-placed microbubbles. We employ a finite element model to investigate the change in subharmonic resonance under ‘small’ and ‘large’ radial excursions. For microbubbles ranging between 1.5 and 2.5 µm in diameter and in its elastic state (σ0 = 0.01 N/m), we demonstrate up to a 10 % shift towards lower frequencies in the peak subharmonic response as the radial excursion increases. However, for a bubble initially in its buckled state (σ0 = 0 N/m), we observe a maximum shift of 8 % towards higher frequencies as the radial excursion increases over the same range of bubble sizes – the opposite trend. We studied the same scenario for a system of two individual microbubbles for which we saw similar results. For microbubbles that are initially in their elastic state, in both cases of a) two identically sized bubbles and b) a bubble in proximity to a smaller bubble, we observed a 6 % and 9 % shift towards lower frequencies respectively; while in the case of a neighboring larger bubble no change in subharmonic resonance frequency was observed. Microbubbles that are initially in a buckled state exert no change, 5 % and 19 % shift towards higher frequencies, in two-bubble systems consisting of a) same-size, b) smaller, and c) larger neighboring bubble respectively. Furthermore, we examined the effect of two adjacent bubbles with non-equal initial phospholipid states. The results presented here have important implications in ultrasound contrast agent applications.

Achieving controllable and reversible snap-through in pre-strained strips of liquid crystalline elastomers.

Deformable, elastic materials that buckle in response to external stimuli can display "snap-through", which involves a transition between different, stable buckled states. Snap-through produces a quick release of stored potential energy, and thus can provide fast actuation for soft robots and other flexible devices. Liquid crystalline elastomers (LCEs) exposed to light undergo a phase transition and a concomitant mechanical deformation, allowing control of snap-through for rapid, large amplitude actuation. Using both a semi-analytical model and finite element simulations, we focus on a thin LCE strip that is clamped at both ends and buckles due to an initially imposed strain. We show that when this clamped, strained sample is exposed to light, it produces controllable snap-through behavior, which can be regulated by varying the light intensity and the area of the sample targeted by light. In particular, this snap-through can be triggered in different directions, allowing the system to be reset and triggered multiple times. Removing the light source will cause the system to settle into one of two stable states, enabling the encoding and storage of information in the system. We also highlight a specific case where removing the light source removes the induced buckling and returns the material to an initially flat state. In this case, the system can be reset and form a new shape, allowing it to function as a rewriteable haptic interface.

An extended 2D Gao beam model

This work derives and simulates a two-dimensional extension of the nonlinear Gao beam, by adding the cross-sectional shear variable, similarly to the extension of the usual Bernoulli–Euler beam into the Timoshenko beam. The model allows for oscillatory motion about a buckled state, as well as adds vertical shear of the cross sections, thus reflecting better nonlinear thick beams. The static model is derived from the principle of virtual elastic energy, and is in the form of a highly nonlinear coupled system for the beams transverse vibrations and the motion of the cross sections. The model allows for general distributive transversal and longitudinal loads and a compressive horizontal load acting on its edges. The model is simulated numerically, using the dynamic version for better insight into the steady solutions. The terms that distinguish our numerical solutions from the solutions of the Gao beam, described in the literature, are highlighted. The numerical scheme and its characteristic finite element matrices allow us to obtain simulation results that demonstrate the type of vibrations of our extended and modified beam, and also the differences between these solutions and those of the Gao beam model.

Stability and load carrying capacity of thin-walled composite columns with square cross-section under axial compression

The study aimed to analyse the stability and load-carrying capacity of compressed thin-walled composite columns subjected to axial compression. The subject of the survey was composite columns with closed square cross-sections made of carbon-epoxy composite. Different lay-ups of the composite material characterised the test specimens - several cases of lay-ups were considered. The application of the subject of the research is closely related to the use of these elements as load-carrying elements of aerospace and building structures. The requirements for such structures are closely related to the provision of a large reserve of load-carrying capacity after buckling. Experimental testing was carried out using a universal testing machine and other testing techniques, where acoustic emission, an optical deformation measurement system, and a digital microscope, among others, were used. Numerical simulations using the finite element method were carried out parallel to the experimental studies. In the case of FEA simulations, original numerical models were developed considering known failure models of the composite material. For both empirical studies and FEM simulations, an in-depth analysis of the buckling and post-buckling states was carried out, considering the failure phase of the composite material. The novelty of the present work was the development of original FEM models, allowing faithful reproduction of experimental studies conducted on physical models, as well as the use of research methods to determine the load-carrying capacity of composite structures.

Analysis of the Effect of Slenderness Ratio on Nominal Moment in T Section

T-section is similar to the single-symmetry plane. Mostly used in railway engineering, temporary work stands and machinery equipment. In the AISC1999 specification, due to the unfamiliarity with the T-section. Therefore, a conservative definition of a tee fracture is a noncompact section. With the evolution of the times, there are more and more researches on T-section. The T-section is defined as the flange slenderness and the web slenderness. The calculation formula of the nominal moment (Mn) is mainly limited by the slenderness ratio. In recent years, the AISC2017 has added limiting laterally unbraced length for the limit state of yielding (Lp) and limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (Lr) to the calculation formula of the nominal flexural strength (Mn) of the T-section. The nominal flexural strength (Mn) shall be the lowest value obtained according to the limit states of yielding moment (Mp), lateral-torsional buckling (LTB). Therefore, this study will analyze and compare the changes in the AISC2017 with the previous norm. Largest laterally unbraced length along either flange at the point of load has 3% difference between AISC2017 and other specifications in plastic moment.

Dynamic buckling experiments for stiffened panels under falling hammer impact

Stiffened panels are the fundamental elements in marine structures to withstand external dynamic loads, such as bow slamming and collision impact. However, the dynamic buckling of stiffened panels under hammer impact has not been widely studied. In this paper, the stiffened panels are chosen as the study object. Firstly, the ultimate capacity and failure modes are investigated by a static experiment under longitudinal compression. Then, a series of impact experiments on stiffened panels of the same scantlings under various failing hammer velocities are designed to find the critical dynamic buckling state. A new criterion of dynamic buckling evaluation is proposed based on the fitted curve of the experiment results. Based on the steel properties measured by tensile tests, the FE analysis of the stiffened panels under hammer impact is validated by the experiment results. The applicability of evaluation criteria for dynamic buckling is investigated based on the plating response and the stiffener web response. The conclusions of this paper will be useful for the safety analysis of stiffened panels under impact loads.

Imperfections in realistic metal wind turbine support towers: a one‐at‐a‐time (OAAT) study

AbstractThe ultimate limit state of buckling is an important consideration for the design of wind turbine support towers (WTSTs) which is increasingly being done with the aid of advanced nonlinear finite element analysis according to EN 1993‐1‐6. As these towers are relatively slender thin‐walled metal shell structures, their response and buckling resistance is invariably affected by geometric imperfections. This paper presents a sensitivity study into the possible relative influences of four different types of realistic imperfections that are likely to arise in WTST construction on the elastic‐plastic buckling resistance as assessed by computational GMNIAs. These include idealised but realistic representations of axisymmetric circumferential weld depressions, unintended eccentricities at curved plate boundaries, a global out‐of‐roundness and corrected parallel flange interface gaps. The relative sensitivity is explored via a ‘one‐at‐a‐time’ (OAAT) study where all factors but one are kept at a constant intensity while the active factor is scaled, with the influence on the computed GMNIA under two load cases recorded. The OAAT study suggests that for shell structures representative of the geometric ranges typical for WTSTs, the weld depression has the most deleterious effect on the predicted buckling resistance.