Buckling Of Structures Research Articles

Torsional deformation dominated buckling of serpentine structures to form three-dimensional architectures with ultra-low rigidity

Buckling of a single ribbon is the simplest type of instability in mechanics. Recently postbuckling has been adopted in three-dimensional (3D) assembly technique to form diverse 3D architectures from planar precursors. amongst various structures, 3D serpentine structures are remarkable, especially in stretchable electronics and micro-electro-mechanical systems, as they provide ultra-low rigidity and high stretchability. Previous studies on those structures are mainly based on finite element analysis and individually focused on features such as the resonant frequency, critical compression for buckling and stretchability. A comprehensive theoretical model that fully reveals the mechanical behaviour of such structures and provides detailed information such as the displacement/rotation, curvature and strain distribution, is essential for applications that require a tailored structural design. Here an analytical model in very concise and explicit form is developed, showing that the postbuckling of serpentine structures obeys similar rules as that of a straight ribbon, with the effective torsional rigidity playing the role of the bending rigidity. The effective torsional rigidity involves not only the cross-sectional profile (ribbon width and thickness) but also the geometry parameters unique in the serpentine structures, which significantly enlarges the design space. Using serpentine structures of unidentical ribbons, an inverse design strategy is proposed to form various architectures buckled from planar precursors, without adopting spatial-varying cross-sectional thicknesses or widths as in previous works. A multi-directional strain sensor with ultra-low rigidity is also presented to demonstrate the application of the theoretical model. The above results also indicate that complexity (rich design space) and conciseness (simple rules) could coexist in 3D serpentine structures, which is rare in other structures formed by the mechanics-guided 3D assembly.

Static Buckling Analysis of a Quadratic-Cubic Model Structure Using the Phase Plane Method and Method of Asymptotics

The exact and asymptotic analyses of the buckling of a quadratic-cubic model structure subjected to static loading are discussed. The governing equation is first solved using the phase plane method and next, using the method of asymptotics. In the asymptotic method, we discuss the possibilities of using regular perturbation method in asymptotic expansions of the relevant variables to get an approximate analytical solution to the problem. Finally, the two results are compared using numerical results obtained with the aid of Q-Basic codes. In the two methods discussed in this work, it is clearly seen that the static buckling loads decrease as the imperfection parameters increase. It is also observed that the static buckling loads obtained using the exact method are higher than those obtained using the method of asymptotics.

Numerical study and experiments on the elasto-visco-plastic bifurcation buckling of thick anisotropic plates

The present work investigates the elasto-visco-plastic buckling of thick plate structures. Methods to estimate the buckling of thin elasto-visco-plastic shells and plates are proposed in literature. To the knowledge of the authors, only few works present experimental results, and none treat the experimental elasto-visco-plastic buckling of thick plate. Thick rectangular plates are chosen as a structure of interest to study elasto-visco-plastic buckling. A modelling/experimental approach is followed to solve such problem. Buckling experiments at room temperature on thick elasto-visco-plastic plates subjected to compressive load are performed. 3D digital image correlation (3D-DIC) is used to measure displacement fields on plate surface during buckling experiments. The experiments are also modelled through a finite element model. Bodner’s approach is coupled to Hencky’s deformation theory to predict buckling of elasto-visco-plastic plates. Bifurcation analysis are performed to estimate buckling critical stresses and strains, and buckling modes. Geometrical and loading imperfections are also discussed. A good correlation is observed between numerical results and experiments. The limitation of Bodner’s approach is also discussed.

Effect of crack location on buckling and dynamic stability in plate frame structures

It is well known that damages affect the dynamic characteristics of the structures in such a way that they may lead those structures to fail. Therefore, it is essential to construct a reliable mathematical model for estimating the effect of the damage in these structures. In this study, the effect of the straight, through-thickness crack and its location on the thin single-bay one-storey, two-bay-one-storey, and single-bay two-storey plate frames is investigated. For this purpose, a four-node quadrilateral plate bending and membrane elements are combined to perform finite element free vibration analysis of the healthy and cracked thin plate frame structures. The Classical Plate Theory is employed to satisfy the strain and stress conditions of these thin structures. A computer code is written using MATLAB to obtain the first three natural frequencies, critical buckling loads, and the first unstable regions of the healthy and cracked thin structures. To ensure the validity of the employed mathematical model, a convergence analysis is performed via ANSYS. The effect of crack location in plate frame structures is investigated by measuring the differences between the healthy and cracked structures’ first three buckling modes and the first unstable region. It is seen that the bending regions of the buckling modes are more affected by the crack than the other zones. Besides, crack occurrence within these regions has more impact on the first unstable regions. Accordingly, it has been revealed that the bending regions are the weakest locations of the frame structures. Therefore, potential cracks occurred within these regions may affect the structural integrity more than those of emerged in other regions.

Buckling of functionally graded carbon nanotubes reinforced composite joined spherical-cylindrical-spherical thin-walled structure

Functionally graded carbon nanotubes reinforced composite joined spherical-cylindrical-spherical thin-walled structure under the actions of axial and lateral distributed loads is considered. The static buckling of this structure is analyzed numerically. The Ritz method is used to derive the governing equations of the joined thin-walled structure buckling. Higher-order shear deformation theory is applied to describe the structure stress-strain state. The continuity conditions of the spherical-cylinder junction are derived. The displacements projections are chosen in the special form to satisfy these continuity conditions. The dependences of the buckling axial load on the CNTs distributions, CNTs volume fractions are analyzed numerically.

Equivalent continuum method of plane-stress dominated plate-lattice materials

An equivalent continuum method based on micro–macro transformations of strains and stresses is developed to analyze the effective mechanical performances of three-dimensional plane-stress dominated plate-lattice materials. The equivalent stiffness matrix of the plate-lattice material is deduced by the equivalent continuum method. Based on the two-dimensional Mises yield criterion of the micro-plate, the yield criterion, yield strength and three-dimensional plastic yield surfaces of the plate-lattice materials are deduced. Anisotropy of the stiffness and strength is discussed for six typical plate-lattice materials. The predicted stiffness and strength are in good agreement with the experimental data, validating the present model in the prediction of the mechanical properties of the plate-lattice materials. Through the research, it is found that the plane-stress dominated topology makes the plate-lattice material stiffer and stronger than stretching-dominated truss-lattice material when there is no elastic buckling in both structures.

On non-linear behavior and buckling of arch-beam structures

This paper investigates analytical predictions for non-linear behavior and buckling of pin-ended arch-beam structures. The nonlinear in-plane equilibrium is derived based on the principle of virtual work and the force balance condition of the ends of arch-beam structures. A new calculation method of the stationary point of inflexion is proposed and used to develop the symmetric buckling requirement for arch-beam structures. The asymmetric buckling requirement as well as all the possible nonlinear buckling behaviors and corresponding buckling requirements for arch-beam structures are also investigated analytically. The accuracy of proposed analytical solutions is validated through the comparisons against finite element analysis results. The major findings of this theoretical investigation are: (1) the analytical solution of the symmetric buckling requirement for arch-beam structures is thoroughly different from that for the single arch structures; (2) a stable bifurcation phenomenon can be observed in the nonlinear asymmetric buckling of arch-beam structures, in which buckling load increases as the asymmetric buckling occurs; (3) the symmetric buckling requirement and the asymmetric buckling requirement of arch-beam structures are independent of each other and the asymmetric buckling can occur before the stationary point of inflexion; and (4) the nonlinear buckling behavior of arch-beam structures is more complicated than the behavior of single arch structures, and six different buckling phenomena can be observed by changing the parameters of compression stiffness ratio between the beam and the arch, modified slenderness and rise-to-span ratio.

Research on the dynamic buckling of a typical deck grillage structure subjected to in-plane impact Load

The dynamic buckling of the main deck grillage would result in the total collapse of the ship hull subjected to a far-filed underwater explosion. This dynamic buckling is mainly due to the dynamic moment of the ship hull when the ship hull experiences a sudden movement under impact load from the explosion. In order to investigate the ultimate strength of a typical deck grillage under quasi-static and dynamic in-plane compressive load, a structure model, in which the real constrained condition of the deck grillage was taken into consideration, was designed and manufactured. The quasi-static ultimate strength and damage mode of the deck grillage under in-plane compressive load was experimentally investigated. The Finite Element Method (FEM) was employed to predict the ultimate strength of the deck grillage subjected to quasi-static in-plane compressive load, and was validated by comparing the results from experimental tests and numerical simulations. In addition, the numerical simulations of dynamic buckling of the same model under in-plane impact load was performed, in which the influences of the load amplitude and the frequency of dynamic impact load, as well as the initial stress and deflection induced by wave load on the ultimate strength and failure mode were investigated. The results show that the dynamic buckling mode is quite different from the failure mode of the structure subjected to quasi-static in-plane compressive load. The displacements of deck edge in the vertical direction and the axial displacements are getting larger with the decrease of impact frequency. Besides, it is found that the dynamic buckling strength roughly linearly decreased with the increase of initial proportion of the static ultimate strength P0. The conclusions drawn from the researches of this paper would help better designing of the ship structure under impact loads.

Curving origami with mechanical frustration

We study the three-dimensional equilibrium shape of a shell formed by a deployed accordion-like origami, made from an elastic sheet decorated by a series of parallel creases crossed by a central longitudinal crease. Surprisingly, while the imprinted crease network does not exhibit a geodesic curvature, the emergent folded structure stemming from mechanical equilibrium yields angles at the vertices between sections of the central fold, producing an effective curvature. Both finite element analysis and manually made origamis show a robust empirical relation between the imprinted crease network’s dimensions and the apparent curvature. Moreover, the emerging structure exhibits various elastic deformations that induce three distinct morphogenesis types, from bent faces to complete faceting to structural buckling. We characterize the corresponding kinematics of crease network deformations and determine their phase diagram. Taking advantage of the frustration caused by the competition between crease stiffness and kinematics of crease network deformations, we provide a novel tool for designing curved origami structures constrained by strong geometrical properties.

Numerical analysis of hat stiffened composite panels for pre and post buckling conditions

This research aims in studying the pre-buckling and post-buckling behaviour of composite panels stiffened by hat stiffeners under compressive loading. Stiffened panels are used in aerospace, marine and also in bridge structures. They are used to make the plate girders stiff. By using composite materials, the strength can be increased, and the weight can be reduced. In Composite panels which are stiffened, local buckling and failure of panel happens because of the applied compressive loads and due to combination of compressive and shear loads. The Collapse of the stiffened composite structure starts from the intersection between the plate and the stiffeners due to stress effect caused by deformation of lamina skin and stiffeners then leads to the structural buckling of skin of the panel. This research uses nonlinear Finite element approach to investigate the collapsing behavior using ABAQUS software.

Experimental and Numerical Analyses on the Buckling Characteristics of Woven Flax/Epoxy Laminated Composite Plate under Axial Compression.

The evolution of a sustainable green composite in various loadbearing structural applications tends to reduce pollution, which in turn enhances environmental sustainability. This work is an attempt to promote a sustainable green composite in buckling loadbearing structural applications. In order to use the green composite in various structural applications, the knowledge on its structural stability is a must. As the structural instability leads to the buckling of the composite structure when it is under an axial compressive load, the work on its buckling characteristics is important. In this work, the buckling characteristics of a woven flax/bio epoxy (WFBE) laminated composite plate are investigated experimentally and numerically when subjected to an axial compressive load. In order to accomplish the optimization study on the buckling characteristics of the composite plate among various structural criterions such as number of layers, the width of the plate and the ply orientation, the optimization tool “response surface methodology” (RSM) is used in this work. The validation of the developed finite element model in Analysis System (ANSYS) version 16 is carried out by comparing the critical buckling loads obtained from the experimental test and numerical simulation for three out of twenty samples. A comparison is then made between the numerical results obtained through ANSYS16 and the results generated using the regression equation. It is concluded that the buckling strength of the composite escalates with the number of layers, the change in width and the ply orientation. It is also noted that the weaving model of the fabric powers the buckling behavior of the composite. This work explores the feasibility of the use of the developed green composite in various buckling loadbearing structural applications. Due to the compromised buckling characteristics of the green composite with the synthetic composite, it has the capability of replacing many synthetic composites, which in turn enhances the sustainability of the environment.

The influence of structural and geometric imperfections on the LDB strength of steel–concrete composite beams

The behavior of structural steel frames is significantly influenced by the presence of structural and geometric imperfections. The structural imperfections, namely, the residual stresses, are generated during most manufacturing processes involving material deformation, heat treatment, machining or processing operations. As the residual stresses, the geometric imperfections are fundamental in the analysis of critical buckling and post-buckling behavior of thin-walled structures. These initial imperfections can be captured using the second order inelastic analysis, also known as advanced analysis. In the modern steel design codes, e.g., European code EC3, Australian code AS4100, North American Code AISC360-16 and Chinese code GB50017 the development of advanced numerical analyses is allowed to predict the behavior of steel and composite frames. However, the random nature of the shapes and magnitudes of the initial imperfections results in difficulties in developing these analyses. Therefore, this paper presents an assessment of the influence of structural imperfections, namely, the residual stresses, and geometric imperfections on the Lateral Distortional Buckling (LDB) strength of steel–concrete Composite Beams (SCCB). The basis of the research is a thorough comparison between numerical and experimental results. Several residual stress patterns found in the literature have been implemented in numerical simulations of four different tests on SCCB subjected to uniform hogging moment. In addition, a sensitive analysis of the geometric imperfection values, namely, the initial bending, was developed. The post buckling numerical analyses were developed with the ABAQUS software. The analysis shown in this work shall help the choice of the initial imperfections on future numerical simulations on SCCB.

Analysis of the Postbuckling Response of Nonlocal Plates Via Fractional-Order Continuum Theory

Abstract We present a comprehensive study on the postbuckling response of nonlocal structures performed by means of a frame-invariant fractional-order continuum theory to model the long-range (nonlocal) interactions. The use of fractional calculus facilitates an energy-based approach to nonlocal elasticity that plays a fundamental role in the present study. The underlying fractional framework enables mathematically, physically, and thermodynamically consistent integral-type constitutive models that, in contrast to the existing integer-order differential approaches, allow the nonlinear buckling and postbifurcation analyses of nonlocal structures. Furthermore, we present the first application of the Koiter’s asymptotic method to investigate postbifurcation branches of nonlocal structures. Finally, the theoretical framework is applied to study the postbuckling behavior of slender nonlocal plates. Both qualitative and quantitative analyses of the influence that long-range interactions bear on postbuckling response are undertaken. Numerical studies are carried out using a 2D fractional-order finite element method (f-FEM) modified to include a combination of the Newton–Raphson and a path-following arc-length iterative methods to solve the system of nonlinear algebraic equations that govern the equilibrium beyond the critical points. The present framework provides a general foundation to investigate the postbuckling response of potentially any type of nonlocal structure.

Iontronic pressure sensor with high sensitivity and linear response over a wide pressure range based on soft micropillared electrodes

Electronic skins and flexible pressure sensors are important devices for advanced healthcare and intelligent robotics. Sensitivity is a key parameter of flexible pressure sensors. Whereas introducing surface microstructures in a capacitive-type sensor can significantly improve its sensitivity, the signal becomes nonlinear and the pressure response range gets much narrower, significantly limiting the applications of flexible pressure sensors. Here, we designed a pressure sensor that utilizes a nanoscale iontronic interface of an ionic gel layer and a micropillared electrode, for highly linear capacitance-to-pressure response and high sensitivity over a wide pressure range. The micropillars undergo three stages of deformation upon loading: initial contact (0–6 kPa) and structure buckling (6–12 kPa) that exhibit a low and nonlinear response, as well as a post-buckling stage that has a high signal linearity with high sensitivity (33.16 kPa−1) over a broad pressure range of 12–176 kPa. The high linearity lies in the subtle balance between the structure compression and mechanical matching of the two materials at the gel-electrode interface. Our sensor has been applied in pulse detection, plantar pressure mapping, and grasp task of an artificial limb. This work provides a physical insight in achieving linear response through the design of appropriate microstructures and selection of materials with suitable modulus in flexible pressure sensors, which are potentially useful in intelligent robots and health monitoring.

Enhancing and controlling parametric instabilities in mechanical systems

We gain new fundamental insights on parametric instabilities that are at the heart of many physical phenomena from the dynamic buckling of slender structures in periodic compression to the emergence of Faraday waves or the spontaneous symmetry breaking in Floquet time crystals. Combining theoretical models and precision desktop experiments, we explain how to periodically vary the evolution function of a dynamical system to enhance and get control on parametric instabilities. We show on a proof of concept that is an electromagnetic pendulum: (i) how to observe extremely high orders of parametric resonance, even in the presence of dissipation, (ii) how to trigger and efficiently sustain the natural vibrations of an oscillator. The presented concepts being universal, they could offer new dynamical functionalities in various fields and at any scale, from actuation in soft robotics to vibrational motions in microelectromechanical resonators.

A Generalized Approach to Estimating the Out-of-plane Buckling of Steel Sections with a Triangularly Corrugated Web

Building practice shows that I-sections consist of flanges and corrugated web could be quite effectively used for the construction of compressed structures. In the present work, an investigation into the behaviour and design of steel bending and compressed members with the triangularly corrugated web is carried out. Based on the result of the finite element analysis (FEA) conducted by the ABAQUS an attempt is made to generalize approaches in the evaluation of the stability of such structures. The necessity for this work is since, in the most building codes and studies, the issues of the global buckling of such structures are considered separately for beam structures and for structures at central and eccentrical compression. Most of the building codes do not provide any recommendations and requirements for the design of compression members with corrugated webs at all and only consider the case of bending. It is shown that beam and column structures with triangularly corrugated web works almost identically in case of out-of-plane buckling. Finally, is proposed an expression allow to calculate the critical force in flanges of the cross-section in case of out of plane buckling caused by transverse bending, axial of eccentrical compression uniformly, that could be useful for practical structural design.

The simplified analysis method of nonlinear buckling and displacement of latticed structure

In order to simplify the modeling process of building complex lattice structures by finite element analysis software, a simplified method for nonlinear buckling and deformation analysis of lattice structures based on equivalent inertia moment method is proposed. By comparison with the displacements, the latticed structure is equivalent to a solid structure, and the expression of the equivalent inertia moment of a typical latticed structure is given. The finite element analysis software ANSYS is used to analyze the buckling problem and the deformation of latticed structure and the equivalent solid structure, furthermore, the load-displacement curves of the actual structure and equivalent model are obtained. The results show that the simplified analysis method of nonlinear buckling and deformation of latticed structure is feasible and can satisfy the needs of engineering design.

Experimental Damage Evaluation of Honeycomb Sandwich with Composite Face Sheets under Impact Load

Aerospace structures are highly vulnerable to impact loads whose damage tolerance, and its resistance vary over the range of impact velocity. Honeycomb sandwich structures are used in aerospace industries where mass efficient and impact resistant structures are needed. However, the structural integrity of these structures is reduced by impact load due to tool drop, runway debris, hailstones and improper handling of the structure. A thorough investigation of the damage behaviour of honeycomb sandwich under low-velocity impact and the post-impact residual strength determination is required to design a crashworthy lightweight structure. This paper presents the experimental evaluation of specific energy absorption using Charpy impact, residual compressive strength by compression after impact and damage evaluation of honeycomb sandwich structures having composite face sheets. Parametric studies on composites and honeycombs are carried out by varying the cell size, cell thickness, core height, impact velocity, thickness and orientation of lamina. Densely packed thick honeycombs provide higher fracture energy. Under transverse compressive loading, the honeycomb core undergoes cell wall buckling, crushing and densification. Load-displacement history under in-plane compression and compression after impact for different impact energies is observed. The present study contributes for the understanding how various parameters affect the characteristics of face sheet indentation and plastic buckling of honeycomb sandwich structures with composite face sheets, thereby providing useful guidelines for its potential applications in impact engineering.

A Cell-Based Smoothed Finite Element Method for Modal Analysis of Non-Woven Fabrics

The combination of a 4-node quadrilateral mixed interpolation of tensorial components element (MITC4) and the cell-based smoothed finite element method (CSFEM) was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures. This formulation was applied to numerous numerical examples of non-woven fabrics. As CSFEM schemes do not require coordinate transformation, spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two, three and four smoothing cells. An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors, which allowed to remove the integral operator in the strain smoothing operation. This procedure conducted both to the simplification of the developed formulation and the reduction of computational cost. A wide range of values for the thickness-to-length ratio and edge boundary conditions were analysed. The developed numerical model proved to overcome the shear locking phenomenon with success, revealing both reduced implementation effort and computational cost in comparison to the conventional FEM approach. The cell-based strain smoothing technique used in this work yields accurate results and generally attains higher convergence rate in energy at low computational cost.

Approximate analytical solution of buckling of multi-damaged column-like structures using a continuous diffused crack model by variational iteration method

Compressive structural members can be locally damaged by overloading, corrosion, car crash and fire. In this work, a continuous diffused crack model is proposed to study the static stability of Euler–Bernoulli rectangular column-like structures under different boundary conditions. The governing differential equation is formulated by adopting a diffused crack model. The powerful variational iteration method is implemented to find the approximate analytical buckling modes and buckling loads based on the buckling response of the intact column. A novel generalized Lagrange multiplier is derived. The proposed method incorporates the effects of the crack width into consideration when deriving the buckling modes. The stability equation allows addressing the influences of multiple damages and can be applied to both concentrated and distributed cracks. The famous Rayleigh–Ritz method is utilized to verify the computed buckling loads. The proposed diffused crack model and the application with VIM is efficient and accurate for handling buckling problems of cracked columns under different boundary conditions.