Postbuckling Behavior Research Articles

Post-buckling behavior and collapse of Double-Double composite single stringer specimens

This paper presents the work on six single-stringer specimens manufactured using the card-sliding technique with non-crimp fabrics and adopting a Double-Double (DD) stacking sequence. These specimens, representative of sub-structure level components, are used to investigate post-buckling and failure in aerospace structures. Two specimens maintain a constant thickness cross-section, while four are tapered, two of which incorporate a Teflon insert in the stringer flange. All specimens are tested under compression loading conditions, inducing skin buckling, skin-stringer separation, and eventual collapse. Numerical simulations are validated by experimental results and serve to analyze the specimens behavior and the failure mode. The load versus displacement curves of both experimental tests and Finite Element Method (FEM) analyses are compared, along with the out-of-plane displacement field. Subsequently, the observed failure modes are discussed, focusing on the various mechanisms that occurred and considering the impact of flanges and stiffener tapering. Both the FEM simulations and experimental tests demonstrate good agreement, with the flanges tapering revealing notable results. This offers promising evidence of a viable solution to optimize aeronautical structures and enhance resistance to skin-stringer separation.

Buckling failure analysis of storage tanks under the synergistic effects of fire and wind loads

Fire-induced domino effect is one of the main threats to hazardous material storage tanks, and many attempts have been conducted to assess the vulnerability of storage tanks exposed to fire to evaluate domino effect risk. However, past research ignored the influence of wind load on the thermal buckling behavior of storage tanks exposed to fire, which may underestimate the risk of exposed tanks. This paper thus conducts a numerical simulation of the thermal buckling behavior of steel vertical dome storage tanks under the synergistic effect of static wind loads and thermal effects. The effects of wind parameters and heat radiation parameters on the thermal post-buckling behavior and the time to failure (ttf) of storage tanks are investigated to analyze the synergistic effects of fire and wind loads. By comparing the circumferential and meridional stresses before and after the thermal post-buckling stage, it is found that under the disturbing effect of the positive wind pressure load, the thermal post-buckling of the tanks on downwind occurs earlier and more severe. Besides, the effects of wind angle, fire location height, and diameter on buckling damage were investigated. The comparative analysis of different scenarios shows that the tanks in the windy scenario are more prone to thermal post-buckling, and the deformation is intensified, with an increased likelihood of failure.

Mechanics and topology of twisted hyperelastic filaments under prescribed elongations: Experiment, theory, and simulation

Soft filaments can be stretched, bent, and twisted, exhibiting complex configurations. When a filament undergoes large torsional deformation, it can display instabilities, and its post-buckling behavior and configuration evolution differs significantly from that observed under small deformation. We study the mechanics and topologically complex morphologies of twisted rubber filaments under prescribed elongation by combining experiment and finite strain theory. Based on the Mooney-Rivlin model, a finite strain theory of the hyperelastic filament under combined tension, bending, and torsion has been established, accounting for both geometrical and material nonlinearities. An experimental and theoretical morphological phase diagram is constructed as a function of the twist density and the initial elongation. The buckling and post-buckling behaviors of the twisted rubber filaments under prescribed elongation are well captured by the theory that considers geometrical nonlinearity and self-contact. By tracking the interconversion of link, twist, and writhe, we accurately determine the configuration and the critical points of phase transitions. The theoretical predictions agree closely with the measurements. This work sheds light on understanding the morphological complexity of the loaded hyperelastic rod.

Exact solution of post-buckling behavior of porous piezoelectric nanobeams with surface effects

Exact solution of post-buckling behavior of porous piezoelectric nanobeams with surface effects

Can we really solve an arch stability problem?

We bring attention to the problem of solving nonlinear boundary-value problems for elastic structures such as arches and shells. Here we discuss a classical problem of a shear-deformable arch postbuckling. Considering a postbuckling behaviour of a circular arch we discuss the possibility to find numerically a solution for highly nonlinear regimes. The main attention is paid to the problem of determination of all solutions. The main conclusion that there is no guarantee to find all solutions, in general.

Buckling and post-buckling analysis of composite wing box under loads with torsion-bending coupling

In this paper, a mathematical model for the effect of different torsion-bending ratios on buckling and failure loads under complex operating conditions was proposed, and the buckling, post-buckling and failure behavior and mechanism of carbon fiber composite wing box were studied by combining experiments and simulations. A high-precision computational simulation model was established by considering detailed bolt arrangement information, as well as damage and failure of composite materials. The predicted buckling loads, failure loads, and damage modes are in good agreement with the experimental results. The results show that, under the condition of constant bending moment, as the torque increases, the linear strain of the box section remains consistent, while the shear strain increases significantly, leading to a change in the buckling mode and failure distribution. When the torsion-bending ratio is less than 2.0, the loading form of the structure is greatly affected by the torque. On the contrary, the buckling and failure loads are exponentially close to the pure torsional state. The mathematical model and simulation model in this study can provide an important reference for the structural design and failure mechanism analysis of large composite wing boxes.

Design, analysis and testing of thermoplastic welded stiffened panels to investigate skin-stringer separation in post-buckling

Thermoplastic composite three-stringer panels with omega stiffeners and conduction welded joints are designed, analysed and tested until final failure to investigate the performance of the welded joint in post-buckling. The three-stringer panels are designed to be structurally representative of the fuselage demonstrator of the Clean Sky 2 project STUNNING. A simplified model of the fuselage keel section is analysed by finite element analysis, using the virtual crack closure technique to model skin-stringer separation of the welded joint. The post-buckling and skin-stringer separation behaviour of the fuselage section is then adopted as the reference for the design of the three-stringer panels. Two panels are then tested. The test setup utilises digital image correlation to measure the deformation of the panels, and a high-speed camera to capture the final failure mode. The panels failed in post-buckling due to the separation of the middle stringer, with unstable separation growth followed by separation of the outer stringers and then stringer fracture. The numerical analysis of the panels, with geometrical imperfections included, is able to predict the structural behaviour accurately, with only minor differences in buckling shape and separation behaviour.

Efficient buckling and post-buckling analysis of porous FG sandwich beams by new RPIM-HOCM mesh-free approach

The main purpose of this paper is to analyze buckling and post-buckling behavior of porous functionally graded (FG) beams and sandwich beams using a new efficient optimal mesh-free high order algorithm. The proposed solver combines mesh-free approach based on radial point interpolation method with high order continuation method (RPIM-HOCM). It is assumed that the FG beam and FG layers of sandwich beam are made from a mixture of ceramic and metal such that bottom surface of the plate is metal-rich, whereas top surface is ceramic-rich. So, constitutive equation as well as material properties are considered to change smoothly and gradually in the thickness direction via a mathematical relationship distribution. Non-linear strong form of the beam buckling problem which is based on the first-order shear deformation theory (FSDT) is derived using the virtual displacements theorem. The proposed coupling (RPIM-HOCM) is presented and validated firstly by comparing obtained numerical results with those computed using a reference algorithm. Then, RPIM-HOCM solver is used to investigate the effect of power-law index, porosity distribution, span-to-height ratio, boundary conditions and skin-core–skin thickness ratio on critical buckling load and post-buckling behavior.

Isogeometric Dynamic Buckling Analysis of Trimmed and Multipatch Thin-Shell Structures

This paper extends our previous work on the isogeometric dynamic buckling analysis of thin-shell structures to the trimmed and multipatch situation where features such as cutouts and stiffeners can be easily incorporated. To be specific, a modified generalized- time integration scheme combined with a geometric nonlinear isogeometric Kirchhoff–Love shell element is used to simulate the complex buckling and postbuckling behaviors of thin-shell structures. The developed method can damp properly high-frequency contents while maintaining second-order accuracy in the dynamic buckling analysis. For the integration of arbitrary-shaped trimmed elements, a geometrically exact blending function method is developed to improve the efficiency of the dynamic shell buckling analysis. To deal with multipatch geometries, a penalty-based weak coupling approach is developed, where coupled patches with nonconforming trimmed interfaces or even with prescribed angles, such as stiffeners, can be analyzed. We demonstrate the accuracy, stability, and flexibility of the proposed framework with several numerical examples. In particular, the influences of “free” and “partially free” control points, penalty factor, trimming, as well as different modeling strategies on the dynamic solutions of shell structures are investigated.

Approximate postbuckling analysis of shear deformable laminates

AbstractIn the lightweight design of aircraft, spacecraft and marine vessels, often advanced materials are utilised. Advanced materials such as laminated composites made of fibre‐reinforced plastics show transverse shear deformations if they are considered “thick” or possess little transverse shear stiffness. In most cases, the effect of the shear deformations is neglected, and few computational models exist that consider the closed‐form approximate analysis of the postbuckling behaviour. Thus, a new computational model based on high‐order shear deformation theories is introduced. The solution is derived based on the principle of the minimum of the total elastic potential and is evaluated in comparison to finite element analyses. The highly efficient approximate computational model is developed to offer a valuable tool for the preliminary design of lightweight structures utilising shear deformable advanced materials.

An explicit analytical description for deep post-buckling behaviors of substrate-free films with complex in-plane biaxial loads

Substrate-free films (i.e., films with in-plane and out-of-plane constraints only on some or all edges) can be found everywhere in nature, daily life, and industrial applications. The theory of their buckling and wrinkling behavior has been mature and widely used in engineering. Significant progress has been made in numerical computation of film instability. However, on the one hand, the inherent drawback of numerical calculations is that they cannot provide explicit results, and the relevant mechanism and parametric analysis are limited; on the other hand, the widely used finite element simulation is difficult to compare the energy of different modes, because the mode is always constrained to a certain order in the simulation (they cannot perform the post-buckling of specified higher order modes as the calculation process is guided by the inherent energy minimization mechanism of the computational frameworks and the higher order modes were excluded). Such two aspects constrain the mechanism study of deep post-buckling related behaviors that dependent on accurate and explicit descriptions of high order modes, e.g., the deep post-buckling bifurcation/secondary buckling. As a result, an explicit analytical description for deep post-buckling behaviors of films is still of significant research value. Reviewing classical explicit analytical descriptions, in any case of the explicit descriptions by multiple trigonometric series method, Galerkin method and perturbation method, in essence, at most three terms of double trigonometric series are used to describe the post-buckling behaviors of thin films explicitly, which always introduces significant error when the film enters deep post-buckling stage. To overcome the stated problems, herein, considering a uniform rectangular film model with arbitrary in-plane loads, and based on the Galerkin method, we firstly develop a high-precision explicit analytical description for the deep post-buckling behaviors of films upon complex in-plane biaxial loads, which proposes a new insight on the buckling mode transition upon extremely deep post-buckling or complex biaxial loads, and suggests that the correct solution of the deep post-buckling bifurcation/secondary buckling requires a complete dynamic model. The research results have theoretical significance on improving the instability mechanical system of thin films, and can also provide theoretical basis for precise control of wrinkle morphology and design of film devices corresponding applications.

Nonlinear stability and design of prestressed stayed columns in fire considering non-uniform temperature distribution

Prestressed stayed columns are vulnerable to fire due to material weakening. The fire behaviour of the stayed columns is investigated with non-uniform temperature distributions considered using steady state analysis within ABAQUS. This study aims to reveal the load-carrying capacity reduction of stayed columns in fire and propose a design method. Results show that ultimate loads decrease with temperature increasing, and the stayed columns approximate failure at the temperatures higher than 600°C. The failure deflected mode maintains similar to the dominant linear buckling mode for the uniform temperature distribution, and the sensitivity of ultimate loads to prestressing levels becomes less significant at higher temperatures. Moreover, compared to buckling and ultimate behaviour, initial post-buckling behaviour shows more significant sensitivity to temperature distributions. The non-uniform distribution can lead to asymmetric deflected mode due to stiffness re-distribution from the material weakening at elevated temperatures, and the post-buckling behaviour of the cases with rotational symmetric mode dominance is sensitive to prestressing levels. Finally, a fire design method is proposed based on the ultimate load reduction in fire.

A new analytical approach to the nonlinear buckling and postbuckling behavior of functionally graded graphene reinforced composite laminated cylindrical, parabolic, and half‐sinusoid shallow imperfect panels

AbstractThis paper presents and analyzes the nonlinear buckling responses of three types of shallow imperfect panels (cylindrical panel, parabolic panel, and half‐sinusoid panel) made from functionally graded graphene reinforced composite (FG‐GRC) on nonlinear elastic foundations subjected to axial compressive load in thermal environments. The nonlinear governing equations are formulated on Reddy's higher‐order shear deformation shell theory (HSDST) and take into account von Karman‐type nonlinearity. A new approximation technique to determine the stress function in average sense is developed and Galerkin's method is used to obtain the algebraically nonlinear equation system. Then, the simple calculation process can be used to solve the obtained equation systems, and the formulations to calculate the critical buckling loads and postbuckling load‐deflection curves are expressed in explicit form. The results can be flexibly applied to FG‐GRC panels with different curvatures in engineering designs. The effects of panel types, geometrical parameters, temperature increase, initial imperfection, and nonlinear elastic foundations on the critical buckling loads and postbuckling curves of cylindrical, parabolic, and half‐sinusoid FG‐GRC panels are discussed in numerical results. Numerical results also show a small disadvantage in the load‐carrying capacity of cylindrical panels compared to parabolic panels and half‐sinusoid shallow panels.Highlights Postbuckling of cylindrical, parabolic, and half‐sinusoid panels are studied. The panels are made of functionally graded graphene reinforced composite. Reddy's higher‐order shear deformation shell theory is applied. A new approximation technique to determine the stress function is developed. Critical buckling loads and postbuckling expressions are explicitly obtained.

Post-buckling behavior and failure analysis of asymmetric sandwich panels under uniaxial compression

Sandwich structures with an asymmetric configuration are employed to introduce in-plane loads as well as to connect them with other structural components. Understanding their failure mechanism is crucial to ensure the safety design of aircraft. This paper investigates experimentally and numerically the mechanical behavior of asymmetric sandwich panels (ASPs) under compression. Quasi-static tests are conducted to obtain the buckling loads, post-buckling behavior, and load-bearing capacity of ASPs. A non-linear finite element (FE) model is developed to elucidate their damage behavior and failure mechanism. Numerical predictions are compared with test results to validate the FE model and failure analysis. The results demonstrate that the presence of a tapered region significantly influences stress distribution and failure initiations. A parametric study is also conducted to investigate the effects of the tapered angle on the compression response of ASPs. The reported results can provide a reference for the optimal design of ASPs.

Material nonlinearities yield doubly negative holey metamaterials

Mechanical metamaterials with negative stiffness and negative Poisson’s ratio are exciting prospects for advanced material design. A plastic column with a series of periodically-spaced holes exhibits both of these properties when buckled under compression. In this paper, the behaviour of such a column under compression is measured experimentally and described with a simple mathematical model. This model predicts the compression, buckling and post-buckling behaviour of the entire column from the mechanical response of the thin ligaments of material that form the column’s microarchitecture to compression, rotation and shear forces, which are characterised experimentally, The softening behaviour in holey columns beyond the critical level of compression for pattern transformation is shown to be due to material constitutive nonlinearities in the rotation and shear response of the microarchitecture. Geometric perturbations to the columns can cause the observed pattern to change, but result in approximately the same force–displacement measurements as for the column with perfect geometry. This approach provides a useful framework to study systems where both geometric and material nonlinearities underpin observed phenomena.

Influence of surface effect on post-buckling behavior of piezoelectric nanobeams

Piezoelectric nanobeams with excellent mechanical, thermal and electrical properties are important components in micro-nano electromechanical systems, which are widely used as sensors, brakes and resonators. Based on the Euler–Bernoulli beam model, the influence of surface effect on the post-buckling behaviour of piezoelectric nanobeams is analysed. According to the surface elasticity theory and the ‘core–shell’ model, the surface energy model is used to introduce the influence of surface effect. The governing equations and boundary conditions of the post-buckling of piezoelectric nanobeams under the influence of surface effect are derived by the principle of minimum potential energy. The analytical solution of post-buckling is obtained by the eigenvalue method. The influence of surface effect on the post-buckling configuration, post-buckling path, amount of induced charge and critical load of piezoelectric nanobeams with different external constraints and cross-sectional dimensions are discussed. The results show that surface effect has a significant influence on the post-buckling of piezoelectric nanobeams. Considering surface effect, the effective elastic modulus and critical load of piezoelectric nanobeams are increased, and the post-buckling configuration, post-buckling path and amount of induced charge are reduced. These findings contribute to the study of micro-nano electromechanical systems based on nanobeam structures and provide a theoretical basis for the design and manufacture of nanodevices.

Unification of Large Amplitude Vibration and PostBuckling Behavior of Structural Members

In the deign of the modern aerospace structural members, due the stringent requirement of light weight and low margins of safety, it is essential to establish the design adequacy by evaluating the stiffness related behavior, like the large lateral amplitude/deflection vibration and postbuckling, through a rigorous geometric nonlinear analysis. Though many complex formulations, either by using the continuum or numerical methods are available in the literature, the heuristic formulae developed recently, for these entirely different nonlinear problems, are similar. Hence, it is possible to unify, these simple formulae, not recognized till now. The unification of these formulae facilitates to obtain the solution for the large amplitude vibration problem from the known solution of the postbuckling of the structural members and vice versa, for a specified lateral amplitude/deflection. This novel concept of the unification is successfully demonstrated through the isotropic uniform beams/columns and thin square plates.

Thermal Postbuckling Analysis of Thin Uniform Square Plates On Winkler Foundation - Effect of Use of Green’s Strain-Displacement Relations

A new simple formulation is developed in this paper, to predict the realistic thermal postbuckling behavior of the square plates, on Winkler foundation. If the plate is subjected to a uniform temperature rise, and also undergoes large deflections, mechanical equivalent inplane compressive, and tensile loads are developed, with the condition of the inplane immovability of the normal edge displacements of the plate. The nature of the distribution of these inplane compressive and tensile loads are similar, but have different magnitudes, which act along the x- and y- directions of the plate. The use of the Green’s nonlinear strain-displacements relations, which do not impose any restriction on the magnitude of the large deflections, to predict the realistic thermal postbuckling loads. The thermal postbuckling results of the plates obtained from this formulation, are validated indirectly, as the corresponding results are not available in the literature, with those of the columns without the elastic foundation. For the non-zero values of the foundation parameter, the present numerical results of the plates, with respect to the central deflection, show the proper physical trends of the nonlinearity, and demonstrate the simplicity of the present formulation.

Prediction of Thermal Postbuckling Behavior Of Uniform Shear Flexible Column Undergoing Large Lateral Deflections Through An Intuitive Formulation

This paper presents a simple intuitive formulation to predict the thermal postbuckling behavior of uniform shear flexible columns, subjected a uniform temperature rise from its stress free condition, undergoing large lateral deflections. The two ends of the columns are restrained to move axially, so that a mechanical equivalent of the constant compressive load is developed, due to the increase in temperature. The proposed formulation is based on the use of nonlinearities existing in both the axial displacement and lateral deflection, which differs from the von-Karman type nonlinearity due to the moderately large lateral deflections only. In this paper, a simple analytical formula is developed to predict the thermal post buckling behavior of columns, considering both the nonlinearities. The numerical results obtained from the developed intuitive formulas match very well, for the slender columns. Since, there are no results available in the literature, to compare the current results with the case of the shear flexible columns, the authors are of the opinion that the trends of these results, given in this paper, show that there is a reasonable probability that the present results are reliable.

The Effect of Prefabricated Damage on Compression Behaviour of Stiffened Composite Panels

Experimental investigations were conducted on the post-buckling behaviour and the failure behaviour of hat-stiffened composite panels. Two types of panels were tested, including undamaged and pre-damaged configurations. All panels were loaded under unidirectional compressive loading until collapse. The presence of a disbond between skin and stringer weakened the ultimate failure strength evidently but did not affect the overall structural stiffness significantly. The debonding defect affected the buckling response and changed the post-buckling deformation and failure behaviour of stiffened panels. For the pre-damaged type, massive debonding in the interface between skin and stiffener was detected, which led to the reduction of the load capacity of the structure, and a small margin between buckling load and failure load was observed.