Buckling Of Structures Research Articles

A consistent approach for global buckling of steel structures

AbstractThe ”General Method“ according to chapter 6.3.4 of EN1993‐1‐1 or 8.3.4 of prEN1993‐1‐1 deals with the verification of stability problems of frame and beam structures with loadings in‐plane. The ”General method“ according to Eurocode is intended for the general case of a combined moment and normal force. For the choice of the reduction factor χop, there are two options for applying the reduction curve, either the minimum of lateral torsional buckling (LTB) and flexural buckling (FB) or a weighted combination of both. With the use of analytical derivations, it can be shown that this approach leads to inconsistencies which can possibly lead to incorrect results. In this paper an alternative approach is presented which leads to unification and fully mechanical justification in verification. The approach allows e.g. the verification of stability of an entire frame system directly and without interaction factors (as in the equivalent member method). In addition, the issue of a consistent equivalent imperfection is addressed. With the use of this method, geometrical non‐linear analyses of structures showing out‐of‐plane instability can be omitted; only an in‐plane calculation and a determination of a linear buckling analysis is necessary. Finally, examples are presented in this paper that demonstrate the application of the approach shown.

Installation performance of structurally enhanced caissons in sand

Suction caissons are attractive solutions to support offshore structures. Their capacity, both pull-out and bearing, grows with their embedment depth. However, higher embedment depths increase risks of installation failure due to uncertainty of seabed condition, increased chance of piping and structural buckling. For the first time, this paper investigates installation of structurally enhanced caissons (SECs), in the form of flanges attached to the caisson shaft, through developing a numerical procedure based on finite element analysis. The SEC has the potential to offer additional (over 20%) pull-out and bearing capacity compared with standard caisson and can have substantial positive impacts on torsional capacity. Using the proposed numerical procedure, the impact of adding the flanges on the installation resistance was studied and compared against a standard caisson. A piping criterion was defined which allows tracking the soil region where piping develops and evolves as the installation proceeds. The impacts of flange base sizes and sand compaction on the required suction for installation were studied. The results of this paper can be used as guidance to predict the required suction to install flanged caissons and can facilitate the uptake of the proposed SEC. The proposed numerical framework is applicable to other SEC geometries.

Experimental and numerical investigation of large-scale effect on buckling and post-buckling behavior of tubular structures

In this paper, compressive behavior of tubular structures made of aluminum and multilayer carbon fiber reinforced plastic (CFRP) are studied experimentally and numerically. Results show that current evaluation of aluminum tubes using Johnson–Euler method overestimates the critical stress values of the tubular structure because local failure is ignored. A finite element analysis (FEA) model based on Riks method is proposed to re-evaluate compressive performance and failure modes of aluminum tubes. This model is modified for laminated composites by introducing damage model based on Hashin’s theory, such as matrix tensile/compressive failure, and fiber tensile/compressive failure. Simulation results of CFRP tubular structure show close agreement with experimental results, but also sensitive to geometric constants. Material failure is primarily the failure mode of tubes with slenderness ratios under 21. A mixed failure mode can be found for slenderness ratios of tubes between 21 and 35. For tubes with slenderness ratios above 35, buckling failure is the primary failure mode.

Topology optimization of multiscale structures considering local and global buckling response

Much work has been done in topology optimization of multiscale structures for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based work by Bendsøe and Kikuchi from 1988, which lately has been revived due to advances in manufacturing methods like additive manufacturing. Orthotropic microstructures locally oriented in principal stress directions provide for highly efficient stiffness optimal designs, whereas for the pure stiffness objective, porous isotropic microstructures are sub-optimal and hence not useful. It has, however, been postulated and exemplified that isotropic microstructures (infill) may enhance structural buckling stability but this has yet to be directly proven and optimized. In this work, we optimize buckling stability of multiscale structures with isotropic porous infill. To do this, we establish local density dependent Willam–Warnke yield surfaces based on local buckling estimates from Bloch–Floquet-based cell analysis to predict local instability of the homogenized materials. These local buckling-based stress constraints are combined with a global buckling criterion to obtain topology optimized designs that take both local and global buckling stability into account. De-homogenized structures with small and large cell sizes confirm validity of the approach and demonstrate huge structural gains as well as time savings compared to standard singlescale approaches.

The research of buckling and post-buckling behavior of bidirectional stiffened composite panel under discrete impact

PurposeIn this paper, an attempt is made to obtain buckling loads, ultimate bearing capacity and other required structural characteristics of grid structure panels. The numerical method for post-buckling behavior analysis of panels involving multiple invisible damages is also presented.Design/methodology/approachIn this paper, two bidirectional stiffened composite panels are manufactured and tested. Multiple discrete invisible damages are introduced in different positions of the stringers, and the experimental and simulation investigation of buckling and post-buckling were carried out on the damaged stiffened panels.FindingsThe simulation load–displacement curves are compared with the experimental results, and it is found that the simulation model can well predict the occurrence of buckling and failure loads. The strain curve shows that the rate of strain change at the damaged site is greater than that at the undamaged site, which reflects that the debond is more likely occurred at the damaged site. The simulation verifies that the panel is usually crushed due to matrix compression and fiber–matrix shear.Originality/valueIn this paper, post-buckling tests and numerical simulations of bidirectional stiffened composite panels with impact damage were carried out. Two panels with four longitudinal stringers and two transverse stringers were manufactured and tested. The buckling and post-buckling characteristics of the grid structure are obtained, and the failure mechanism of the structure is explained. This is helpful for the design of wall panel structure.

Multi-material topology optimization for maximizing structural stability under thermo-mechanical loading

Mechanical structures are often simultaneously subjected to thermal and mechanical loading, both of which can lead to buckling failure. Developing efficient structural forms with better capacity for stability is important to keep structures safe. This study aims to optimize structural buckling capacity by using a density-based topology optimization scheme. Instead of treating the mechanical and thermal loadings as a single coupled part in the linearized buckling analysis, the effects of mechanical and thermal loadings are decoupled, which allows to separately analyze and optimize buckling aspects induced by mechanical or thermal loading. Two optimization models based on the decoupled analysis models are developed to respectively maximize the critical load factor of buckling induced by mechanical loading under a specified thermal loading and buckling induced by thermal loading under a specified mechanical loading. Further, based on a three-phase material model, a multi-material topology optimization scheme is employed to optimize the buckling capacity of active structures made of structural and actuating materials and prestressed structures containing prestressed components. The actuation effects are mimicked by the thermal loading of active material. The sensitivities of the objective functions and constraints are derived through the adjoint technique, and the method of moving asymptotes (MMA) is employed to solve the topology optimization problems. Numerical examples are adopted to verify the effectiveness of the proposed approach.

Time-dependent non-linear buckling of 3D CFST arch structures with hybrid random interval uncertainties

Limit point and bifurcation buckling loads are critical concerns in structural stability design. With the inevitable viscoelastic effects of creep and shrinkage in concrete, such critical buckling points may vary due to the time-dependent change of equilibrium configuration. Furthermore, the intrinsic uncertainty and natural randomness in the geometry and material characteristics would affect the structural stability performance significantly. The present study provides a new robust method, called the generalized Chebyshev surrogate model-based sampling approach, in assessing the time-dependent nonlinear buckling behaviour of 3D concrete-filled steel tubular (CFST) arch structures when both random and interval uncertainties are involved. In the proposed approach, the relationships between the uncertain parameters and the critical nonlinear limit and bifurcation buckling loads are formulated using Chebyshev surrogate model strategy combined with finite element method. The extreme bounds of the statistical features, including means, standard deviations, of the critical nonlinear buckling loads are furnished by using Monte Carlo method and Quasi Monte Carlo simulation method. Finally, the applicability and the validity of the proposed approach are illustrated with a series of numerical investigations.

Tuning the elastic buckling of a soft block with graded material stiffness

Elastic buckling of slender structures is of high interest in engineering since the buckling could bring many unintended and disastrous consequences. The critical load of buckling in nonlinear elasticity can be highly affected by either the structure’s geometry or the material properties. This paper studies the buckling behaviors of an elastic block of soft materials with graded modulus at finite deformation. We give the total potential energy of the conservative system and formulate a boundary-value problem and its incremental forms. We solve the buckling problem analytically for an elastic block of neo-Hookean materials. Though our problem is different from Euler’s buckling, our results agree well with the Euler’s formula in the case of slender columns. In addition, our analysis can be used to predict the buckling load of short columns. Since our loading device controls the displacement of the block, the critical load is computed by using the critical stretch at which the loaded block begins to buckle. Depending on the varied forms of the moduli, the graded modulus can tune the critical load. The forms of the linear and exponential functions of the Young moduli of the material can only reduce the critical load. However, the quadratic form can either reduce or increase the critical load by about 50%, making a weaker or stronger structure without changing its geometry. This paper contributes to our understanding of the buckling behaviors of elastic structures with graded moduli.

Prediction on Welding Induced Buckling of Plate Panel Structure and Its Mitigation by Transient Thermal Tensioning

Prediction on Welding Induced Buckling of Plate Panel Structure and Its Mitigation by Transient Thermal Tensioning

Study on vibration isolation system using buckling of beams and honeycomb structures

Study on vibration isolation system using buckling of beams and honeycomb structures

Numerical investigation of thermal buckling and post-buckling behavior of an EN AW 6016-T4 car roof assembled in a steel body-in-white

The automotive industry is undergoing significant changes driven by factors such as reducing carbon dioxide emissions, advancing technology, evolving regulations, and the emergence of new energy sources. Lightweight materials, particularly aluminum alloys, are being extensively researched and integrated into vehicles to reduce weight and improve performance. However, the heating process during vehicle production can cause thermal buckling in thin aluminum alloy structures, affecting their appearance and quality. While thermal buckling has been studied in other industries, research in the automotive sector, particularly for non-structural parts like car roofs, is limited. This study uses numerical simulation to predict thermal buckling and post-buckling behavior of a EN AW 6016-T4 alloy car roof assembled in a predominantly steel body-in-white. The research findings indicate that roof buckling occurs at a relatively low temperature difference of approximately 60 °C, which is lower than the maximum temperatures experienced during the painting phases in the automotive industry. Consequently, undulations in the roof's shape become apparent, underscoring the importance of design modifications to ensure visual conformity. Validation through physical testing confirms the model's accuracy, providing valuable insights for designing lightweight structures with improved performance and aesthetics.

Energy harvesting from mechanical vibrations: self-rectification effect.

The use of environmental vibrations as an energy source for stimulating small-scale energy harvesting (EH) devices has received significant attention in recent years. The conversion of alternating currents (AC) to direct currents (DC) is essential to powering electronic devices effectively. This study proposes a method where hexagonal boron nitride nanoribbons and nanotubes harvest energy and rectify the output voltage simultaneously with no need for an external rectifying circuit. This is a step to eliminate the necessity of batteries for EH devices, which require a constant power supply to generate electrical energy while maintaining their nanoscale dimensions. A molecular dynamics approach was used to simulate the response of boron nitride structures to mechanical vibrations. The polarization and voltage generated under tensile and compressing strain fields were calculated, and it was demonstrated that the buckling of the nano-mechanical structures could be engineered to rectify the generated voltage. This paves the way for the design of more efficient and scalable energy harvesting devices.

Methodology and application to assess thermo-mechanical buckling in composite marine structures

This paper describes the research performed within the scope of H2020 project FIBRE4YARD in the development of a suitable thermo-mechanical framework to analyse composite structures under fire loads. The thermo-mechanical model uses the adiabatic temperature to obtain the through-thickness distribution of temperature of the triangular shell element, this formulation is able to predict phenomena such as pyrolysis, thermo-mechanical yielding and large displacements (non-linear buckling). An application case of a load-bearing section of a container ship is shown to demonstrate the correctness of the methodology, two type of materials are considered in the analysis, traditional materials such steel and advanced materials like fibre reinforced plastic (FRP) composites.

Revision of EN 1993‐1‐1 – Design rules for structural analysis, cross‐sectional resistance and member buckling

Revision of EN 1993‐1‐1 – Design rules for structural analysis, cross‐sectional resistance and member buckling

Comprehensive analyses of buckling and stress failure of high-field pulsed magnets under biaxial Lorentz force body load

This paper will discuss the failure mechanism of high field pulsed magnets based on a failed pulsed magnet of 85 T. Firstly, the stress failure possibility is analyzed by an ANSYS-ACP finite element model. The results show that the stress failure risk is low. Then a comprehensive model including both stress failure and structural buckling is proposed and discussed. It is found that the structural buckling and stress failure would co-exist and interact with each other. The model predicts the pulsed magnet suffered from stress failure after structural buckling and finally collapsed at 79 T. The consistency of the theoretical results with that in experiments show the validity of the comprehensive model.

Phononic Stiefel-Whitney topology with corner vibrational modes in two-dimensional Xenes and ligand-functionalized derivatives

Two-dimensional (2D) Stiefel-Whitney (SW) insulator is a fragile topological state characterized by the second SW class in the presence of space-time inversion symmetry. So far, SWIs have been proposed in several electronic materials but seldom in phononic systems. Here we recognize that a large class of 2D buckled honeycomb crystals termed Xenes and their ligand-functionalized derivatives realize the nontrivial phononic SW topology. The phononic SWIs are identified by a nonzero second SW number $w_2=1$, associated with gaped edge states and robust topological corner modes. Despite the versatility of electronic topological properties in these materials, the nontrivial phononic SW topology is mainly attributed to the double band inversion between in-plane acoustic and out-of-plane optical bands with opposite parities due to the structural buckling of the honeycomb lattice. Our findings not only reveal an overlooked phononic topological property of 2D Xene-related materials, but also afford abundant readily synthesizable material candidates with simple phononic spectra for further experimental studies of phononic SW topology physics.

Buckling and post-buckling of variable stiffness plates with cutouts by a single-domain Ritz method

Structural components with variable stiffness can provide better performances with respect to classical ones and offer an enlarged design space for their optimization. They are attractive candidates for advanced lightweight structural applications whose functionalities often impose the presence of cutouts that requires accurate and effective analysis for their design. In the present work, a single-domain Ritz formulation is proposed, implemented and validated for the analysis of buckling and post-buckling behaviour of variable stiffness plates with cutouts. The plate model is based on the first-order shear deformation theory with nonlinear von Karman strain–displacement relationships. The plate generalized displacements are approximated with trial functions built as products of one-dimensional Legendre orthogonal polynomials. The non linear governing equations system is then deduced from the stationarity of the energy functional; the involved matrices are numerically computed by a special integration algorithm based on the implicit description of the cutout via suitable level-set functions. The formulation has been implemented in a computer code which has been used to validate the method through comparison with literature solutions for variable angle tow laminates with circular cutouts. Several investigations on buckling and post-buckling behaviour of variable angle tow composite plates with cutouts having different shapes and dimensions are then presented to illustrate the approach capabilities, provide benchmark results and point out features and design opportunities of the variable stiffness concept for the buckling and post-buckling design of advanced lightweight structures.

On the influence of manufacturing parameters on buckling and modal properties of sandwich composite structures

Sandwich structures with honeycomb cores are widely used in several applications given their promising properties, like high strength, light weight, and specific stiffness. However, these unique structures present complex behavior with failure modes that are not trivial when subjected to different loading conditions. Evaluation studies about the structural performance and failure modes of honeycomb sandwich structures with different face sheets and cores in static and dynamic conditions are scarce. Therefore, the structural behavior and failure modes of different honeycomb sandwich structures need to be evaluated to promote optimal performance in accordance with project requirements. This study seeks to characterize the structural behavior of different sandwich structures with honeycomb cores using a complete experimental comparative study. First, combinations of different types of cores and face sheets were elaborated using the Design of Experiments Method with Factorial Design, and then both the static and dynamic experimental tests were performed to obtain response variables and failure modes. The results showed that a polypropylene core in sandwich structures can increase damping. The sandwich structures manufactured with glass/aramid hybrid fabrics on the face sheets showed high strength under bending and buckling conditions, supporting a maximum bending loading of 1989 N and a maximum buckling loading of 12,700 N. Most sandwich structures had failure modes in “semi-circle” shapes. Only sandwich structures with glass fabric face sheets have failure modes in “V” shapes. Lastly, statistical results revealed that the type of core design variable contributed more to the response variability and was responsible for significantly changing the properties of stiffness, structural mass, and damping.

Revision of EN 1993‐1‐1 – Design rules for structural analysis, cross‐sectional resistance and member buckling

AbstractIn the framework of the revision of Eurocode 3, Part 1–1, several amendments have been proposed and accepted in order to improve the rules for the resistance to member buckling. For clarification, a flow chart connecting the global analysis (first or second order), the imperfections and the type of verification has been implemented for ease of use. Since the publication of the standard in 2005, many research projects have been conducted across Europe on this topic and their results have contributed to provide appropriate answers to problems identified in practice. Therefore, the revised code provides new design rules for stability. Important works of calibration have been performed in these different projects to derive appropriate values of the partial factor on the resistance side. For example, a new formulation for lateral–torsional buckling has been introduced for the calculation of the reduction factor. The consequence is a reduction of the discrepancy between the results obtained by these new methods and those from experimental or numerical tests. In order to extend the scope of Eurocode 3, Part 1–1, additional methods have been implemented in an annex to cover the stability of members with mono‐symmetric cross‐section under compression axial force, biaxial bending, with or without torsion. The format of the resistance criteria remains similar to the format of the current interaction formulae so that the designers can easily identify the evolution of the rules. This article presents in a systematic way the new implementations in the formal vote version FprEN 1993‐1‐1 of the code.

Stochastic modeling of geometric imperfections for buckling analysis of suction buckets

Recently, suction buckets have become a very prominent foundation for bottom fixed and floating offshore wind turbines. They are embedded with an installation force that stems from water evacuation inside the bucket. This internal negative pressure leads to a high risk of structural buckling. The buckling strength is significantly reduced by geometric imperfections. In previous work, equivalent geometric imperfection forms were introduced and the lower bound was evaluated. However, it has not yet been possible to identify a generally appropriate imperfection form. A probabilistic design approach based on realistic imperfections was not yet considered for suction buckets. Therefore, in this work, a stochastic modeling approach is introduced, which bases on measured data. The imperfection is decomposed to the half-wave cosine Fourier representation. Realizations of the imperfection pattern are generated by filtering white noise with the amplitude spectrum. They are then applied as out of plane deviations on a geometrically and materially nonlinear finite element model and evaluated. The resulting buckling pressure distribution can then be evaluated for different reliability levels. By considering more realistic imperfections and a plastic soil model, the buckling pressure increases by up to a factor of two compared to the conservative stress-based buckling approach.