Bending Buckling Research Articles

Bending, torsion and flexural-torsional buckling of back-to-back cold-formed steel channels

The bending moment resistance of cold-formed steel channels can be improved by combining two channel sections with a pair of screw fasteners in the webs spaced intermediately along the member. By combining the two channels in this way, the moment capacity of the beam can be increased beyond the capacity of two single channels. Another advantage of this type of section is the coincidence of the centroid and shear centre which reduces the effects of stresses due to eccentric load and torsion. Most research on back-to-back channels in bending has focused on local and distortional buckling while data on flexural-torsional buckling is scarce. The flexural-torsional buckling resistance of a beam depends on various section properties which include the minor axis second moment of area, and the torsion and warping constants of the section. Although the flexural-torsional buckling moment can be easily determined for a single channel section because these section properties are relatively straightforward to calculate, the calculation of the flexural-torsional buckling moment for back-to-back channels with intermediately spaced screw fasteners is much more complicated due to the discontinuity of the cross-section along the length of the beam. In this paper, the shear stiffness of the screw fasteners connecting the channels is obtained from test results. The shear stiffness is then used to model the screw fasteners in a finite element analysis to analyse a beam composed of back-to-back channels under bending and torsion. The results are compared with two single channel sections and with back-to-back channels assuming full composite action. The effect of different screw fastener spacings is also investigated. Simple relationships between the bending and torsion section properties for single channels and back-to-back channels are presented. Suggestions for the design of back-to-back channels in bending are also proposed.

Micromechanical characteristics of titanium alloy (Ti-6Al-4V) made by laser powder bed fusion using an in-situ SEM micropillar compression technique

While titanium alloy (Ti-6Al-4V) made by laser powder bed fusion (L–PBF) exhibits complex deformation behaviors, its important micromechanical properties in relation to loading directions are not fully understood. This research aims to investigate the micromechanical behaviors of printed L–PBF Ti-6Al-4V alloys under vertical (i.e., the loading direction perpendicular to printed layers) and horizontal (i.e., the loading direction parallel to printed layers) compressions using in-situ scanning electron microscopy (SEM) micropillar techniques. Ti-6Al-4V alloys were L-PBF-printed using a 45° rotate scanning strategy with vertical and horizontal build directions. The microstructures of the two alloys were analyzed using the SEM with energy-dispersive X-ray spectroscopy (EDS). The titanium alloy micropillars were produced using focused ion beam (FIB) milling in the SEM. In-situ SEM micropillar compressions were conducted using a flat diamond indenter. Vertical alloy had smaller cross-patterned finer α′ martensite than horizontal one. While both vertical and horizontal micropillars showed elastic-plastic behaviors, the former had significantly higher yield, fracture, and compression strength values, as well as resilience and toughness, than the latter, leading to the formation of favorable shear bands. Both micropillars exhibited ductile fractures but had distinct failure mechanisms. The ductile fracture in the vertical micropillars was due to strain hardening, large plastic deformation, and shear band formation, while the ductile fracture in the horizontal ones was attributed to compression-induced bending and plastic buckling. The micromechanical characteristics of L–PBF Ti-6Al-4V materials provides an important insight into the small-scale deformation and failure mechanisms of the alloys influenced by loading directions.

Study on dynamic post-buckling stability of fast reactor vessels subjected to vertical vibration

Abstract As a lesson learned from the Fukushima nuclear accident, the importance of accident mitigation for Beyond Design Basis Events (BDBEs) is recognized. Excessive earthquake is a typical BDBE. During such events, the Fast Reactor Vessel (FRV) is vulnerable to buckling. The safety goal of FRV under excessive earthquake is to achieve a stable post-buckling state. Our previous study on bending buckling confirmed a global response stability under horizontal vibration. As a parallel study, this paper focuses on axial compression buckling under vertical vibration. Shaking table experiments using thin-walled cylindrical models (R/t=260) are carried out. Similar methodology is applied to investigate the buckling and post-buckling behavior. It is found that axial compression buckling shares an extensive similarity with bending buckling in both buckling mode and post-buckling behavior. Similar global response stability is confirmed due to phase-inverse phenomenon. After buckling, buckling failure becomes stable and does not progress further even when an intense input amplitude is continuously applied. The vibrational load acts as a displacement-controlled load in the out-of-phase domain such that immediate collapse is prevented. Most input energy is dissipated in hysteresis loops rather than being carried by the mass. These mechanisms are independent of input waveform and can be applied to an arbitrary seismic input. In addition, a conservative limit displacement for global response stability is identified. Moreover, the effect of the input frequency ratio, the initial geometrical imperfection and the gravitational force on the post-buckling behavior are clarified.

A Computational Framework to Optimize the Mechanical Behavior of Synthetic Vascular Grafts.

The failure of synthetic small-diameter vascular grafts has been attributed to a mismatch in the compliance between the graft and native artery, driving mechanisms that promote thrombosis and neointimal hyperplasia. Additionally, the buckling of grafts results in large deformations that can lead to device failure. Although design features can be added to lessen the buckling potential, the addition is detrimental to decreasing compliance (e.g., reinforcing coil). Herein, we developed a novel finite element framework to inform vascular graft design by evaluating compliance and resistance to buckling. A batch-processing scheme iterated across the multi-dimensional design parameter space, which included three parameters: coil thickness, modulus, and spacing. Three types of finite element models were created in FEBio for each unique coil-reinforced graft parameter combination to simulate pressurization, axial buckling, and bent buckling, and results were analyzed to quantify compliance, buckling load, and kink radius, respectively, from each model. Importantly, model validation demonstrated that model predictions agree qualitatively and quantitatively with experimental observations. Subsequently, data for each design parameter combination were integrated into an optimization function for which a minimum value was sought. The optimization values identified various candidate graft designs with promising mechanical properties. Our investigation successfully demonstrated the model-directed framework identified vascular graft designs with optimal mechanical properties, which can potentially improve clinical outcomes by addressing device failure. In addition, the presented computational framework promotes model-directed device design for a broad range of biomaterial and regenerative medicine strategies.

Prediction of sectional collapse of thin-walled structure under pure bending by nonlinear composite beam theory

Brazier (1927) found that when one dimension of the beam cross-section was relatively smaller than the others, large in-plane displacements over the cross-section might occur, even though the strains could remain very small. Under this circumstance, the so-called Brazier effect refers to the cross-sectional ovalization, which leads to nonlinear bending buckling and collapses. This paper studies the Brazier effect by the nonlinear Variational Asymptotic Beam Sectional Analysis (VABS) theory which considers finite cross-sectional deformations. Nonlinear VABS reduces three-dimensional (3D) continuum to a one-dimensional (1D) beam analysis and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities without unnecessary kinematic assumptions. The present theory is implemented using the finite element method (FEM) in the VABS code, a general-purpose beam cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model using the Euler–Bernoulli beam theory. The deformation gradient tensor is directly used to deal with finite deformation, various strain definitions, and several types of material laws. Numerical examples demonstrate the capabilities of VABS to predict the sectional collapse of thin-walled structures under pure bending.

Numerical analysis of running resistance of a completion string with packers and sliding sleeves in horizontal wells

The installation of a completion string in small-diameter horizontal wells often presents challenges such as instability, bending, and high frictional resistance. To accurately estimate the running resistance during deployment and ensure safe descent to the bottom of the well, a three-dimensional numerical model has been developed incorporates real-time contact interaction between the completion string and the wellbore, while maintaining precision and field applicability. The analysis evaluates several factors, including buckling behavior, average and dynamics transient value of contact force, axial forces, and frictional forces. Results reveal that the upper pipe string exerting thrust on the lower pipe string causes bending and spiral buckling along with resulting contact with wellbore. Maximum hook load and maximum negative axial force occur at a inclination angle of 65°. Contact strength is more pronounced in inclined and horizontal section compared to vertical section. Leveraging extensive data, the study has yielded a quick prediction formula for quickly calculating the resistance experienced by a completion string of field area. The numerical results offer valuable insights into comprehending the resistance encountered during the descent of a completion string in horizontal wells, and provide robust theoretical support for predicting descent resistance.

Modeling of flexible shaft for robotics applications

Reducing moving mass and effective inertia is essential for achieving safe human–robot collaboration. This can be achieved either by employing remote actuation, which moves the mass of actuators away from the moving elements of the robot, or by elastic actuation, which decouples the inertia of the actuator from the inertia of the robot’s link. Flexible shafts, being torsionally compliant slender long shafts, offer a combination of remote and series elastic actuation over an obstacle. Modeling such transmission is complicated due to its three-dimensional deformation in torsion, bending, and helical buckling. This paper proposes an algorithm for estimating the polar moment of inertia and stiffness of the flexible shafts using their physical dimensions of length and diameter. Using an inertia-spring–damper model, the stiffness parameters are estimated experimentally for nine flexible shafts with variable diameters and lengths in straight and bent configurations. The proposed algorithm is validated with experimental stiffness values for variable diameters and lengths in straight configuration. For bent configuration, an empirical formulation is provided to incorporate the bending deformation effect till a bending angle of 45∘.

Fragile points method for Euler–Bernoulli beams

In this paper, the recently introduced Fragile Points Method (FPM) is extended to study the static bending, free vibration, and mechanical buckling of isotropic and homogeneous case as well as functionally graded Euler–Bernoulli beams. The beam kinematics is based on the Euler–Bernoulli theory that assumes plane sections remain plane and perpendicular to the neutral axis of the deformed beam. The salient feature of the FPM is that it is a truly meshless method that employs simple local point-based polynomial test and trial functions. The key distinction is that the polynomial test and trial functions are discontinuous and constructed using radial basis functions, in contrast to the conventional Galerkin framework. Further, as the trial and test functions are discontinuous, the continuity requirement imposed by the continuous Galerkin framework is circumvented. The discontinuous trial and test functions lead to inconsistency; to alleviate this, we employ numerical flux corrections inspired by the discontinuous Galerkin method. The efficiency and robustness of the approach are tested with a few standard benchmark examples.

Evaluation on structural performance of hybrid composite post-tension plate girder through finite element analysis

ABSTRACT Plate girders are typically formed by the built-up of I-shaped plates. It is vulnerable and weak in resisting buckling. In this study, FE analysis models were developed to evaluate the flexural performance of a hybrid composite post-tension (HCPt) plate girder. The HCPt plate girder is made of double-web and in-fill concrete with pre-stressed tendon to prevent shear web buckling and improve flexural resistance. The sensitivity of design parameters to the performance of the girder was also investigated through a parametric study using four different configurations. The selected parameters are span length, steel grade, concrete grade, and level of pre-stressed force. The statistical analysis was performed using linear multiple regression model to predict the girder’s flexural load and displacement. The results showed that web shear buckling was eliminated for models with in-fill concrete and pre-stressed tendon and failed by bending. Failure of the girder with double web was demonstrated by the combination of bending and web shear buckling. The concrete in-fill prevents the web plate from buckling and the beams generally fail in bending with high ductility. The load capacity of the hybrid composite plate girders with pre-stressing improved by 76% and 44% compared to conventional single-web plate girders and double-web plate girders, respectively.

Mechanics of Pure Bending and Eccentric Buckling in High-Strain Composite Structures.

To maximize the capabilities of nano- and micro-class satellites, which are limited by their size, weight, and power, advancements in deployable mechanisms with a high deployable surface area to packaging volume ratio are necessary. Without progress in understanding the mechanics of high-strain materials and structures, the development of compact deployable mechanisms for this class of satellites would be difficult. This paper presents fabrication, experimental testing, and progressive failure modeling to study the deformation of an ultra-thin composite beam. The research study examines the deformation modes of a post-deployed boom under repetitive pure bending loads using a four-point bending setup and bending collapse failure under eccentric buckling. The material and fabrication challenges for ultra-thin, high-stiffness (UTHS) composite boom are discussed in detail. The continuum damage mechanics (CDM) model for the beam is calibrated using experimental coupon testing and was used for a finite element explicit analysis of the boom. It is shown that UTHS can sustain a bending radius of 14 mm without significant fiber and matrix damage. The finite element model accurately predicts the localized transverse fiber damage under eccentric buckling and buckling stiffness of 15.6 N/mm. The results of the bending simulation were found to closely match the experimental results, indicating that the simulation accurately shows deformation stages and predicts damage to the material. The findings of this research provide a better understanding of the structure characteristics with the progressive damage model of the UTHS boom, which can be used for designing a complex deployable payload for nano-micro-class satellites.

Experimental study and numerical analysis on the dynamic response of steel tube confined concrete with a circular hollow section (STCC-CHS) under transverse impact loading

The dynamic response to lateral impact of steel tube confined concrete with a circular hollow section (STCCCHS) was investigated via pendulum impact tests in the laboratory. Nine STCCCHS columns and two concrete-filled double skin steel tubes (CFDST) were tested under lateral impact. The hollow ratio, the thickness of the outer steel tube, the impact height, and axial load ratio were varied. The failure pattern was observed along with the time histories of the impact force and the mid-span deflection. Strain development in the outer steel tube was quantified. The failure mechanism was integral bending and local buckling under lateral impact. Increasing the outer wall thickness and adopting an appropriate hollow ratio can effectively improve the impact resistance of such columns. Changes in impact energy have a significant influence on the plastic deformation of the members. Modest axial loading has little effect on the impact resistance. The test results were used to tune a finite element simulation of the process. A whole dynamic response investigation of STCCCHS columns under impact loads was carried out, and compared with the impact resistance of CFDST columns.

Buckling, bending and dynamic analyses of laminated three-phase polymer/graphene/carbon fiber composite rectangular plates

The bending and dynamic buckling analysis of graphene reinforced with carbon fiber reinforced polymer (CFRP) composite plates was investigated in this study. The CFRP composites were fabricated using the hand layup method. The mechanical characteristics of CFRP composites with 0–1 wt% graphene reinforcement were evaluated using ASTM tests. The experimental dynamic analysis is carried out on graphene reinforced CFRP composites. A higher order finite element (FE) formulation is implemented to compute the characteristics of the CFRP plate using MATLAB software. The FE model's validity is compared to numerical data reported in the literature, and the results demonstrate excellent agreement. Furthermore, parametric analysis is performed to explore the influence of wt.% of graphene, aspect ratios, and end conditions on the bending and dynamic buckling properties of graphene reinforced with CFRP composite plates.

A Coupled Behaviour of Web and Flange on Bending Buckling of the Web of Steel Box Girder

AbstractIn general, a web of the steel box girder is designed as an independent. However, in actual behaviour, since the web and the flange behave in couple, the web is considered to have a higher bending buckling strength than the designed standard due to the restraint by the flanges. Therefore, horizontal stiffeners for the web of the steel box girder might be omitted. In this study, focusing on the effect of the coupled behaviour of the web and flange on the bending buckling strength of the web of a box girder, FE analyses were carried out of steel box girder model with different structural configuration and of a panel model under identical boundary conditions as the design. From these results, it was found that the web of box girders without horizontal stiffeners have a higher bending buckling strength than the panel model due to restraint by the top of end of the web by the flange. In the case that buckling parameters of the flange are smaller than those critical buckling parameters, the influence of the bending buckling of the web of the box girder on the buckling strength of the flange is slight.

Predicting the wrinkling in AA5052 seamless tubes manufactured by free bending forming technology

Wrinkling is a significant defect during forming of thin-walled metallic tubes via free-bending forming (FBF) technology. Thus, it's quite important to predict the wrinkling in the tubes to improve the quality of the final products. Accordingly, new theoretical and numerical frameworks were proposed for predicting the wrinkling of the tubes manufactured via FBF technology. The theoretical wrinkling prediction model is based on the energy criteria and the thin shell theory. The numerical prediction model was constructed on the ABAQUS/Implicit FE code. Besides, The Knoop microhardness test characterized the anisotropy of the tube. The tube's imperfection was introduced to the numerical model through pure bending buckling analysis. The bending experiments were conducted to verify the results obtained from the proposed theoretical and numerical frameworks and showed good agreement with them. Furthermore, it was noticed that the additional axial force in the FBF process reduces the tube's ability to resist wrinkles. The larger additional axial force makes tubes more sensitive to imperfection in free bending than in other bending technologies. The numerical prediction model with the perfect tube exhibits good accuracy in predicting the initiation of the tube wrinkling in free bending but not in terms of the wrinkling shape. The model considering the imperfection can predict the onset and development of wrinkling properly.

Development of Bi-hexagonal hybrid crash box subjected to axial loading for enhancement of crashworthiness

Crash box design had been developed to increase crashwortiness performance. The crash box cross section is one important parameter to increase the energy absorption as crashwortiness performance. In the previous study, hexagonal cross section provide the higher energy absorption than other cross section. One of strategy to increase cross section is using two cross section put together in one component of crash box design. Bi-tubular crash box shows higher energy absorption with easy manufacture opportunity. In other study, hybrid crash box is investigated to reduce crash box mass. In this study, development of bi-hexagonal hybrid crash box subjected to axial loading to enhance crashworthiness were investigated. Analysis of crash box design is developed by using computer simulation with ANSYS Workbench 19.2. The crash box materials used are Aluminum Alloy and carbon-epoxy woven. The material modeling in the crash box is assumed as deformable body while the impactor is a rigid body. The axial loading is modelled by setting impactor impact the crash box with a speed of 7.67 m/s. Fixed support is set on the bottom of crash box. Nine of frontal test models were simulated for the bi-hexagonal hybrid crash box with different layups orientation angle and composite hexagonal tube diameter. Energy absorption and deformation patterns were observed. The results indicated that the highest energy absorption and specific energy absorption is occured on the A60 model with layups orientation angle of [0/60/0/60] and composite hexagonal tube diameter of 41 mm are 3693.8 J and 19.121 kJ/kg. The deformation pattern in the aluminum part is diamond mode, while in the composite part, the deformation pattern produce transverse shearing, lamina bending, brittle fracturing and local buckling mode

Enhancing bending buckling strength of hollow tubes using concrete filling

Hollow tubular components are widely used in industries as structural elements which are subjected to bending loads. These tubes are susceptible to bending (transverse) buckling, more so in tubes with thinner cross sections. The presented work investigates the effect of adding an inexpensive core like concrete (with good compressive strength) on the bending buckling strength of thin hollow tubes. This study is based on the results obtained from three-point bend tests performed on hollow and concrete filled thin stainless-steel tubes of small diameter. The size of test specimens was chosen such that the bending buckling mode dominates over the yielding as a failure mode. The experimental results are validated by finite element-based simulations. It was observed that addition of a concrete core significantly improves the bending buckling strength of the thin hollow tubes.

Structural Stability Verification for Steel Beam‐columns in Fire ‐ a Consistent Approach with Ambient Temperature Rules

AbstractSteel structures are characterized by a slender design, which makes stability verifications particularly important. While the design methods for steel members at ambient temperatures have been continuously developed and revised for the second generation of Eurocode 3, the method for elevated temperatures in prEN 1993‐1‐2 is still based on the corresponding rules of ENV 1993‐1‐1 of 1992. This leads to a divergence of methodology for ambient and elevated temperatures and to unnecessarily complex design methods for the engineering practice. Therefore, a harmonization of design models for ambient temperature and fire design is desirable.This paper presents a theoretical and numerical study on the stability behaviour of steel members at elevated temperatures. The structural fire behaviour of steel beams, columns and beam‐columns, i.e. flexural buckling under pure compression, lateral torsional buckling under major axis bending and spatial buckling of members under combined bending and axial compression has been investigated. Based on results available in the literature as well as an extensive numerical parametric study, reduction factors and interaction factors were determined. The new reduction and interaction factors were used to develop a design model for the member stability verification in fire that follows the format of FprEN 1993‐1‐1. Thus, engineering practice is provided with a harmonized verification method for steel members in bending and compression for ambient temperature and fire design.

Bending and buckling analysis of functionally graded Timoshenko nanobeam using Two-Phase Local/Nonlocal piezoelectric integral model

Previous studies indicate that nonlocal piezoelectric differential model would lead to an inconsistent bending response of Euler-Bernoulli nanobeam. In this paper, static bending and elastic buckling of functionally graded piezoelectric (FGP) Timoshenko nanobeam are studied through two-phase local/nonlocal piezoelectric integral model. The differential governing equations and standard boundary conditions are derived on the basis of the principle of minimum potential energy. The relations between general strain and nonlocal stress components are expressed as integral forms and then transformed equivalently into differential forms with constitutive boundary conditions. Several nominal variables are introduced to simplify the mathematical formulation. It shows that Timoshenko nanobeam based on purely nonlocal piezoelectric integral model would lead to ill-posed mathematical model and inconsistent size-dependent response with and without considering constitutive boundary conditions, respectively. The general differential quadrature method is applied to obtain the numerical results for bending deflections and buckling loads. The influence of nonlocal parameters, boundary conditions, functionally graded index and buckling order on the bending deflections and buckling loads is investigated numerically. A consistent softening response is obtained.

Analytical and finite element analyses of flexural and torsional buckling of I-columns with discrete braces

The present study investigates the buckling strength of braced thin-walled columns under bending and torsional modes. Unlike the well-known bending modes, the torsion buckling modes of braced columns are not adequately assessed in design and are often overlooked. In order to control the buckling behaviour, the effects of elastic discrete springs in bending and torsion are taken into account. Analytical solutions are derived for bending and torsion buckling modes in the case of simply supported struts with doubly symmetric cross sections. Further, the threshold bracing stiffness to achieve the higher buckling modes is found in both bending and torsion modes. For more general cases, the finite element approach of the model is implemented and it is able to carry out the buckling modes of columns under compression in the presence of 3D elastic springs and for any arbitrary cross sections. The analytical and the numerical results of the present models are compared to some available solutions in the literature and to finite element simulations of the commercial code Abaqus. The efficiency of the closed-form solutions and the numerical approach is successfully verified. The post-buckling of braced columns is considered at the end in the presence of elastic bending and torsion springs. The effect of braces to enhance the buckling capacity concludes the study.

Testing, numerical analysis and design of stainless steel equal-leg angle section beams

The stability and design of stainless steel equal-leg angle section members subjected to uniaxial bending are studied herein. An experimental investigation, comprising material testing, initial geometric imperfection measurements and physical tests on hot-rolled austenitic stainless steel equal-leg angle section beams is first presented. The test results are then used to validate shell finite element models developed within ABAQUS, which are in turn used to undertake numerical parametric studies that consider both hot-rolled and cold-formed equal-leg angle section beams in austenitic, duplex and ferritic stainless steel with a wide range of slenderness values. Recent studies have shown that for angles under major-axis bending, both lateral-torsional and local buckling can arise, while under minor-axis bending, lateral-torsional buckling and Brazier-type flattening can occur. When designing for major-axis bending according to Eurocode 3, both local and lateral-torsional buckling are considered; it is shown herein that equal-leg angle sections under major-axis bending can be designed using a normalised slenderness based on the minimum of the local and lateral-torsional elastic buckling moments, while also considering their ratio. Under minor-axis bending, however, in comparison with the current provisions in Eurocode 3 that only require cross-section checks, it is shown that both safer and more accurate resistance predictions can be achieved when account is taken for lateral-torsional buckling and Brazier-type flattening. New design proposals for stainless steel equal-leg angle section beams, covering both major- and minor-axis bending, are therefore developed. The proposed design rules offer substantially more accurate and consistent resistance predictions compared to existing codified design rules. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.1, is verified following the procedure provided in EN 1990.