Buckling Load Capacity Research Articles

NUMERICAL MODELLING OF STRUCTURAL BAMBOO UNDER COMPRESSION

Bamboo is a sustainable and eco-friendly material with great potential to replace traditionally available construction materials like concrete and steel. However, accurately predicting the behavior of bamboo is essential for improving the structural design codes, which will enhance the wider usage of bamboo as a structural member. In this study, the buckling of bamboo is modelled numerically as both cylindrical and tapered circular columns with varying elastic moduli across the cross-sections in ABAQUS. Then, the results were compared with Euler's equation derived for the cylindrical and tapered circular columns having homogeneous cross-sections. Finally, it was observed that columns with varying elastic moduli across the cross-section have 1.5 to 2.3 times a lesser buckling load capacity than columns with homogeneous cross-sections with outer Young's modulus value (Eo). Also, compared to buckling load homogeneous cross-sections with inner Young's modulus value (Ei), varying elastic modulus cross-sections have 1.7 to 2.7 times higher buckling load. This study emphasizes the necessity of having a simple analytical equation with varying elastic modulus for calculating the buckling load for bamboo columns.

NUMERICAL MODELLING OF STRUCTURAL BAMBOO UNDER COMPRESSION

Bamboo is a sustainable and eco-friendly material with great potential to replace traditionally available construction materials like concrete and steel. However, accurately predicting the behavior of bamboo is essential for improving the structural design codes, which will enhance the wider usage of bamboo as a structural member. In this study, the buckling of bamboo is modelled numerically as both cylindrical and tapered circular columns with varying elastic moduli across the cross-sections in ABAQUS. Then, the results were compared with Euler's equation derived for the cylindrical and tapered circular columns having homogeneous cross-sections. Finally, it was observed that columns with varying elastic moduli across the cross-section have 1.5 to 2.3 times a lesser buckling load capacity than columns with homogeneous cross-sections with outer Young's modulus value (Eo). Also, compared to buckling load homogeneous cross-sections with inner Young's modulus value (Ei), varying elastic modulus cross-sections have 1.7 to 2.7 times higher buckling load. This study emphasizes the necessity of having a simple analytical equation with varying elastic modulus for calculating the buckling load for bamboo columns.

Post fire performance of galvanized cylindrical shells for buckling failure

This study examines the impact of anti-fire paint with different thicknesses of 100, 200, and 400 microns on the post-fire behavior of cylindrical tanks under external pressure. For this purpose, we investigate the buckling modes of the cylindrical tank specimens after they are exposed to fire. Different fire temperatures of 300, 450, and 600 ℃ were investigated. A total of 22 specimens were fabricated in the laboratory. The specimens have been divided into three groups, the first group without any anti-fire, the second group include the anti-fire paint on their inner skin and the last group have the anti-fire paint both on inner and outer faces of the tank. In the second part of the study, to determine the effects of anti-fire paint numerically, the finite element models were created in Abaqus software. Numerical models were verified by Experimental data, with an error rate at initial buckling 5.4%, overall buckling 6.17% and collapse 7.88%. The results showed that the samples with 100-micron-thick anti-fire paint on both outer and inner surfaces did not show any significant difference compared to unpainted specimens under buckling load. However, the cylindrical specimen with 200-micron-thick anti-fire paint on both outer and inner surfaces was found to be fire resistant up to 450 ℃ and displayed similar behaviors with the perfect one (unpainted and not exposed to fire). Moreover, the specimens with 400-micron-thick anti-fire paint were also found to be resistant to fire up to 450°; however, the collapse loads of these specimens were greater than the overall buckling load of the specimens with 200-micron thick anti-fire paint. Numerical and experimental results show a good agreement, the stress distribution and plastic equivalent strain values were parallel with the buckling load capacity of the specimen. As a result, the thickness of the anti-fire paint directly affects the fire resistance of cylinder steel, and with a validated finite element model, it is possible to predict the paint thickness that can withstand specific fire temperatures in large shell structures.

Numerical Investigation on the Buckling Load Capacity of Novel Compound Cross-Sections Used in Crane Construction

Although a crane is exposed to a wide range of loads, there is a growing need for a lighter, more slender design. As a result, double girder cranes are becoming single girder cranes, aiming to make the steel structure as light as possible. The optimization potential of the classic design as a hollow-box girder is approaching its end. In order to meet today’s requirements, a new design was developed, which combines beams with curved panels into a new cross-section to be used as the crane’s main girder. Compound cross-sections pose a challenge for the mechanical engineer as there are usually no comparative data available and designing using numerical methods is complex. For this reason, a scaled model was abstracted for which a load determination will be carried out in 2024. This article deals with the finite element calculations for the design of the test specimen. A global numerical analysis was used to determine the buckling load, and several imperfection patterns were investigated. The results revealed that the buckling loads are similar to each other. This finding may lead to the conclusion that the most damaging imperfection pattern has yet to be found, which supports the need for an accompanying series of tests.

Influence of Aspect Ratio on the Flexural and Buckling Behavior of an Aluminium Sandwich Composite: A Numerical and Experimental Approach.

In the field of engineering materials, lightweight and ultra-lightweight composites are used in real time to a greater extent, with high-performance targeting for tailor-made systems in aerospace, automotive, and biomedical applications. Sandwich composites are among the most popular lightweight materials used in structural and vehicle-building applications. In the present investigation, one such sandwich composite laminate composed of aluminum face sheets and a high-density polyethylene core was considered to analyze sandwich composites' flexural and buckling behavior experimentally and numerically. The influence of aspect ratios, such as length to thickness and width to thickness, on the flexural and buckling performance of sandwich composite laminates was explored in the study. Laminates with different widths, namely, 10, 12, and 15 mm, and a uniform thickness and length of 3 mm and 150 mm, respectively, were used for flexural analysis, whereas laminates with widths of 10, 12, and 15 mm and a uniform thickness and length of 3 mm and 350 mm, respectively, were used for buckling analysis. The geometrical influence of the laminates on mechanical performance was studied through performance measures such as critical bending load, flexural stiffness, inter-laminar shear stress, and critical buckling load. A significant influence of aspect ratio on the mechanical behavior of the laminates was observed using both experimental and numerical approaches. Flexural behavior was observed to be better at greater widths, namely, 15 mm, and with a minimum support span of 90 mm due to reduced spring back effects and increased bending resistance. A maximum width of 15 mm allowed for a higher buckling load capacity similar to that of bending resistance. A critical buckling load of 655.8 N seemed to be the maximum and was obtained for the highest aspect ratio, b/t = 5. The soft core and ductile metal face sheets offered combined resistance to both bending and buckling. A lower aspect ratio (span to thickness) rendered these sandwich laminates better in terms of both bending and buckling.

Static and global buckling analysis of sandwich panels with improved star-shaped honeycomb using VAM-based downscaling model

Enhancing the stiffness of high-porosity honeycomb sandwich panels is a critical research field. To address this issue, a novel improved star-shaped honeycomb sandwich panel (SP-ISH) is designed by replacing the sharp corners with cubic struts and elongating the inclined ribs of the traditional star honeycomb. To fill the gap between global behaviors and local field distribution, an asymptotic analysis of the energy functional stored in periodic unit cells is performed. Based on the obtained effective plate properties, a two-dimensional equivalent downscaling model (2D-EDM) is developed and validated through comprehensive comparisons with results from 3D-printed experiments and 3D FE models, including assessments of static displacement, global buckling, and local field distribution. Furthermore, the effects of material and structural parameters on the effective plate properties and static performance are systematically investigated. The results reveal that the slenderness ratio of the rib and the core height-width ratio have the strongest influence on the equivalent tensile stiffness and bending stiffness, respectively. Notably, the SP-ISH outperforms other star-shaped honeycomb panels in specific stiffness, deformation resistance, and buckling load capacity due to the extended ribs and added struts. The study’s findings provide valuable insights for future designs and applications of this honeycomb structure.

Effect of Ovality on the Buckling Behavior of Thin-Walled Liquid-Filled Conical Tanks

This study investigates the influence of ovality on the buckling behavior of thin-walled liquid-filled conical tanks through comprehensive numerical simulations. The structural stability of conical tanks is of paramount importance in various engineering applications, such as storage vessels and aerospace structures. However, the presence of ovality, characterized by deviations from perfect circularity, can significantly affect the structural response and integrity of these tanks. To explore the effects of ovality, a finite element analysis (FEA) approach is employed, considering various ovality levels in the tank geometry. A comprehensive parametric study is conducted, varying key parameters such as tank dimensions, material properties, and liquid filling levels. The buckling behavior of the tanks is assessed by examining critical buckling loads and corresponding deformation modes. Results from the numerical simulations reveal that even small levels of ovality can substantially reduce the buckling load capacity of conical tanks. As ovality increases, the onset of buckling occurs at lower applied loads, leading to premature structural failure. The presence of liquid filling further exacerbates the buckling phenomenon, with the liquid sloshing effect amplifying the structural response. The study also investigates the influence of different materials on the buckling behavior of conical tanks subjected to ovality. It is found that the material stiffness and yield strength play a crucial role in determining the critical buckling load and mode shape. Furthermore, the effect of liquid fill level is explored, demonstrating that higher fill levels increase the vulnerability to buckling.

Effect of wear rings on buckling load capacity of Two-Stage hydraulic cylinder

In a two-stage hydraulic cylinder, the rod is a critical component for stability against buckling failure. A small disturbance in the rod may increase the instability that may lead to catastrophic failure. A small support against the instability may increase the system's flexural strength to make it more stable. The wear rings provide an elastic support against the rod and cylinder's instability and increase the flexural strength of the connections. In this paper, a theoretical model for the buckling load of a pin-pin-mounted two-stage hydraulic cylinder is proposed. The buckling load calculation by the proposed approach is in close match (6.96% deviation) with the experimental results reported in the literature for the case of single-stage hydraulic cylinders. The effect of bending stiffness on stability is considered by considering the stiffness of the rod and cylinder along with the wear rings. A hyperelastic model is used to determine the bending stiffness of wear rings in three different cases: first when all wear rings are present, second when three wear rings are present, and third when only two wear rings are present. The stiffness of the rod and piston head is determined with the help of the conjugate beam method. Eigenvalue buckling analysis (finite element method) is carried out to verify the buckling load of a two-stage hydraulic cylinder with two, three, and four wear rings. Theoretical results are observed to be in good agreement with the numerical simulations (FEA) results, with a percentage deviation of 0.22 % − 9.22 % for different cases of wear rings positions. It is observed that when all four wear rings are present, the buckling load capacity increases by 1.14 times, whereas the removal of wear rings on the gland side decreases it by 0.96 times.

Foreword to the special issue on new developments in structural stability.

Foreword to the special issue on new developments in structural stability.

Multi-objective optimization of a sandwich structure with a hybrid composite grid core

This study evaluated two multi-objective optimization problems of a hybrid composite grid core sandwich structure, aiming at maximizing the critical buckling load while minimizing the structural weight or the costs of raw materials. The sandwich structure had a core with a composite isogrid pattern covered by two composite skins, and design variables included the space between core ribs, the core rotation angle, and the dimensions and materials of ribs. The stiffeners of the core were considered with I and box cross sections to investigate the cross section effect of ribs. The results showed that materials with high density and low mechanical properties are not suitable for reducing cost and weight. Geometrically, the use of cross-section and box has a significant effect on the buckling load capacity of the structure. Although two different criteria have been used to design the structure, the end results are almost the same. Moreover, the First-order Shear Deformation Plate Theory and the Ritz method were utilized to obtain the buckling load. Finally, the optimal alternative was found among the existing ones using the continuous genetic algorithm approach.

Recent developments in manufacturing, mechanics, and design optimization of variable stiffness composites

The functional advantages of tailored stiffness, often seen in nature, are also utilized in composite structures. Advancements in the multiaxis tow placement and automated fiber placement (AFP) machines led to the development of variable angle tow (VAT) composites, also referred further as variable stiffness composites (VSC). These composites are shown to effectively enhance the stress distribution and buckling load capacity of structures with greater flexibility on the design space. This review systematically presents the status of recent research on the topic of VSCs. Various manufacturing techniques of VSC are discussed; constraints and the defects associated with the manufacturing processes are enlisted. The review highlights the optimization studies based on the fiber profile and macro-scale stiffness invariants. Several studies existing in the domain of buckling, vibration, and aeroelastic tailoring of angle tow composites are summarized to connect the important aspects of analysis and present a holistic approach for future studies in this area.

Uncertainty quantification for initial geometric imperfections of cylindrical shells: A novel bi-stage random field parameter estimation method

Thin-walled cylindrical shells are widely used as main load-carrying structures in the aerospace industry. Considering the high sensitivity of the buckling load capacity to initial geometric imperfections (GIs), uncertainty quantification (UQ) of GIs is crucial to both structural safety as well as lightweight design. However, the inherent strong random characteristics of GIs and limited experimental data exacerbate the difficulty. Therefore, a novel bi-stage random field parameter estimation method with limited samples is proposed for the UQ of GIs. In stage I, a new optimization formula based on average coefficient of determination (AR) is established to overcome the complexity caused by both parameter coupling and limited samples and then, Kriging-based method via chunking and selecting mechanism (KM-CMS) is proposed to find the optimal correlation length and number of truncated terms. In stage II, a maximum likelihood (ML) based method for estimating standard deviation (SD) of random field is established, benefitted from the SD-independence of AR. Numerical results show that the proposed random field parameter estimation method achieves the best performance in terms of accuracy, efficiency and stability. Finally, a high-fidelity UQ model of measured GIs of cylindrical shells is obtained by proposed method in a rational manner.

Nonlinear Finite Element Analysis and Comparison of In‐Plane Strength of Circular and Parabolic Arched I‐Section Cellular Steel Beam

The advancement in steel fabrication technology extends the structural and constructional advantages of cellular steel beams into arched cellular steel structure members. However, less attention is given to understanding the in‐plane and out‐of‐plane structural behavior and performance of arched cellular steel beams. This article presents a numerical study using the finite element package ABAQUS to investigate the effect of arch axis geometry (circular and parabolic) and the impact of end support types on the in‐plane inelastic buckling strength and buckling mode of I‐section arched cellular steel beams. In the nonlinear finite element analysis of the model material nonlinearity, a second‐order effect due to large deformation and initial geometric imperfection was incorporated in predicting inelastic buckling load and buckling mode. Furthermore, finite element analysis results were verified by comparing them to the existing experimental work. Test models covering shallow to deep arches of subtended angle in a range of 45–180 were investigated under uniformly distributed vertical loads and mid‐span point loads. It was found that nonlinear finite element results fairly replicate the experimental work in predicting inelastic buckling load and post‐buckling behavior. From the parametric investigation, it was found that deep parabolic arched cellular steel beams are structurally more efficient than their equivalent circular arched cellular steel beams. Pinned in‐plane and free out‐of‐plane end support conditions result in a reduced inelastic ultimate buckling load capacity of arched cellular steel members when compared to other possible end support types. The geometry of an arch axis has no noticeable impact on the buckling mode of arched cellular steel beams.

Numerical and experimental studies of the influence of curing and residual stresses on buckling in thin-walled, CFRP square-section profiles

The study provides the first comprehensive experimental and numerical study of thin-walled, carbon fibre square-section columns subjected to static compression. The profiles were manufactured from unidirectional prepreg tape of Hexcel AS4 high-strength carbon fibres in HexPly® 8552 thermoset resin with ply angles [45/−45/45/−45]s. The dimensions of the columns were: (height × width × length) 80 mm × 80 mm × 240 mm and the wall thickness was 0.92 mm.Advanced Finite Element Models (FEM) of the residual stresses generated during production were used as a basis for simulations of static compression. The deformation predicted by these models showed excellent agreement with 3D scans of the columns. These results also highlighted the residual stress concentrations generated at sample corners during production.It was found that the residual stresses from the autoclaving process significantly enhance the buckling load performance (by ~35%) and that the models provide an effective comparison with the experimental results (<10% error). This demonstrates the importance including residual stresses in FEM of buckling, but also highlights residual stress tailoring as a route to significantly enhance the buckling load capacity of carbon fibre systems used in industrial applications.

Buckling solutions for compression members with end restraints defined along non-principal directions

The classical flexural-torsional buckling solution for compression members with asymmetric cross-sections is intended for members with end fixity conditions defined along the principal directions. In a number of practical situations, member ends can be rotationally restrained about a non-principal direction and rotationally free about the orthogonal non-principal axis. This may occur, for example, when one of the legs of a compression member with an angle or the web of a zed cross-section is connected to a gusset plate. The buckling loads in such cases cannot be determined from the classical solution. Within this context, the present study formulates the variational principle, governing neutral stability conditions, and associated boundary terms based on general non-principal directions, and then develops analytical solutions for the resulting coupled equations. The validity of the solutions is then demonstrated though comparisons with shell and thin-walled beam-based finite element solutions. The solutions are then used to investigate the influence of the orientation of the restraining axes on the buckling load capacity and associated buckling modes for single angles and zed shaped compression members with common end conditions.

Form finding of assembled lattice structure considering the effect of joint stiffness

Joint stiffness can have a significant effect on the stability of single-layer lattice structure. However, it is yet unclear what is the degree of influence of joint stiffness on the form finding of assembled lattice structures. This paper presents a form finding method that suits assembled free-form single-layer lattice structures while the effect of joint stiffness on the form finding of the structure is investigated. Based on the experimental results of Ring-Sleeve joint, spring elements are initially used to simulate the joint stiffness and then finite element models of the assembled single-layer lattice structures with semi-rigid joints are established. The effect of joint stiffness on the structural form finding is studied by changing the spring stiffness. Thereafter, the optimal shapes of the assembled lattice structures with different joint stiffness and improved buckling load capacity are obtained. Finally, the mechanical properties of the resulted structures with different joint stiffness are extensively compared. The results show that different joint stiffness generate different structural shapes, and the greater joint stiffness results in higher structural height. Furthermore, both the structural buckling load capacity and the imperfection sensitivity increase with the increase of joint stiffness. Overall, the buckling load capacity of the semi-rigid model is lower than that of the replaced model that obtained based on the rigid structure.

Coupled flexural torsional analysis and buckling optimization of variable stiffness thin-walled composite beams

Present work examines flexural–torsional coupling for static and stability analysis of thin-walled composite beams having variable stiffness. Variable stiffness composites (VSCs), manufactured with curvilinear fibers, are considered in this work. Compared to straight fiber laminates, variable angle tow (VAT) sections may significantly improve structural response as they redistribute the in-plane stresses. A generalized beam kinematic model which considers the effect of flexural, torsional and, warping deformation is adopted and using the principle of minimum potential energy, governing equations are derived. The variable fiber angles can be defined using a general Lagrangian polynomial and as a particular case, the solution is presented for linearly varying fiber angles. Stability analysis considers geometric nonlinearity. The present model neglects transverse shear deformations, and governing equations are numerically solved using a set of C 1 continuous finite elements. Important observations are made on the coupled response of thin-walled VSCs for static and stability analysis, which indicates the necessity of optimization study. An efficient ‘Teaching Learning Based Optimization’ (TLBO) algorithm is applied to obtain the most efficient curvilinear fiber path. The results show that lateral torsional buckling load capacity can be increased by approximately 15% in optimized VSCs compared to unidirectional fiber composites. The present kinematic model and numerical scheme can be easily extended to the optimization studies considering manufacturing constraints, which may be further implemented in commercial designs.

Multi-objective optimization of sandwich composite pressure hull for decreasing weight and drag force and increasing buckling load capacity

In underwater applications, space vehicles, and aircrafts, the weight becomes an important factor. Additionally, the design of composites structures greatly depends on the number of layers and the fiber orientation angle. Therefore, this work presents the optimization of sandwich composite pressure hull in order to minimize (weight and drag force) and maximize the buckling load capacity using ANSYS Parametric Design Language (APDL). Tsai-Wu and maximum stress failure criteria were incorporated for predicting the first-ply failure. The major and minor radius of the pressure hull, the ring and long beams dimensions, the fiber orientation angle and layer thickness are taken as design variables. The results illustrated that, core thickness (Tcore ) has a great effect to resist the shell buckling. While, has a little effect on both Tsai-Wu and maximum stress failure index.

Lateral-Torsional Buckling Strength of Two-Span Glass Fiber Reinforced Polymer Beams

This paper presents the outcome of a study of two-span glass fiber reinforced polymer (GFRP) I-section beams susceptible to lateral-torsional buckling when subjected to gradually increasing concentrated vertical load(s) in the presence of two different types of lateral bracing schemes. It is found that loading one span results in a smaller buckling load as compared with the cases with loading in both spans regardless of the type of bracing scheme used. Also, the study shows that the addition of midspan braces for the GFRP beams results in up to 5.5 times increase in the buckling load capacity.

Lateral-Torsional Buckling Strength of Two-Span Glass Fiber Reinforced Polymer Beams

This paper presents the outcome of a study of two-span glass fiber reinforced polymer (GFRP) I-section beams susceptible to lateral-torsional buckling when subjected to gradually increasing concentrated vertical load(s) in the presence of two different types of lateral bracing schemes. It is found that loading one span results in a smaller buckling load as compared with the cases with loading in both spans regardless of the type of bracing scheme used. Also, the study shows that the addition of midspan braces for the GFRP beams results in up to 5.5 times increase in the buckling load capacity.