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The elastic stability performance of constant- and variable-stiffness based composite curved beams with general layups is evaluated using an enriched finite element that accounts for three-dimensional structural response features. The variable stiffness is spatially created over the beam by layers with curvilinear fibers. The structural model in the present work is represented by sinusoidal variation based higher-order shear deformable model, augmented with improved in-plane response by zig-zag function and stretching in thickness direction by higher polynomial order. The appropriate constitutive relationships for laminated composite curved beam with arbitrary layup producing stiffness coupling effects are deduced from three-dimensional elasticity relations. The beam governing equations are formed applying the total potential energy minimum principle and the buckling parameters are predicted employing the eigenvalue analysis. The curved laminated beam element efficacy is examined for the known analytical solutions in the literature. Extensive numerical analysis by opting for different structural parameters like curved beam angle, thickness, ply-angle, curvilinear fiber angle variation from center-to-edge, layup, and beam end condition are made to visualize the buckling characteristics of general layup composite curved beams. [ABSTRACT FROM AUTHOR]

AbstractIn present study, a numerical analysis of a sandwich structure with a lattice core consisting of two outer layers of sheets and an internal lattice core was undertaken. A two-step finite element method was applied to explore their mechanical behavior. The investigation primarily focused on evaluating the natural frequencies, critical buckling load, and maximum deformations of these plates. In first step, the finite element method was used to meticulously calculate the extensional stiffness, bending-extensional coupling stiffness, and bending stiffness matrices for a unit cell of lattice core. A cell was modeled in SAP2000 initially and then the entire structure was expanded. After that, in second step, the response of lattice structures was conveniently calculated by employing the stiffness matrices that were calculated in the first step. The obtained results were thoroughly compared with existing literature, ensuring the precision and reliability of the findings. These findings offer valuable insights for the design and optimization of sandwich structures with lattice core configurations across various engineering applications. [ABSTRACT FROM AUTHOR]

For a homogeneous incompressible 2D fluid confined within a bounded Lipschitz simply connected domain, homogeneous Neumann pressure boundary conditions are equivalent to a constant boundary vorticity. We investigate the rigidity of such conditions. [ABSTRACT FROM AUTHOR]

Aiming at the problems of large deviation of plastic machining accuracy and different buckling instability loads of bionic egg-shaped shells under different flexible medium forming technologies, it is proposed to adopt unidirectional loading rubber bulging and granular medium bulging technologies of bionic egg-shaped shells. By comparing the plastic machining accuracy, geometric accuracy, and strength of bionic egg-shaped shells with different flexible mediums, the machining accuracy and overall quality of bionic egg-shaped shells can be improved. In order to explore the stress and strain conditions at different stages and in different regions of the egg-shaped shell flexible medium forming technologies under the ideal case considering the thick directional stress conditions, a mechanical analysis of the egg-shaped shell flexible medium forming technologies is carried out. The combination of numerical analysis and experiment is used to analyze the forming process of egg-shaped shell under the action of different flexible mediums, and the accuracy of the numerical analysis model is verified. And then, through the study of the influence of different flexible medium forming technologies on the plastic processing accuracy, geometric accuracy, and strength of the egg-shaped shells, the plastic deformation and quality of the egg-shaped shell is mastered by the influence law of the flexible medium forming technology. The study shows that the results of the numerical analysis of the egg-shaped shell flexible medium forming technology have an average error of no more than 11% with the test, and the numerical analysis model can be considered accurate. Moreover, the plastic machining accuracy of egg-shaped shell process parts and egg-shaped parts with granular medium is better than that of rubber medium. The geometric accuracy deviation of the egg-shaped part of the egg-shaped shell with the granular medium is 10% smaller than that of the rubber medium, and the process parts are also superior to the rubber medium. The buckling load of the egg-shaped shell process parts under granular medium are higher than that of the rubber medium, while the egg-shaped parts are slightly smaller. Considering the experiment error and the overall buckling load distribution, the overall strength of the egg-shaped shell is higher under the action of granular medium. [ABSTRACT FROM AUTHOR]

Background: This study aims to investigate the impact of test conditions on the results of the compression testing of microneedle arrays (MNAs). Methods: Uniaxial compression tests were conducted on polyglycolic acid-fabricated biodegradable MNAs. Load–displacement curves were obtained for varying conditions, including the number of microneedles (MNs) compressed simultaneously, compression speeds, and compression angles. Subsequently, the buckling load and stiffness were calculated, and the MN deformation during compression was observed. Results: The buckling load and stiffness per MN decreased significantly with a simultaneous increase in compressed MNs. The mean buckling load and stiffness of 52 MNs in single-needle compression tests were 0.211 ± 0.008 N and 13.9 ± 1.3 N/mm, respectively, with no variation among the three MNAs. However, a significant difference in buckling load and stiffness was observed among the MNs within the MNAs. Additionally, buckling loads and stiffnesses were significantly lower in certain MNs at the same location in different MNAs. Buckling load and stiffness decreased significantly during inclined compression compared to during vertical compression. While the tests evaluate the mechanical properties of MNAs, test results may vary depending on test conditions. Conclusions: Compression testing of the individual MNs comprising an MNA helps evaluate the mechanical properties of MNs and ensure the quality of MNAs. [ABSTRACT FROM AUTHOR]

AbstractThe buckling characteristics of PC/PET spherical–cylindrical combined pressure cabins under uniform external pressure were studied via experimental and numerical methods. The material properties of the PC/PET plastic alloy were tested. Six spherical–cylindrical combined pressure cabins with different structures were designed and fabricated, and the thickness and geometry of each model were measured. The hydrostatic pressure experiment was carried out on all the pressure cabins, and the ultimate load of the pressure cabin was recorded. Linear buckling analysis and nonlinear buckling analysis of PC/PET spherical–cylindrical combined pressure cabins were carried out, and the numerical and experimental results were found to be consistent. Moreover, the effects of the spherical shell radius and the thicknesses of different combinations on the buckling load were studied. [ABSTRACT FROM AUTHOR]

The critical lateral buckling load of cantilever beams with IPE cross-section was calculated using analytical closed-form equations and numerical finite element analyses within the scope of the research. The equations suggested in the specifications for simply supported beams were used to calculate the buckling load of cantilever beams. The rationality of the values calculated due to this is not fully known. In the research, a single loading was made to the shear center at the free end of the cantilever beam. Cantilever length and section height were kept variable. As a result, it has been determined that there are partial differences in the analysis result obtained from the elastic stability theory and finite element method. Accordingly, the results obtained from ANSYS and SAP2000 analyses confirm each other. On the other hand, the results obtained using the formulation of Timoshenko and Gere, the calculation results made according to the AISC and DCCPSS regulations, and the results obtained from the LTBeam program confirm each other. However, it differs from the FEA analysis due to the cantilever beam length’s shortening and the section height increase. Thus, to obtain accurate and reliable results in the buckling load calculation of cantilever beams, the equations used in analytical calculations were optimized according to finite element analysis (FEA) results. As a result of the study conducted according to the error criteria, it was determined that the updated equation results gave similar results to the FEA results. [ABSTRACT FROM AUTHOR]

PVC pipe jacking is prone to cause yielding or buckling under the jacking force and may lead to engineering failure. The relationship between the buckling modes, ultimate bearing capacity, different diameter–thickness ratios, and length–diameter ratios of PVC pipe jacking under different load forms was analyzed. The calculation methods for allowable jacking force and the single allowable jacking distance are obtained through theoretical analysis and three-dimensional finite elements. The buckling mode of the pipe under uniform load changes from symmetric buckling to asymmetric buckling and then to the overall Euler buckling form as the length–diameter ratio increases. The ultimate bearing capacity of the pipe approaches the theoretical value of yield failure when L/D ≤ 6. For L/D > 6, the pipe undergoes buckling, and the ultimate bearing capacity determined by the axial buckling value and the buckling load can be calculated according to the long pipe theory formula when L/D > 8.5. Under eccentric loads, the failure mode transitions from local failure to Euler buckling with increasing pipe length. The ultimate bearing capacity of pipe is obviously lower than that of uniform load, but as the length–diameter ratio increases, this difference decreases until it becomes consistent. [ABSTRACT FROM AUTHOR]

The primary focus of traditional topological optimization in continuum structures is addressing stress, compliance, and other relevant factors associated with single-phase materials. However, the optimal design of structural buckling performance has gained increasing attention due to its significant economic loss and safety risk. Furthermore, the versatility, lightweight nature, and adjustability of composite multiple-phase materials offer significant potential for application in various fields. Therefore, this paper presents a novel methodology for optimizing multi-phase materials' design by concurrently incorporating structural buckling criteria and compliance design. Linear buckling analysis is utilized to determine the critical buckling load of the structure, and a buckling constraint is incorporated into the topology optimization model to regulate its buckling performance. A refined material interpolation model scheme is introduced to enhance the algorithm's robustness and eliminate pseudo-eigenmode in buckling analysis. The numerical results demonstrate that the final topology optimization design exhibits distinct and discernible boundaries for the topological configurations of multiple-phase materials. Moreover, it is possible to effectively regulate the buckling property while minimizing any compromise on stiffness. [ABSTRACT FROM AUTHOR]

Presented herein is an investigation for the nonlinear vibration and stability analysis of rotating functionally graded (FG) piezoelectric nanobeams based on the nonlocal strain gradient theory. The present model can be regarded as a simplified version for the rotating nanowire of biomechanical nanogenerators. The Hamilton principle is used to derive nonlinear equations of motion and their related boundary conditions, which are then discretized to form a set of algebraic equations. Accordingly, the nonlinear vibration frequencies and buckling loads of the nanobeams can be determined by an iterative method. A parametric study of rotational velocity, nonlocal parameter, material length parameter, power-law index, and electrostatic voltage on the dynamic stability behavior of such nanobeams is also presented. In the cantilever case, increasing the nonlocal parameter and material length parameter can result in a stiffness-hardening effect that is unaffected by rotational velocity and the material length parameter to nonlocal parameter ratio. Yet, this has not been reported previously. More importantly, incorporating the effect of geometric nonlinearity on the dynamic responses and stability results of the nanobeams is indispensable. In particular, new observations for the coupling effect of vibration amplitude and power-law index on the electric potential effect are useful for the design of rotating microelectromechanical devices. [ABSTRACT FROM AUTHOR]

Dynamic and buckling of a composite beam reinforced with a combination of carbon and aramid fibers is studied in this paper. The beam is under a thermal gradient through the thickness. Timoshenko beam is made of a polymer matrix (epoxy resin) reinforced with layers of high–strength carbon and high-toughness aramid fibers in order to create a balance between stiffness and toughness and create a type of structural composite beam with excellent strength and toughness. The mechanical and thermal properties of the hybrid composite beams are obtained based on the mixed law method. The equations of motion are extracted based on the Hamilton principle and then solved by the generalized differential quadrature method (GDQ). In this study, a thermal gradient is applied to the beam and then the vibration and buckling response of this hybrid composite beam are studied. The main contribution of this paper is the vibration and buckling responses of a hybrid composite structure strengthened by carbon and aramid fibers. The effect of the hybrid ratio as well as the stacking sequence on the free vibrations and critical buckling load are presented. The fundamental frequency and critical buckling load are largely affected by the stacking sequence. The conclusions show that the use of aramid fibers in the composite beam reinforced with carbon fibers decreases the natural frequency as well as the critical buckling load of the beam. The conclusions also show that for the symmetric hybrid composite beam, despite the critical buckling temperature being the same, the critical buckling load is different and depends on the location of the fibers.

This study focuses on investigating how grid-stiffened composite shells behave under external hydrostatic pressure. The critical buckling load is calculated using the first-order shear deformation theory (FSDT) and the Ritz method. Various factors, including shell thickness, angle of helical stiffeners, rib section area, and the number of stiffeners, are examined to understand their impact on the buckling load. To optimize the design, three multi-objective optimization algorithms are employed: Nondominated Sorting Genetic Algorithm II (NSGAII), Multiobjective Particle Swarm Optimization (MOPSO), and a hybrid method that combines NSGAII and MOPSO. The hybrid method intelligently divides the population into two groups and uses NSGAII and MOPSO to efficiently explore and exploit the solution space. The results yield a Pareto optimal front that showcases diverse solutions across different regions, providing decision-makers with the flexibility to select the solution that best fits their preferences. The solutions obtained through these algorithms are compared based on their diversity and distribution throughout the Pareto front.

Background: This study aims to investigate the impact of test conditions on the results of the compression testing of microneedle arrays (MNAs). Methods: Uniaxial compression tests were conducted on polyglycolic acid-fabricated biodegradable MNAs. Load–displacement curves were obtained for varying conditions, including the number of microneedles (MNs) compressed simultaneously, compression speeds, and compression angles. Subsequently, the buckling load and stiffness were calculated, and the MN deformation during compression was observed. Results: The buckling load and stiffness per MN decreased significantly with a simultaneous increase in compressed MNs. The mean buckling load and stiffness of 52 MNs in single-needle compression tests were 0.211 ± 0.008 N and 13.9 ± 1.3 N/mm, respectively, with no variation among the three MNAs. However, a significant difference in buckling load and stiffness was observed among the MNs within the MNAs. Additionally, buckling loads and stiffnesses were significantly lower in certain MNs at the same location in different MNAs. Buckling load and stiffness decreased significantly during inclined compression compared to during vertical compression. While the tests evaluate the mechanical properties of MNAs, test results may vary depending on test conditions. Conclusions: Compression testing of the individual MNs comprising an MNA helps evaluate the mechanical properties of MNs and ensure the quality of MNAs.

Dynamic and buckling of a composite beam reinforced with a combination of carbon and aramid fibers is studied in this paper. The beam is under a thermal gradient through the thickness. Timoshenko beam is made of a polymer matrix (epoxy resin) reinforced with layers of high-strength carbon and high-toughness aramid fibers in order to create a balance between stiffness and toughness and create a type of structural composite beam with excellent strength and toughness. The mechanical and thermal properties of the hybrid composite beams are obtained based on the mixed law method. The equations of motion are extracted based on the Hamilton principle and then solved by the generalized differential quadrature method (GDQ). In this study, a thermal gradient is applied to the beam and then the vibration and buckling response of this hybrid composite beam are studied. The main contribution of this paper is the vibration and buckling responses of a hybrid composite structure strengthened by carbon and aramid fibers. The effect of the hybrid ratio as well as the stacking sequence on the free vibrations and critical buckling load are presented. The fundamental frequency and critical buckling load are largely affected by the stacking sequence. The conclusions show that the use of aramid fibers in the composite beam reinforced with carbon fibers decreases the natural frequency as well as the critical buckling load of the beam. The conclusions also show that for the symmetric hybrid composite beam, despite the critical buckling temperature being the same, the critical buckling load is different and depends on the location of the fibers. [ABSTRACT FROM AUTHOR]

This study focuses on investigating how grid-stiffened composite shells behave under external hydrostatic pressure. The critical buckling load is calculated using the first-order shear deformation theory (FSDT) and the Ritz method. Various factors, including shell thickness, angle of helical stiffeners, rib section area, and the number of stiffeners, are examined to understand their impact on the buckling load. To optimize the design, three multi-objective optimization algorithms are employed: Nondominated Sorting Genetic Algorithm II (NSGAII), Multiobjective Particle Swarm Optimization (MOPSO), and a hybrid method that combines NSGAII and MOPSO. The hybrid method intelligently divides the population into two groups and uses NSGAII and MOPSO to efficiently explore and exploit the solution space. The results yield a Pareto optimal front that showcases diverse solutions across different regions, providing decision-makers with the flexibility to select the solution that best fits their preferences. The solutions obtained through these algorithms are compared based on their diversity and distribution throughout the Pareto front. [ABSTRACT FROM AUTHOR]

This research endeavors to examine the effect of stiffener shapes on the structural capacity of stiffened-plate structures, specifically focusing on Tee (T), Angle (L), and Flat (I) stiffened plates. The primary objectives are threefold: firstly, to quantify the critical load values during the buckling phenomenon for T, L, and I stiffened plates; secondly, to assess model deformation upon failure; and thirdly, to investigate whether the buckling behavior of T, L, and I stiffened plates correlates with distinct failure patterns. Employing numerical simulation through the finite element method, this study sheds light on previously unexplored aspects of structural behavior. The findings indicate that angle stiffeners exhibit superior load-bearing performance compared to flat bars. Notably, the research reveals a substantial increase in maximum compressive load by at least 15.90% with Tee bar and 8.25% with angle bar stiffeners when the stiffened panels undergo a 5 mm displacement, presenting a potential avenue for structural enhancement. Additionally, the study demonstrates that T bars outperform in terms of resisting buckling. Noteworthy is the novel approach of examining the combined effect of transverse frame, longitudinal frame, and hull girder under buckling scenarios, a facet not explored in previous research. Furthermore, the utilization of steel S355JR-EN10210 as a material introduces a unique dimension not previously considered in these scenarios. [ABSTRACT FROM AUTHOR]

New or in-service truss bridges, with or without upper bracing systems, may display instability phenomena such as general lateral torsional buckling of the upper chord. The buckling of structural elements, particularly in the case of steel bridges, can be associated with the risk of collapse or temporary/permanent withdrawal from service. Such incidents have occurred in the case of several bridges in different countries: the collapse of the Dee bridge with truss girders in 1847 in Cheshire, England; the collapse of the semi-parabolic truss girder bridge near Ljubičevo over the Morava River in Serbia in 1892; the collapse of the Dysart bridge in Cambria County, Pennsylvania in 2007; the collapse of the Chauras bridge in Uttarakhand, India in 2012; and the collapse of a bridge in Nova Scotia, Canada (2020), and such examples may continue. Buckling poses a significant danger as it often occurs at lower load values compared to those considered during the design phase. Additionally, this phenomenon can manifest suddenly, without prior warning, rendering intervention for its prevention impossible or futile. In contemporary times, most research and design calculation software offer the capability to establish preliminary values for buckling loads, even for highly intricate structures. This is typically achieved through linear eigenvalue buckling analyses, often followed by significantly more complex large displacement nonlinear analyses. However, interpreting the results for complex bridge structures can be challenging, and their accuracy is difficult to ascertain. Consequently, this paper aims to introduce an original method for a more straightforward estimation of the buckling load of the upper chord in steel truss bridges. This method utilizes the theory of beams on discrete elastic supports. The buckling load of the upper chord was determined using both the finite element method and the proposed methodology, yielding highly consistent results. [ABSTRACT FROM AUTHOR]

The woven structure made of naturally curved (in-plane) ribbons has smooth geometry and fewer geometric imperfections, but there is no study of its buckling mechanical properties under vertical loads. The aim of this paper is to investigate buckling mechanical properties of spherical woven structures. Three spherical woven structures with different ribbon types and six new spherical woven structures with different ribbon widths and thicknesses were designed and the quasi-static vertical compression tests were carried out. The buckling load of spherical woven structures were studied by nonlinear finite element and ring buckling theory. Results indicate that the failure mode of the spherical weave structure under vertical loading can be divided into two stages, where a flat contact region forms between the spherical weave structure and the rigid plate and inward dimple of ribbons. Spherical weave structures using naturally curved (in-plane) ribbon weaving have better buckling stability than those woven with straight ribbon. Based on theoretical and finite element analysis, we propose a buckling load equation and buckling correction factor equation for the new spherical weave structure under vertical compression load. The formula is validated and has good agreement with the test results, which could help to design the stability of spherical weave structures with in-plane ribbons. [ABSTRACT FROM AUTHOR]

Grid-stiffened composite shells are one of the most important structures in many industries. These structures based on their fabrication method, provide both high strength and light structural weight. In this study, buckling analysis under external hydrostatic pressure is performed to obtain critical buckling pressure and the optimum values of parameters for stiffeners. First-order shear deformation theory (FSDT) based on the Ritz method is used to calculate the critical buckling load of these structures. The effects of shell thickness, angle of helical stiffeners, rib section area, and the stiffeners number into the buckling load are determined. Comparing the calculated buckling load for stiffened and non-stiffened structures shows that stiffeners significantly optimize structural performance. Furthermore, optimization of stiffener parameters is done by Genetic Algorithm. The results show that the introduced structure has the minimum mass. So, the stiffener parameters would be better. According to the results, the optimum dimensions for stiffener buckling load for the optimal stiffener have been increased by about 80% compared to non-stiffened.

This study presents a numerical investigation of the in-plane elastic-plastic performance, post-buckling mode, and arched web-post shear resistance of a pinned end circular arched cellular steel beam using ABAQUS nonlinear finite element analysis package. The trustworthiness of the finite element analysis results was confirmed by comparing them to the existing experimental investigation results. The main study parameters, such as the effect of a rise-to-span ratio, the radius of curvature, the impact of opening, the types of loading on elastic-plastic performance, and the buckling mode of an arched cellular steel beam, were investigated. Furthermore, the arched web-post finite element model was proposed and the shear resistance of the arched web-post was investigated. Also, the appropriateness of the currently existing different web-post shear resistance analysis approaches was reviewed and evaluated in determining the shear resistance of arched web-posts. The results showed that the web post-structural stiffness of a circular arched cellular steel beam was improved as the rise-to-span ratio increased under the mid-span concentrated load regardless of the rise-to-span ratio. However, under uniformly distributed vertical load, increasing a rise-to-span ratio beyond 0.35 or 140° subtended angles reduces the stiffness of circular arched cellular steel beams. The web post shear resistance analyzing approaches proposed by Panedpojaman et al. and SCI P-100 overestimate and yield unsafe results in determining the web-post shear resistance of arched web post cellular steel of low rise-to-span ratio.

Composite cylindrical shells play a crucial role in aerospace and marine structures. This study investigates the optimal structure for cylindrical multilayer composite shells under the effect of axial pressure using the finite element method and NSGA-II genetic algorithm to determine the maximum buckling load capacity. The critical buckling load of multilayer composite shells depends on various parameters, such as fiber angle, the number of layers, the material of the layers, and their thickness. The objective functions are used to increase the structure load capacity and reduce its weight. ABAQUS software was used to perform finite element analysis on the composite cylindrical shell for determining the buckling load. Using the response surface model, the relationship between variables and objective functions has been determined. Results of the proposed response surface model for the training stages are evaluated using various statistical indices and the root mean square error for buckling load and shell weight variables is 0.065 and 0.140, respectively. In the next step, the NSGA-II genetic optimization algorithm was used to modify the layout and thickness of the composite layers to optimize the buckling strength and weight of the structure. A genetic algorithm based on NSGA-II was used to optimize the geometric characteristics. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive review of the literature on hollow tubular structures, with applications ranging from traditional engineering structures to from simple circular tubes to modern corrugated structures. As such it provides an important reference for researchers to have a broad epigrammatic cognizance of the mechanical behavior of these structures. Hollow structures have long been seen as a simple and effective means of light weight structures with high stability under buckling load and energy absorption capability. This has been used in numerous industrial and academic applications. In recent years there have been numerous innovative developments to hollow tubular structures, involving more bewildering and inventive hollow structures which are better than solid structures as well as aesthetically more appealing. The use of corrugation and advanced composite materials are giving an added advantage by the virtue of which researchers can easily alter these structures and can make it beneficial or transform it according to their desired application. [ABSTRACT FROM AUTHOR]

To design a class of full cover trajectories that satisfy curvature limitations and enhance the buckling load of constructed laminates, a variable stiffness laminate is proposed by applying the cubic Ferguson curve. First, the traditional explicit form of the cubic Ferguson curve is redefined as polar coordinates, two connected Ferguson curve segments with three extra parameters are applied to describe full cover trajectories, and the effects on trajectories introduced by these modifications are discussed. Then, the finite element method is used to introduce parameters for analyzing the buckling load of the designed variable stiffness laminates. Numerical experiments show that automatic fiber placement (AFP) trajectories described by the cubic Ferguson curve can automatically reach C 1 continuity and can be locally modified by adjusting the introduced parameters. Compared with traditional constant stiffness laminates, the variable stiffness laminates designed using the proposed method exhibit a higher buckling load and better stability. [ABSTRACT FROM AUTHOR]

PVC pipe jacking is prone to cause yielding or buckling under the jacking force and may lead to engineering failure. The relationship between the buckling modes, ultimate bearing capacity, different diameter–thickness ratios, and length–diameter ratios of PVC pipe jacking under different load forms was analyzed. The calculation methods for allowable jacking force and the single allowable jacking distance are obtained through theoretical analysis and three-dimensional finite elements. The buckling mode of the pipe under uniform load changes from symmetric buckling to asymmetric buckling and then to the overall Euler buckling form as the length–diameter ratio increases. The ultimate bearing capacity of the pipe approaches the theoretical value of yield failure when L/D ≤ 6. For L/D > 6, the pipe undergoes buckling, and the ultimate bearing capacity determined by the axial buckling value and the buckling load can be calculated according to the long pipe theory formula when L/D > 8.5. Under eccentric loads, the failure mode transitions from local failure to Euler buckling with increasing pipe length. The ultimate bearing capacity of pipe is obviously lower than that of uniform load, but as the length–diameter ratio increases, this difference decreases until it becomes consistent.

This study proposes a new numerical method for the free vibration analysis of elastically restrained tapered Rayleigh beams with concentrated mass and axial force. The beam model had elastic support, concentrated mass at both ends, and axial force at the right end. The elastic supports were modeled as translational and rotational springs. The shear force and bending moment were determined under the assumption that the sum of the forces at arbitrary positions and the joint between the beam and elastic supports always becomes zero. Therefore, a frequency determinant is established considering the free-free end condition at both ends, but various boundary conditions were constructed by adjusting the values of the elastic springs in the frequency equation. This assumption simplified the deduction procedure, and the method's efficiency was demonstrated through various comparisons. In particular, the value of compressive loading at which the first natural frequency vanished was investigated by considering the taper ratio based on the relationship between the elastic support and compressive loading. The analyzed results can be adopted as benchmark solutions for other approaches. The frequency determinant employs the transfer matrix method; however, numerical methods can easily be utilized in other approaches. [ABSTRACT FROM AUTHOR]

In this paper, a new method using the backpropagation (BP) neural network combined with the improved genetic algorithm (GA) is proposed for the inverse design of thin-walled reinforced structures. The BP neural network model is used to establish the mapping relationship between the input parameters (reinforcement type, rib height, rib width, skin thickness and rib number) and the output parameters (structural buckling load). A genetic algorithm is added to obtain the inversely designed result of a thin-wall stiffened structure according to the actual demand. In the end, according to the geometric parameters of inverse design, the thin-walled stiffened structure is reconstructed geometrically, and the numerical solutions of finite element calculation are compared with the target values of actual demand. The results show that the maximal inversely designed error is within 5.1%, which implies that the inverse design method of structural geometric parameters based on the machine learning and genetic algorithm is efficient and feasible. [ABSTRACT FROM AUTHOR]

In recent years, the use of hybrid composites, in which natural fibers combine with synthetic fibers, in place of composite structures consisting only of synthetic fibers has become increasingly popular due to growing environmental concerns and the need to develop sustainable, more lightweight, recyclable materials required for engineering applications. In this regard, the present paper is an attempt to show the usage of sitka spruce as an alternative to synthetic E-glass fiber and natural flax fiber in design of interply hybrid composite structures in terms of fundamental frequency, buckling resistance and weight. The single-objective and multi-objective approaches are considered to acquire optimum design for non-hybrid and hybrid structures. The modified versions of the optimization methods Differential Evolution (MDE), Nelder Mead (MNM) and Simulated Annealing (MSA) algorithms are considered to solve problems. The results show that the optimum design of the hybrid graphite/epoxy-sitka spruce laminated plate to obtain the structure having a more lightweight (e.g., 53%), higher frequency (e.g., 65%) and buckling resistance (e.g., 90%) was computed and compared with those of the hybrid graphite-flax/epoxy, neat sitka spruce, neat flax/epoxy and neat glass/epoxy laminated composite plates. [ABSTRACT FROM AUTHOR]

This study investigated the buckling behavior of Porous Functionally Graded Material (PFGM) plates. The present model assumes unevenly distributed porosity along the plate thickness and the use of the novel hyperbolic shear deformation functions and hyperbolic tangent and secant thickness stretching functions. In the present work, a porous Functionally Graded (FG) plate was analyzed by the principle of virtual work in order to understand the buckling behavior under uniaxial and biaxial compressive loading. The Rayleigh quotient method was applied to find the critical buckling load. The mesh convergence was investigated on a Finite Element (FE) model, and the accuracy of the results was compared with the prior research. The results of the proposed model match reasonably well with the ones of the published literature. Thorough parametric studies were performed to investigate the effect of porosity on the critical buckling load of the PFGM plate. [ABSTRACT FROM AUTHOR]

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This article studies the large deflection stability of axially functionally graded (AFG) cantilever column for analyzing post-buckling behavior. Consideration is given to a nonlinearly tapered column with a regular polygon cross section, whose volume is constant. The governing differential equations of the problem are derived based on the large deflection beam theory. To calculate the elastica and buckling load of the AFG column, the differential equations are solved with the direct integration method together with the nonlinear solution method. The computed results are compared with those reported in literature and obtained from finite element method. Numerical examples are provided to ascertain the effects of the geometric and material parameters on the elastica and buckling load. The elastica shape is shown to depend on applied load and column properties, and the optimal shape such that the AFG column with fixed volume enables to bear the maximum buckling load is discussed. [ABSTRACT FROM AUTHOR]

New or in-service truss bridges, with or without upper bracing systems, may display instability phenomena such as general lateral torsional buckling of the upper chord. The buckling of structural elements, particularly in the case of steel bridges, can be associated with the risk of collapse or temporary/permanent withdrawal from service. Such incidents have occurred in the case of several bridges in different countries: the collapse of the Dee bridge with truss girders in 1847 in Cheshire, England; the collapse of the semi-parabolic truss girder bridge near Ljubičevo over the Morava River in Serbia in 1892; the collapse of the Dysart bridge in Cambria County, Pennsylvania in 2007; the collapse of the Chauras bridge in Uttarakhand, India in 2012; and the collapse of a bridge in Nova Scotia, Canada (2020), and such examples may continue. Buckling poses a significant danger as it often occurs at lower load values compared to those considered during the design phase. Additionally, this phenomenon can manifest suddenly, without prior warning, rendering intervention for its prevention impossible or futile. In contemporary times, most research and design calculation software offer the capability to establish preliminary values for buckling loads, even for highly intricate structures. This is typically achieved through linear eigenvalue buckling analyses, often followed by significantly more complex large displacement nonlinear analyses. However, interpreting the results for complex bridge structures can be challenging, and their accuracy is difficult to ascertain. Consequently, this paper aims to introduce an original method for a more straightforward estimation of the buckling load of the upper chord in steel truss bridges. This method utilizes the theory of beams on discrete elastic supports. The buckling load of the upper chord was determined using both the finite element method and the proposed methodology, yielding highly consistent results.

Analytical methods cannot find the exact solution for inelastic lateral torsional buckling. This study aims to develop innovative solutions by creating closed-form equations. A series of numerical studies (ANSYS) have been conducted for buckling load calculation on European I-section cantilever beams reinforced with transverse stiffener plates at different intervals. Formulations were developed using two methods to estimate the found load values more practically. Multiple linear regression analysis and multigene genetic programming methods were used to obtain these formulations. According to the error statistics, the multigene genetic programming method gave more accurate results than the multiple linear regression analysis methods in buckling load estimation. The estimates obtained from the multigene genetic programming method and the numerical results calculated in the ANSYS program were found to be compatible with each other. The scientific novelty brought by the research is to develop more original formulations for cantilever beams instead of using the buckling load calculation described for simply supported beams in the specifications. The scientific difference is that the developed formulations can calculate in a way that can consider the contribution of transverse stiffeners to the buckling load. This study will show that formulations designed with computer technologies can be an alternative calculation method for estimating the lateral buckling load according to the transverse stiffener plate spacing for European I-section cantilever steel beams. [ABSTRACT FROM AUTHOR]

A novel analytical approach for predicting the buckling load with its mode shape of friction piles fully embedded in soil is proposed, in which the lateral subgrade and axial friction resistances change linearly. The proposed approach considers uniform rectangular piles that are either free or pinned or fixed at the pile and toe. The differential equation that governs the mode shape of the buckling pile along with the boundary conditions was analytically derived and numerically solved using the Runge–Kutta method and the Regula-Falsi method. The buckling loads of this study agreed well with those reported in the literature. The buckling behavior of piles was discussed as factors affecting the end condition, aspect ratio, subgrade ratio, friction ratio, subgrade parameter and friction parameter. [ABSTRACT FROM AUTHOR]

Buckling‐restrained braces (BRBs) can effectively improve the stiffness, strength, and energy dissipation capacity of building structures. The key feature of the proposed truss‐confined BRB (TC‐BRB) is an additional truss confining system attached outside the central steel casing. The truss system is composed of several steel open‐web truss frames, thereby providing the required restraining rigidity and reducing the central casing section size and infilled mortar. The overall self‐weight is decreased compared with a conventional BRB, especially in cases of long‐span and large force capacity BRB applications. This research program was conducted to investigate the hysteresis behavior of the TC‐BRBs in terms of truss member response, buckling resisting ability, and cumulative deformation capacity. Six one‐third‐scale TC‐BRB specimens, each 6.3 m long and with different yield capacities, truss frame shapes and sizes, were tested using cyclically increasing loads with or without an out‐of‐plane end drift. The six specimens eventually failed either from global flexural buckling of the entire restraining system or a tensile fracture of the steel core at a very large axial strain. The experimental results demonstrated that the TC‐BRBs can be designed and fabricated to have a very stable and highly repeatable hysteretic response, meeting the American Institute of Steel Construction acceptance criteria. It provides a valuable database to support the further development of design guidelines for the engineering application of the proposed TC‐BRBs. [ABSTRACT FROM AUTHOR]

We prove the existence of an optimal domain for minimizing the buckling load among all, possibly unbounded, open subsets of R n ( n ≥ 2 ) with given measure. Our approach is based on the extension of a two-dimensional existence result of Ashbaugh and Bucur and on the idea of Alt and Caffarelli to focus on the eigenfunction. [ABSTRACT FROM AUTHOR]

In this paper, a novel framework is proposed to optimize variable stiffness (VS) composite circular cylinders designed with the direct fiber path parameterization technique using cubic and quadratic Bézier curves as curvilinear fiber paths. The Bézier curves allow generating fiber paths with nonlinear angle variation, and they are defined by simple design variables such as segment/station angles and multipliers/curvatures. A finite element model of VS shells under pure bending with stiffness variation in circumferential direction due to axially shifted courses is implemented and optimized for maximum buckling load considering curvature and strength constraints. The proposed design optimization framework, called pre-trained multi-step/cycle surrogate-based optimization, is conducted in two steps using a non-dominated sorting genetic algorithm (NSGA-II). The framework leverages prior knowledge of the design space by using laminated VS shells with single ply definitions in the first step before performing the optimization of all VS plies in the second step. Four different stacking sequences are considered, consisting of all VS plies and partial VS plies in combination with unidirectional fibers. The VS composite shell modeled using cubic Bézier curves of constant curvature as the fiber path for all plies shows a 41% increase in buckling load compared to the reference quasi-isotropic composite cylindrical shell. [ABSTRACT FROM AUTHOR]

The large fluctuation of uncertain parameters introduces a great challenge in the stability analysis of structures. To address this problem, a novel stochastic residual error based homotopy method is proposed in this article. This new method used the concept of homotopy to reconstruct a new governing equation for stochastic elastic buckling analysis, and the closed‐form solutions of the isolated buckling eigenvalues and eigenvectors are obtained by the stochastic homotopy analysis method. On this basis, a pth order origin moment of the stochastic residual error with respect to the elastic buckling equation is defined. Then, the optimal form of the homotopy series can be determined automatically by minimizing the pth order origin moment, which overcomes the disadvantage of highly relying on sample values of the existing homotopy stochastic finite element method. Moreover, the proposed method is developed to deal with the stochastic closely spaced buckling eigenvalue problem. Three mathematical examples and three buckling eigenvalue examples, including a variable cross‐section column, a 7‐story frame, and a Kiewitt single‐layer latticed spherical shell, are performed to illustrate the accuracy and effectiveness of the proposed method by comparing with the existing methods when dealing with large fluctuation of random parameters. [ABSTRACT FROM AUTHOR]