Ratio Of Buckling Load Research Articles

Numerical Optimization of the Dendritic Arm of a Radial Gate Based on Stability and Light Weight

A new dendritic arm structure was proposed to achieve the stability and lightness of a large-scale radial gate arm. The arm structure was arranged in accordance with the current gate design specifications for steel. The optimization aims were to achieve the highest possible overall structural stability and the lowest possible weight. As the failure criterion for the entire structure, the simultaneous instability of the trunks and branches of the dendritic arm was considered. The constraints of strength, stiffness, and stability were identified, and an optimization model of a dendritic arm with two branches was established. A geometric and material nonlinear buckling analysis and optimization solution was implemented for the dendritic arm with a different radius, type, and unit rigidity ratios. Compared to a conventional radial gate structure with two arms, the Y-type dendritic arm structure was lighter and more stable. The optimal dendritic arm had the following parameter settings: the angle ratio between two branches and two arms was [1.92, 2.04], the unit rigidity ratio between the trunk and branch was [5.33, 6.02], the length ratio between the branch and trunk was [0.96, 1.09], the height ratio of the trunk and branch was 1.805, and the flange thickness ratio of the trunk and branch was 1.405. In this case, the overall buckling load ratio between the dendritic arm and two arms was [2.50, 4.34], and the material saving rate was [37, 53] (%). Within the aforementioned parameters, the Y-type dendritic arm performed better overall. Moreover, the radius of the radial gate had minimal influence on the shape and mechanical properties of the Y-type dendritic arm structure. This paper proposes a dendritic arm that can be utilized in most radial gate projects.

Behaviour, finite element modelling and design of cruciform section steel columns

A study into the mechanical behaviour and design of steel equal-leg cruciform section members subjected to axial compression is presented. Experimental data from the literature are used to validate shell finite element models developed within the commercial package ABAQUS for their load-deformation and ultimate behaviour. A numerical parametric study then considers cruciform section columns with a wide range of slenderness ratios and various common boundary conditions. The mechanical response and load-carrying capacity are shown to be dependent not only on the column slenderness but also on the torsional to flexural elastic buckling load ratio. Finally, a recently established design approach for steel angle section columns is extended to include cruciform section members, and verified against the available results. It is found through reliability analysis based on the EN 1990 procedure that the new proposal also offers substantially improved accuracy and consistency in strength predictions compared to the existing codified design rules for cruciform section columns; a recommended partial safety factor of 1.0 is determined.

Experimental and numerical study of hybrid (CFRP-GFRP) composite laminates containing circular cut-outs under shear loading

Previous works have established the response and failure behaviour of hybrid (CFRP-GFRP) laminates when subjected to a wide range of destabilising loads. However, to date no works have focused on plates with cut-outs under shear loading and quantified the influence of selective laminate shapes and hybridisation on their post-buckling response. Herein, the plate collapse behaviour of a novel X-braced hybrid (CFRP-GFRP) twill woven laminate containing a large circular cut-out (diameter to width ratio of 0.35), subjected to in-plane shear loading is investigated. The study includes a hybrid and a baseline pure CFRP design and employs both experimental and numerical analysis. The experimental results illustrate that despite having less CFRP material, a hybrid laminate design with shaped CFRP plies exhibits greater failure load (+9%), and a greater failure load to buckling load ratio (1.26 compared to 1.12). However, this comes at the cost of a marginally lower initial plate buckling load (-3%). Additionally, the combined experimental and numerical analysis reveals the detailed failure mechanism of both the pure CFRP and hybrid laminates, demonstrating similar behaviour but that the hybrid design endures significantly more widespread shear damage of the matrix.

Global–global interaction in cold-formed steel plain and lipped channel columns

While investigating how accurately the current Direct Strength Method (DSM) global strength curve predicts the major-axis flexural–torsional failures of cold-formed steel columns, the authors (Dinis et al., 2019; 2020) found strong evidence that, for some column lengths and end support conditions, the ultimate strength is eroded by the coupling between major-axis flexural–torsional (FMT - critical) and minor-axis flexural (Fm) bucking (the first two global buckling modes) - i.e, a global–global (G–G) coupling/interaction. This finding is at the root and provided the motivation for the ongoing numerical investigation whose first results are reported in this work. The paper presents and discusses results concerning the behaviour and DSM design of cold-formed steel (CFS) fixed-ended plain and lipped channel columns that buckle in FMT modes and undergo G–G interaction. After a brief review of the DSM-based design approach that was proposed to handle column FMT failures (Dinis et al., 2020), attention is turned to investigating the column (i) buckling behaviour, essential for the selection of column geometries susceptible to G–G interaction, and (ii) FMT non-linear (post-buckling) behaviour — special care is devoted to the identification of the most detrimental initial geometrical imperfection shape. Then, the FMT failure loads of the selected columns are obtained for five yield stresses (to cover wide slenderness ranges) and the gathered failure load data are used (i) to clearly show that the existing DSM-based design approach cannot adequately predict them and (ii) as guidance for its modification, which brings about the Fm-to-FMT buckling load ratio and enables the adequate handling of also G–G interactive failures. The excellent failure load prediction quality exhibited by this modified design approach is very encouraging and makes the authors believe that its domain of application can be extended to CFS columns with other cross-sections and/or end support conditions — research is under way to assess whether this belief is well founded.

Stability analysis of restrained nanotubes placed in electromagnetic field

In this present work, buckling analysis of restrained nanotubes placed in electromagnetic field is studied on the basis of Euler–Bernoulli beam theory in conjunction with Eringen’s nonlocal elasticity theory. The modal displacement function is assumed for the stability analysis in order to discretize the derived governing equation. A Fourier sine series with Stoke’s transformation is utilized to investigate the buckling response. The essential advantage of this transformation is its ability of dealing with various boundary conditions to determine the buckling loads. For demonstrate the effects of various parameters such as Hartmann parameter, spring parameter and mode number on the stability response and critical buckling load of electromagnetic nanobeam a detailed study is presented. Variations of buckling loads, critical buckling loads and buckling load ratios of the nanobeam are exhibited with a number of tables and plotted figures. The results obtained from the analysis are discussed on the tables and figures.

Experimental investigation on cold-formed steel stiffened lipped channel columns undergoing local-distortional interaction

Abstract The objective of this work is to report a careful experimental investigation, planned at the University of Lisbon and carried out at The University of Hong Kong, concerning the behaviour and ultimate strength of cold-formed steel web-flange-stiffened (WFSLC) and web-stiffened (WSLC) lipped channel columns undergoing local-distortional (L-D) interaction. It involves 31 specimens (16 WFSLC+ 15 WSLC), brake-pressed from high-strength zinc-coated grades G450, G500 and G550 structural steel sheets, exhibiting critical distortional-to-local buckling load ratios ranging between 0.75 and 1.88. The column geometries were carefully selected to enable testing fixed-ended columns undergoing true L-D interaction and secondary distortional-bifurcation L-D interaction (ensuring evidence of the latter required selecting rather slender columns) − all tested specimens exhibited the expected L-D interactive failures. The specimen material properties were obtained from tensile coupon tests and their initial geometrical imperfections were measured prior to testing. The experimental results presented and discussed consist of column (i) load-displacement equilibrium paths, (ii) photos evidencing the evolution of the column deformed configurations along those paths (including the failure mode) and (iii) failure loads. Finally, the experimental failure load data obtained are compared with their estimates provided by the currently codified DSM design approaches for columns failing in L and D modes, showing their inadequacy to handle L-D interactive failures − the fresh light shed by this comparison will contribute to the timely codification, in the near future, of a DSM design procedure for columns affected by L-D interaction.

Multiobjective optimization of modular structures: Weight versus geometric versatility in a Truss‐Z system

AbstractThis paper proposes an approach for multicriterial optimization of modular structures with respect to their structural and geometrical properties. The approach is tested using the quickly deployable and reconfigurable modular ramp system Truss‐Z intended for pedestrian traffic. The focus is on modular structures composed of a moderate number of relatively complex modules, which feature an irregular, noncuboidal geometry. Such modules can be assembled into a variety of geometrically different configurations which do not adhere to any predefined spatial grid; their global geometry can be treated as free‐form and determined in situ during construction. The optimization variables represent local‐level geometrical and structural properties of a single module. The Pareto front is used to balance between two kinds of objectives. The geometrical objective quantifies the ability of the modules to generate geometrically versatile global structures that are well‐suited to comply with spatial constraints of real construction sites. The structural objective is formalized in analogy to the minimum weight problem with upper bound constraints imposed on the von Mises stress and the Euler buckling load ratio. A two‐level optimization scheme is employed with NSGA‐II at the top level and a simulated annealing with adaptive neighborhood at the lower level.

Post-buckling behaviour of thin-walled regular polygonal tubular columns undergoing local-distortional interaction

This work presents and discusses numerical results of an ongoing investigation concerning the elastic post-buckling behaviour and imperfection sensitivity of regular convex polygonal cross-section (RCPS) tubular columns affected by local-distortional (L-D) interaction. This investigation is conducted by means of geometrically non-linear Generalized Beam Theory (GBT) analyses, extending the knowledge on the “pure” local and distortional post-buckling behaviours of RCPS tubes recently reported by Martins et al. [1]. Due to their inherent modal nature, the GBT analyses make it possible to acquire in-depth knowledge on the structural behaviour of RCPS tubes and also to include, in a straightforward fashion, arbitrary member initial geometrical imperfections. Columns with distortional-to-local critical buckling load ratios (i) close to 1 (“true L-D interaction” – the most trivial L-D interaction type) and (ii) significantly above 1 (“secondary-distortional bifurcation L-D interaction” – the most relevant L-D interaction type) are investigated. Local/distortional critical-mode initial geometrical imperfections and (linear) combinations of both are considered in the former columns, while only local initial imperfections are dealt with in the latter ones – several amplitudes are dealt with to assess the imperfection sensitivity. For comparison and validation purposes, ABAQUS shell finite element analysis results are also reported.

On the local and distortional post-buckling behaviour of thin-walled regular polygonal tubular columns

This paper presents and discusses numerical results concerning the (i) elastic local and distortional post-buckling behaviours and (ii) imperfection sensitivity of regular convex polygonal cross-section (RCPS) simply supported tubes under uniform compression (columns). Although it was shown recently that the local and distortional buckling behaviours may be often characterised by duplicate bifurcation modes, knowledge concerning the corresponding post-buckling behaviour is still lacking. The results presented are obtained through a geometrically non-linear Generalised Beam Theory (GBT) formulation previously reported by the authors. This GBT formulation is first employed to characterise the column bifurcation behaviour, namely by helping to pinpoint the occurrence of the above two distinct buckling behaviours. Then, post-buckling results are presented and discussed for (i) different combinations of the local-to-distortional buckling load ratio and the (ii) amplitude of the critical-mode initial geometrical imperfections, in order to characterise the RCPS column imperfection sensitivity. Such results provide the evolution, along given equilibrium paths, of the column deformed configurations (expressed in GBT modal form), relevant displacement profiles and participation diagrams based on either stress resultant strain energies or amplitude functions. For comparison and validation purposes, ABAQUS shell finite element values are reported.

Postbuckling and Free Nonlinear Vibration of Microbeams Based on Nonlinear Elastic Foundation

In this paper, post-buckling and free nonlinear vibration of microbeams resting on nonlinear elastic foundation subjected to axial force are investigated. The equations of motion of microbeams are derived by using the modified couple stress theory. Using Galerkin’s method, the equation of motion of microbeams is reduced to the nonlinear ordinary differential equation. By using the equivalent linearization in which the averaging value is calculated in a new way called the weighted averaging value, approximate analytical expressions for the nonlinear frequency of microbeams with pinned–pinned and clamped–clamped end conditions are obtained in closed-forms. Comparisons with previous solutions are showed accuracy of the present solutions. Effects of the material length scale parameter and the axial compressive force on the frequency ratios of microbeams; and effect of the material length scale parameter on the buckling load ratios of microbeams are investigated in this paper.

On the distortional-global interaction in cold-formed steel columns: Relevance, post-buckling behaviour, strength and DSM design

This work reports the available results of an ongoing numerical (shell finite element) investigation on the post-buckling behaviour, strength and design of fixed-ended cold-formed steel columns undergoing distortional-global (D-G) interaction. Columns with different cross-section shapes are analysed, namely plain lipped channel (LC), web-stiffened lipped channel (WSLC) and zed-section (Z) columns, in order to investigate distinct D-G interaction natures: involving either distortional and (global) flexural-torsional buckling (LC and WSLC columns) or distortional and (global) minor-axis flexural buckling (Z columns). In particular, the relevance of these D-G interaction types is discussed, by assessing when they affect visibly the column ultimate strength and/or failure mode. The results presented and discussed concern columns with various geometries and yield stresses, thus ensuring a wide variety of range combinations involving (i) global-to-distortional critical buckling load ratios (RGD) and (ii) squash-to-non critical buckling (distortional or global) load ratios (Ry) and leading to non-negligible failure load erosion. The possible occurrence and failure load impact of “secondary (distortional or global)-bifurcation D-G interaction” (RGD<1.0 or RGD>1.0 and high Ry) are investigated - it is well known that such impact may be significant in columns experiencing “true D-G interaction” (RGD≈1.0). The above results consist of (i) relevant non-linear (elastic and elastic-plastic) equilibrium paths, (ii) deformed configuration evolutions along those paths, evidencing D-G interactive effects, and (iii) figures providing the failure mode characterisation. Then, the numerical failure load data obtained are compared with their predictions by (i) the currently codified DSM (Direct Strength Method) column global and distortional strength curves, and (when necessary) (ii) proposed DSM-based design approaches, specifically developed to handle D-G interactive failures - a few design considerations are drawn from these comparisons.

Free vibration and biaxial buckling analysis of double magneto-electro-elastic nanoplate-systems coupled by a visco- Pasternak medium via nonlocal elasticity theory

Abstract This paper deals with the analysis of free vibration and biaxial buckling of double-magneto-electro-elastic nanoplate-systems (DMEENPS) subjected to initial external electric and magnetic potentials, using nonlocal plate theory. It is supposed that the two nanoplates are bonded with each other using a visco-Pasternak medium, and are also limited to the external elastic substrate. Hamilton's variational principle is applied to acquire the partial differential equations of motion and corresponding boundary conditions for three modes (out-of-phase, in-phase and one nanoplate fixed) and solved analytically to determine clear closed-form phrase for complex natural frequencies natural frequencies and buckling loads. Numerical examples are performed to demonstrate the changes of the vibration frequency and buckling load ratio ( N L L ) of DMEENP against to different values of the nonlocal parameters, initial external electric and magnetic potentials, aspect ratio, damping and transverse stiffness coefficients of the viscoelastic foundation, shear stiffness coefficient of Pasternak medium, length to thickness ratio, nanoplate thickness and higher modes. Also, the effect of biaxial compression ratio on the buckling load is investigated. Results of this study show that considering the interaction between two Magneto-electro-elastic nanoplates lead to achieving greater frequencies and biaxial buckling loads. Moreover, the influences of the nonlocal parameter become more pronounced when the half wave number, initial external electric potential and aspect ratio increase, while the effect of the length to thickness ratio and initial external magnetic potential has the opposite trend.

Free vibration and biaxial buckling analysis of magneto-electro-elastic microplate resting on visco-Pasternak substrate via modified strain gradient theory

This paper deals with the theoretical analysis of free vibration and biaxial buckling of magneto-electro-elastic (MEE) microplate resting on Kelvin–Voigt visco-Pasternak foundation and subjected to initial external electric and magnetic potentials, using modified strain gradient theory (MSGT). Kirchhoff plate model and Hamilton’s principle are employed to extract the governing equations of motion. Governing equations were analytically solved to obtain clear closed-form expression for complex natural frequencies and buckling loads using Navier’s approach. Numerical results are presented to reveal variations of natural frequency and buckling load ratio of MEE microplate against different amounts of the length scale parameter, initial external electric and magnetic potentials, aspect ratio, damping and transverse and shear stiffness parameters of the visco-Pasternak foundation, length to thickness ratio, microplate thickness and higher modes. Numerical results of this study illustrate that by increasing thickness-to-material length scale parameter ratio, both natural frequency and buckling load ratio predicted by MSGT and modified couple stress theory are reduced because the non-dimensional length scale parameter tends to decrease the stiffness of structures and make them more flexible. In addition, results show that initial external electric and initial external magnetic potentials have no considerable influence on the buckling load ratio and frequency of MEE microplate as the microplate thickness increases.

Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

In this study, nonlocal elasticity theory in conjunction with Gurtin–Murdoch elasticity theory is employed to investigate biaxial buckling and free vibration behavior of nanoplate made of functionally graded material (FGM) and resting on a visco-Pasternak standard linear solid-type of the foundation. The material characteristics of simply supported FGM nanoplates are assumed to be varied continuously as a power law function of the plate thickness. Hamilton’s principle is implemented to derive the non-classical governing equations of motion and related boundary conditions, which analytically solved to obtain the explicit closed-form expression for complex natural frequencies and buckling loads. Finally, attention is focused on considering the influences of various parameters on variation of damped natural frequency and buckling load ratio such as nonlocal parameter, surface effects, geometric parameters, power law index and properties of visco-Pasternak foundation and it is clearly demonstrated that these factors highly affect on vibration and buckling behavior.

Biaxial buckling analysis of double-orthotropic microplate-systems including in-plane magnetic field based on strain gradient theory

Background/purposeThis paper deals with analysis of biaxial buckling behavior of double-orthotropic microplate system including in-plane magnetic field, using strain gradient theory. MethodsTwo Kirchhoff microplates are coupled by an internal elastic medium and also are limited to the external Pasternak elastic foundation. Utilizing the principle of total potential energy, the equilibrium equations of motion for three cases (out-of-phase buckling, in-phase buckling and buckling with a plate) are acquired. In this study, we assumed boundary conditions of all the edges are simply supported. In order to get exact solution for buckling load of system, Navier approach which satisfies the simply supported boundary conditions is applied. ResultsVariations of the buckling load of double-microplate system subjected to biaxial compression corresponding to various values of the thickness, length scale parameter, magnetic field, stiffness of internal and external elastic medium, aspect ratio, shear stiffness of the Pasternak foundation and biaxial compression ratio are investigated. Furthermore, influence of higher modes on buckling load is shown. By comparing the numerical results, it is found that dimensionless buckling load ratio for in-phase mode is more than those of out of phase and one microplate fixed. Also it is shown that the value of buckling load ratio reduces, when non-dimensional length scale parameter increases. ConclusionHowever, we found when properties of plate are orthotropic the buckling load ratio is more than isotropic state. Also, by considering the effect of magnetic field, non-dimensional buckling load ratio reduces.

An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory

Abstract In this paper, analytical closed-form solutions in explicit forms are presented to investigate small scale effects on the buckling and the transverse vibration behavior of Levy-type rectangular nanoplates based on the Reddy's nonlocal third-order shear deformation plate theory. Two other edges of Levy-type rectangular nanoplates may be restrained by different combinations of free, simply supported, or clamped boundary conditions. Hamilton's principle is used to derive the nonlocal equations of motion and natural boundary conditions of the nanoplate. Two comparison studies with analytical and numerical techniques reported in literature are carried out to demonstrate the high accuracy of the present new formulation. Comprehensive benchmark results with considering the small scale effects on frequency ratios, buckling load ratios, non-dimensional fundamental natural frequencies and non-dimensional buckling loads of rectangular nanoplates with different combinations of boundary conditions are presented for various values of nonlocal parameters, aspect ratios and thickness to length ratios. It is observed that except for SFSF rectangular nanoplates, as the aspect ratio increases, buckling load and natural frequency decreases, while keeping all other parameters fixed. For SFSF rectangular nanoplates, by increasing the aspect ratio, the values of the buckling load and frequency ratio increase.

Large amplitude dynamics of beam subjected to a compressive axial force resting on non -linear elastic foundation

In this paper, the large amplitude of free vibration and buckling of Euler–Bernoulli beam rests on a non-linear elastic foundation subjected to an axial force are studied. Hamilton’s principle is followed to derive governing equation of the beam response. Using an analytical method based on the Galerkin technique,the nonlinear governing equations of motion was simplified to a time-dependent Duffing equation with cubic nonlinearities and then solved using Laplace Iteration Method. Comparison between results of the present work and those available in literature review shows reasonable agreement of this method. Effects of vibration amplitude, elastic coefficients of foundation and axial force on the non-linear natural frequencies and buckling load of beams are presented. Results reveal that decreasing linear and shear parameters and increasing nonlinear parameters of foundation lead to increasing frequency ratio and buckling load ratio. Furthermore, increasing axial force decreases absolute values of both linear and nonlinear frequencies as well as natural frequency ratio.

Elastic stability of thick auxetic plates

Auxetic materials and structures exhibit a negative Poisson’s ratio while thick plates encounter shear deformation, which is not accounted for in classical plate theory. This paper investigates the effect of a negative Poisson’s ratio on thick plates that are subjected to buckling loads, taking into consideration the shear deformation using Mindlin plate theory. Using a highly accurate shear correction factor that allows for the effect of Poisson’s ratio, the elastic stability of circular and square plates are evaluated in terms of dimensionless parameters, namely the Mindlin-to-Kirchhoff critical buckling load ratio and Mindlin critical buckling load factors. Results for thick square plates reveal that both parameters increase as the Poisson’s ratio becomes more negative. In the case of thick circular plates, the Mindlin-to-Kirchhoff critical buckling load ratios and the Mindlin critical buckling load factors increase and decrease, respectively, as the Poisson’s ratio becomes more negative. The results obtained herein show that thick auxetic plates behave as thin conventional plates, and therefore suggest that the classical plate theory can be used to evaluate the elastic stability of thick plates if the Poisson’s ratio of the plate material is sufficiently negative. The results also suggest that materials with highly negative Poisson’s ratios are recommended for square plates, but not circular plates, that are subjected to buckling loads.

Strength and stability of steel beam columns under blast load

A Single-Degree-of-Freedom (SDOF) model is used to determine the effect of axial load on column strength and stability during a blast event. The model, which accounts for the axial load–bending interaction (P–δ effect) and strain rate effect on the column dynamic response, is validated by comparing its results with experimental data from blast tests on full scale steel columns and with the results of the finite element software LS-DYNA. Maximum displacements and moments obtained from SDOF analysis are also compared with the results of the interaction formulas recommended by the Unified Facilities Criteria (UFC 3-340-02) design manual for steel structures. It is shown that the UFC method overestimates the column capacity for ductility ratios μ greater than one, irrespective of the axial load to Euler elastic buckling load ratio (P/Pe). Also for P/Pe>0.5, even if μ<1.0, the UFC method still overestimates the actual column capacity. For dealing with this problem in practical applications, non-dimensional beam column curves are developed to include the effects of the blast load and column properties on both its strength and stability.

Stability Analysis of Circular Nanorings Under Different Loading Behavior by Nonlocal Elasticity Theory

In this article, the small-scale effect on buckling analysis of radially compressed nanorings is investigated. The effect of small length scale is taken into account using nonlocal elasticity theory. The principle of virtual displacement is implemented to circular nanorings to derive the governing differential equations which are solved analytically. Inextensibility constraint exerted using Lagrange’s multiplier method. The effects of nonlocal parameter and load behavior on buckling loads, mode shapes and critical buckling load ratios are investigated. It is shown that the small length scale decreases the buckling load and also nonlocal parameter does not affect the mode shapes. It is also found that by increasing small scale effect, the relative difference between the classical and the nonlocal solutions increases.