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Purpose: This paper proposes a novel shear deformation theory to study the static bending and buckling of nanoplates subjected to flexomagnetic influence. This is done using the revolutionary shear strain theory and establishing finite element formulations based on the finite element technique. Methods: This study uses a finite element method to solve the nanoplate bending and buckling problem while taking into consideration the flexoelectromagnetic effect. Results: The investigation's novel aspects are summarized: since the flexomagnetic effect makes the plate stiffer, the maximum deflection is lowered when this effect is included. This effect also has varying influences on the plate under various boundary conditions, particularly the maximum position of the deflection, stress, Hz, and Bz responses. The thinner the plate thickness, the more pronounced the flexomagnetic effect. The flexomagnetic effect causes the thickness distribution of the stress components, Hz, and Bz to diverge from that of conventional structures (where this effect is disregarded), particularly for plates with CFFF boundary conditions. The longer the length of the compression zone increases, the lower the critical buckling load of the plate. The greater the stiffness of the elastic foundation, the better the plate can withstand compressive loads. Conclusion: The findings of this work provide a significant scientific foundation for the computation and development of nanoplates with magnetic properties. To design a structure that meets the necessary criteria, it is crucial to carefully choose geometric characteristics, boundary conditions, and stiffness parameters of the elastic foundation. According to this study, potential areas for additional research include investigating the impact of the flexomagnetic effect on nanoplates including fractures, optimizing nanostructures that exhibit flexomagnetic effects, and calculating the influence of flexomagnetic effects and temperature on nanostructures. [ABSTRACT FROM AUTHOR]

The stability behaviour of unsymmetrical laminated structures made of fibre-reinforced plastics is significantly influenced by bending–extension coupling and the comparatively low transverse shear stiffnesses. The aim of this work is to improve the analytical stability analysis of unsymmetrically laminated structures. With the discrete plate theory, the stability of laminated structures can be reduced to single laminated plates. The structure is divided into individual segments, and the surrounding structure is modelled by rotational elastic restraints. The governing equations for single plates under specific boundary conditions can be solved exactly with Lévy-type solutions. In this study, Lévy-type solutions for the mentioned boundary conditions under biaxial compressive load is described for the classical laminated plate theory, the first-order shear deformation theory and the third-order shear deformation theory (TSDT). In addition to transverse shear, bending–extension couplings of unsymmetrical cross-ply and antisymmetrical angle-ply laminates are considered. For the implementation of boundary conditions for the rotational restraints in the context of TSDT, a new set of conditions is formulated. The investigation shows very good agreement of the buckling load with comparative finite element analyses for different layups. [ABSTRACT FROM AUTHOR]

Propose: Investigation of mathematical solutions for including the self-weight of a column for calculating buckling critical load. The complexity of including self-weight resides in the fact that the mathematical formulation depends on elliptical integral solutions related to differential equations of the problem. Method: Comparing the analytical solutions with computation modeling. The obtained results with these computational models are approximate since they depend on the discretization of the domain of the problem while analytical solutions tend to be exact. An experimental activity was carried out for analyzing mathematical accuracy. Results: The investigation of buckling was performed through static as well as dynamic analysis. The results found shown differences smaller than 5% among the mathematical investigated solution. Besides that, all solutions represented well the problem in comparison with a laboratory test. Conclusion: It has been evaluated solutions for stability analyses of bars under self-weight, using Euler–Greenhill analytical approach, solutions with the eigenvalues from FEM analysis, and also a dynamic solution based on the Rayleigh's method, comparing them with dynamic laboratory tests. Can be concluded that the mathematical ways and the experimental investigation had a good agreement. Level of evidence: IV, evidence obtained from multiple mathematical methods, static and dynamic, is experimentally confirmed. [ABSTRACT FROM AUTHOR]

The study investigates the effect of eccentric load on the stability and post-critical states of thin-walled composite top-hat cross-section columns made of CFRP under compression. The specimens were subjected to compressive load on the universal testing machine Zwick Z100 with regard to both axial and eccentric compressive loads. On the basis of the experimental studies, numerical models of thin-walled composite profiles were designed and verified by numerical analysis based on the FEM. The first stage of the conducted studies was performing a linear buckling analysis of stability of composite structures. The second stage of the analysis involved performing a nonlinear analysis of the thin-walled structures with geometric imperfections reflecting the lowest buckling modes. The obtained test results showed various effects of non-axial compressive load on the critical load values and stiffness of the construction in the post-critical state. In the case of eccentric loading in the direction parallel to the web of the top-hat profiles, the critical load values practically did not change – a drop in the force did not exceed 1.5%, as well as there was no change in the stiffness of the structure in the post-critical state. The realization of the eccentricity in the direction perpendicular to the profile web caused a drop in the critical force equal 43% and a significant decrease in the stiffness of the structure. On the other hand, implementation of the eccentricity load toward the web caused an increase in the critical force by more than 20%, despite very small eccentricity values of only 4 mm were applied. This proved high sensitivity of the tested structures to the non-axial load in the direction perpendicular to the web of the profile. The FEM results and the experimental findings showed satisfactory agreement. [ABSTRACT FROM AUTHOR]

Abstract The present paper applies Sobol's variance-based global sensitivity analysis (SSA) to quantify the contribution of input imperfections to the load-carrying capacity (LCC) of an IPN 200 steel compressed member. LCC is evaluated using the geometrically and materially non-linear finite element solution with regard to the effects of initial random imperfections including residual stresses. Comparison of results of SSA for (i) buckling about the minor principal axis, (ii) buckling about the major principal axis and (iii) lateral–torsional buckling due to bending moment is performed on the non-dimensional slenderness interval of 0–2. SSA for (i) and (ii) is performed for steel grade (a) S235 and (b) S355, SSA for (iii) is performed only for steel grade S235. SSA found similarities in results (ia) and (ib), (iia) and (iib) and identified significant differences between results (ia) and (iiia), (iia) and (iiia), where sensitivity to the initial axial curvature is more than two times higher in (ia) than in (iiia). The relationships between the effects of initial imperfections on LCC and the design criteria of reliability of Eurocode 3 are discussed. [ABSTRACT FROM AUTHOR]

The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for allowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, t ] is guaranteed provided the product of its maximum growth rate (determined by the maximum eigen-root p >0) and the duration t does not exceed 2, i.e., p t <2. The proposed criterion ( p t =2) is applied to several problems of impacted buckling of elastic columns: (i) an elastic column impacted by a striking mass, (ii) longitudinal impact of an elastic column on a rigid wall, and (iii) an elastic column compressed at a constant speed ('Hoff problem'), in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion ( p t =2) can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients. [ABSTRACT FROM AUTHOR]

The localized analytical sensitivity for eigenfrequency is extended to the non-linear problem of 3D continuum buckling analysis. Implemented in a finite element approach the inherent complexity of mode switching and multiple eigenvalues is found not to be a practical problem. The number of necessary redesigns is of the order 10-20 as illustrated by a specific example, where also different cases of stiffness interpolation are exemplified. [ABSTRACT FROM AUTHOR]

This paper deals with a limit load assessment and preliminary experimental testing of a lattice-type steel tower used to support a newly designed, prototype small wind turbine having nine blades and a rotor diameter of 3.4 m. Small wind turbine and structural engineering codes of standards were followed with the purpose of implementing a system that meets European Union countries' legislation. The supporting lattice tower structure was subjected to a full-scale load test. This test verified that the structure can withstand the design loads. The finite element software ANSYS Mechanical was used to model and analyse the actual structure, and to determine the possible failure modes and their associated load levels. The most probable mode of failure for such a structure was found to be elastic buckling of the main corner posts. A number of finite element lattice tower models utilising different modelling strategies and solution methods are presented and analysed. The paper highlights the importance of using non-linear analyses as opposed to linear analyses and gives recommendations on the most reliable available modelling technique. Computational analyses' results are compared with measurements from a full-scale test on the tower structure. [ABSTRACT FROM AUTHOR]

This paper studies the buckling behavior of simply-simply supported Single-walled Carbon nanotubes (SWCNTs) with and without defects. The buckling of carbon nanotubes without defects was investigated using the Finite element method (FEM) and analytical treatment and that of carbon nanotubes with defects was studied only by FEM. The carbon nanotubes were modeled as beams and shells. Computations showed that beam elements in the given form provided varying results as shells in their numerical or analytical manner for a small aspect ratio. The defects resulted from the removal of randomly determined carbon atoms and beam elements connected to the nodes. The increasing number of defects decreased the critical buckling force of SWCNTs. The decrease in the critical buckling force was almost the same for SWCNTs with the same diameter but with different chirality. [ABSTRACT FROM AUTHOR]

This paper focuses on the buckling analysis of composite sandwich conical shells subjected to a uniform external lateral pressure based on the first-order shear deformation theory. Approximate analytical solutions are assumed to satisfy fully clamped boundary conditions and then Fourier decomposition and Galerkin method is applied to achieve closed-form relations of buckling loads. The closed analytical formula for the critical pressure has been verified by comparison with the finite-element solutions and a special case where the angle of the conical shell approaches zero, that is, a cylindrical shell. Based on this formula buckling analyses of sandwich conical shells with different types of core materials have been accomplished. The outcomes are achieved considering the effects of half-vertex cone angle, core thickness and indicating applicability, accuracy, and stability of the present method. [ABSTRACT FROM AUTHOR]

Uniformly stretched thin plates do not buckle unless they are in special boundary conditions. However, buckling commonly occurs around discontinuities, such as cracks, cuts, narrow slits, holes, and different openings, of such plates. This study aims to show that buckling can also occur in thin plates that contain no defect or singularity when the stretching is local. This specific stability problem is analyzed with the finite element method. A brief literature review on stretched plates is presented. Linear and nonlinear buckling stress analyses are conducted for a partially stretched rectangular plate, and various load cases are considered to investigate the influence of the partial loading expanse on the critical tensile buckling load. Results are summarized in iso-stress areas, tables and graphs. Local stretching on one end of the plate induces buckling in the thin plate even without geometrical imperfection. [ABSTRACT FROM AUTHOR]

This paper investigates topology design optimization for maximizing critical buckling loads of thin-walled structures using a moving iso-surface threshold (MIST) method. Formulation for maximizing linear buckling loads with additional constraints on load-path continuity and lower bound of eigenvalue is firstly presented. New physical response functions are proposed and expressed in terms of the strain energy densities determined in the two-steps of finite element buckling analysis. A novel approach by introducing a connectivity coefficient is developed to ensure continuity of effective load-path in optimum topology. The lower bound of eigenvalue is defined to eliminate spurious localized buckling modes. The MIST algorithm and its interfaces with commercial finite element (FE) software are given in detail. Numerical results are presented for topology optimization of plate-like structures to maximize critical buckling forces or displacements considering in-plane and out-of-plane buckling respectively. The FE analyses of the re-meshed final solid topologies with and without void material reveal that the presence of the void material has a significant effect on the out-of-plane buckling loads and a minor influence on the in-plane buckling loads. [ABSTRACT FROM AUTHOR]

Boron nitride nanotubes, like carbon nanotubes, possess extraordinary mechanical properties. Herein, a three-dimensional finite element model is proposed in which the nanotubes are modeled using the principles of structural mechanics. To obtain the properties of this model, a linkage between the molecular mechanics and the density functional theory is constructed. The model is utilized to study the buckling behavior of single-walled boron nitride nanotubes with different geometries and boundary conditions. It is shown that at the same radius, longer nanotubes are less stable. However, for sufficiently long nanotubes the effect of side length decreases. [ABSTRACT FROM AUTHOR]

Buckling of steel thin-walled semi-spherical shells with square cutout due to axial compressive loads has been studied by numerical simulations, and results were compared with those from the experiments. Three vertical compression loadings were applied to specimens using the following methods: a rigid flat plate and a rigid bar with circular and spherical cross sections. The main aim of this study is to determine the influence of the cut out size-to-location (a/H) and the thickness-todiameter (t/D) on the mean collapse load of the semi-spherical shells. The finite element models were analyzed using ABAQUS nonlinear buckling analysis and the experimental tests were performed using an INSTRON 8802 servo-hydraulic machine. Finally, the different results obtained using the two analysis methods were compared. The comparison reveals that experimental and numerical nonlinear model results match closely with each other. [ABSTRACT FROM AUTHOR]

Buckling analysis of sandwich plate was investigated using layerwise method. The formulation was based on the first-order shear deformation theory, and the Rayleigh-Ritz method was used for approximating and determining the displacement field. The results obtained from layerwise theory was compared with finite element results and showed good agreement. This study demonstrated that layerwise theory could describe buckling behavior of sandwich plates with high accuracy and represents a more realistic and acceptable description of behavior of the plates with much less computational cost. [ABSTRACT FROM AUTHOR]

A finite strain formulation is developed for elastic circular arches and rings in which the effects of shear deformations are included. Timoshenko beam hypothesis is adopted for incorporating shear. Finite strains are defined in terms of the normal and shear component of the longitudinal stretch. The constitutive relations for stress and finite strain are based on a hyperelastic constitutive model. Virtual work and equilibrium equations are derived. Closed-form in-plane buckling solutions are developed for circular rings and high arches under hydrostatic pressure. The effects of axial deformation prior to buckling as well as shear deformations are included in the buckling analysis. The formulation developed is compared with solutions in the literature and to the predictions of the finite element package ANSYS. The importance of including the effects of shear deformations for deep arches is investigated. [ABSTRACT FROM AUTHOR]

Thin-walled members that have one dimension relatively large in comparison to the cross-sectional dimensions are usually modelled by using beam-type one-dimensional finite elements. Beam-type elements, however, are based on the assumption of rigid cross-section, thus they only allow considerations associated with the beam axis behaviour such as flexural-, torsional- or lateral-buckling and cannot consider the effects of local deformations such as flange local buckling or distortional buckling. In order to capture the local effects of this type shell-type finite element models can be used. Based on the Bridging multi-scale approach, this study proposes a numerical technique that is able to split the global analysis, which is performed by using simple beam-type elements, from the local analysis which is based on more sophisticated shell-type elements. As a result, the proposed multi-scale method allows the usage of shell elements in a local region to incorporate the local deformation effects on the overall behaviour of thin-walled members without necessitating a shell-type model for the whole member. Comparisons with full shell-type analysis are provided in order to illustrate the efficiency of the method developed herein. [ABSTRACT FROM AUTHOR]

Conical shells are extensively used in numerous types of engineering structures with various types of geometric imperfections. Nonetheless, quite few are the studies investigating the effect of special types of imperfections on the buckling load of conical shells under external pressure. In the present study, depression type of imperfection which is found in the zone of longitudinal weld is in the center of attention. To this end, this paper reports on different simulations including finite element results and discusses the effect of this type of imperfection on the critical buckling load of such structures. Obtained results are compared with the previous corresponding test results, some theoretical predictions, recommendations and codes. [ABSTRACT FROM AUTHOR]

A mixed atomistic and continuum model is applied to carbon nanotubes, in order to study their buckling behavior. Herein, the term 'atomistic' refers to the underlying constitutive model that is formulated on the basis of interatomic potentials, whereas 'continuum' means the application of the Cauchy-Born rule, which links the bond vectors before and after deformation via the deformation gradient of the continuum. Because the bond vectors are not infinitesimal and the continuum is modeled as surface, the Cauchy-Born rule has to be appropriately adapted to crystalline sheets. This is done via an exponential mapping in a new and surprisingly simple form such that in the analysis the current configuration has never to be left. The numerical buckling analysis of carbon nanotubes using the mixed atomistic and continuum model is carried out by means of the finite element method. For this purpose, the linearization of the equilibrium equations is provided. [ABSTRACT FROM AUTHOR]

In the present work, an avant-garde study on Buckling of honeycomb sandwich panel of hexagonal cell has been carried out by considering simply supported boundary constraints explicitly. A novel theoretical formulation has been developed for the buckling of honeycomb panel as per Mil Standard (MIL-HDBK-23A). The laminate element type has been considered for linear static analysis using Lanczos Method (finite element method (FEM)). The buckling analysis carried out by FEM has been compared and validated with theoretical and experimental investigation for different panel aspect ratio under static load. [ABSTRACT FROM AUTHOR]

Making use of a mixed variational formulation based on the Green function of the substrate, which assumes as independent fields the structure displacements and the contact pressure, a simple and efficient finite element-boundary integral equation coupling method is derived and applied to the stability analysis of beams and frames resting on an elastic half-plane. Slender Euler-Bernoulli beams with different combinations of end constraints are considered. The examples illustrate the convergence to the existing exact solutions and provide new estimates of the buckling loads for different boundary conditions. Finally, nonlinear incremental analyses of rectangular pipes with compressed columns and free or pinned foundation ends are performed, showing that pipes stiffer than the soil may exhibit snap-through instability. [ABSTRACT FROM AUTHOR]

Many historically and culturally significant buildings have sandstones that contain swelling clay inclusions in the binding phase. Differential strains that evolve during wetting and drying cycles can generate stresses that are on the order of the strength of the stone, leading to degradation. Most damage observed in the field is surface delamination and buckling of the stone over a flaw, indicating that the damage is occurring during wetting. Classical buckling theory predicts buckling to occur at a particular aspect ratio, or flaw size. The results of this study confirm buckling theory experimentally. Through finite-element simulation and experiment, the study then explores a potential flaw propagation mechanism whereby nonuniform wetting patterns generate stress intensities capable of flaw propagation. As a result, small natural flaws can grow to the critical size necessary for buckling. [ABSTRACT FROM AUTHOR]

In this study, out-of-plane stability analysis of tapered cross-sectioned thin curved beams under uniformly distributed radial loading is performed by using the finite-element method. Solutions referred to as Bolotin's approach are analysed for dynamic stability, and the first unstable regions are examined. Out-of-plane vibration and out-of-plane buckling analyses are also studied. In addition, the results obtained in this study are compared with the published results of other researchers for the fundamental frequency and critical lateral buckling load. The effects of subtended angle, variations of cross-section, and dynamic load parameter on the stability regions are shown in graphics [ABSTRACT FROM AUTHOR]

In the present study optimal design of composite laminates, with and without rectangular cut-out, is carried out for maximizing the buckling load. Optimization study is carried out for obtaining the maximum buckling load with design variables as ply thickness, cut-out size and orientation of cut-out with respect to laminate. Buckling load is evaluated using a 'simple higher order shear deformation theory' based on four unknown displacements u, v, w and w. A C continuous shear flexible finite element based on HSDT model is developed using Hermite cubic polynomial. It is observed that for thick anti-symmetric laminates, the non-dimensional buckling load decreases with increase in aspect ratio and increase in fibre orientation angle. There is a decrease in the non-dimensional buckling load of symmetric laminate in the presence of cut-out. [ABSTRACT FROM AUTHOR]

The axisymmetric buckling (delamination) of a circular disk (plate) with a penny-shaped crack is analyzed using a continuum model, piecewise-homogeneous model, and the three-dimensional linearized theory of stability. The FEM is used. The analysis is carried out using various singular and ordinary finite elements. The numerical results obtained indicate that it is not necessary to use singular finite elements to solve the problem [ABSTRACT FROM AUTHOR]

The current paper addresses the problem of 2-D modelling of the onset of failure process in a layered composite with periodic array of interfacial cracks under static compression along layers. The statement of the problem is based on the most accurate approach, the model of piecewise-homogenous medium. The condition of plane strain state is considered. The shear and the extensional buckling modes are examined. The laminae are modelled by transversally isotropic material (a matrix reinforced by continuous parallel fibres). The complex non-classical failure mechanics problem is solved utilizing finite element analysis. It is found that the 0°-plies volume fraction, the crack length and the mutual position of cracks influence the critical strain in the composite. [ABSTRACT FROM AUTHOR]

The dynamic buckling of thin copper plate induced by laser beam, was analyzed with the numerical integration and disturbance methods of controlling equation. The buckling and post-buckling of thin plate were shown, with the consideration of the temperature distribution, inertia effect and initial deflection. At last, the buckling criterion about the circular plate was obtained and used to investigate the relation between the critical laser intensity and the ratio of thickness and diameter of the plate. The results fit the experimental observation and the FEM simulation very well, and benefit to the understanding of failure phenomenon of structures irradiated by laser beam. [ABSTRACT FROM AUTHOR]

The purpose of the present study is to develop a new finite element method for analyzing buckling of delaminated composite plates and shells. This is achieved by establishing a new finite element called the reference-surface element. By use of the compatibility condition under Mindlin assumptions, the formulation of the reference-surface element was derived from whichever plate-element or shell-element being capable of analyzing composite plates and shells. This method assures a reasonable description of displacement field and the satisfaction of compatibility conditions for delamination problem. Numerical results for linear delamination buckling of axially compressed shells are presented to validate the method. [ABSTRACT FROM AUTHOR]