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The application of Topology Optimisation (TO) to help in the manufacture of metallic components in highly technological industries has increased recently. To equally benefit from TO, the construction industry must address its specific issues, such as adherence to code requirements and challenges in using cutting-edge software packages in complex joints with non-linear behaviour. To assist in such a challenge, the current study offers a methodology proposal to synthesise code and structural behaviour requirements into geometrical constraints for the optimisation problem of laminar steel parts under compression while integrating Non-linear Finite Element Analyses (NLFEA) that ensure the safety of the solution. It has been found that, for a real case-study, the initial volume of a connection's cover-plate can be decreased by up to 40% while maintaining the connection's original capacity and that a 30% volume decrease may be achieved while keeping the original plate capacity. In both cases, the plate's ultimate deformation capacity was enhanced. Evidence has been found that Linear Elastic TO may not provide safe-sided solutions for parts with an intrinsic non-linear behaviour. With the attained volume reductions, less raw materials may be consumed, assembly and transportation will be facilitated, and the goals of the sector's decarbonisation, energy intensity and sustainability will be favoured. [ABSTRACT FROM AUTHOR]

This paper deals with the determination of numerical and experimental buckling loads for circular plates. In the study, plates made of isotropic material and laminated composites were taken into consideration. For the experimental part of the study, a buckling apparatus for circular plates (BACIP) was designed and manufactured to apply radial compression on plates simply supported along the outer edge, which was the most important aspect of the study. Experimental buckling loads were determined by connecting this apparatus to a tension machine. ANSYS software based on the Finite Element Method (FEM) and the analytical buckling load formula found in textbooks were also used for the determination of the numerical and analytical buckling loads. The effects of parameters such as plate thickness, number of layers, cutout sizes, and so on on critical buckling loads were investigated within the scope of the work. Comparisons of analytical, theoretical and experimental buckling loads were presented in both graphical and tabular form. The results of the experimental and theoretical buckling were found to be comparatively compatible. [ABSTRACT FROM AUTHOR]

This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations. [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]

In this study, an analytical solution based on the first-order shear deformation theory was performed for free vibration and buckling analysis of functionally graded porous beams (FGM-P) subjected to various boundary conditions. Also, this problem is solved by using finite element (FEM) and artificial neural network (ANN) methods. Here a Ritz-based analytical solution is used, and different polynomial series functions are proposed for each boundary condition. Lagrange's principle was used while deriving the equations of motion. A power-law rule describes the variation of the beam's materials in volume. The normalized fundamental frequencies and critical buckling loads are obtained for various boundary conditions, power-law index (k), slenderness (L/h), porosity coefficient (e), and porosity distribution (FGM-P1, FGM-P2). The polynomial series functions used in this study were verified with the literature, and the numerical results obtained were compared with FEM and ANN. The results obtained are quite compatible with each other. [ABSTRACT FROM AUTHOR]

This paper presents a hyperbolic shear deformation theory and discusses its application to investigate the bending and buckling behavior of functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) beams. The proposed theory satisfies the parabolic variation of shear stress distribution throughout the thickness and fulfills the zero condition of shear stress on the upper and bottom surfaces of the FG-CNTRC beams. Therefore, there is no need to use any correction factor concerning conventional equivalent single-layer theories. Five different types of CNTs reinforcement distribution are considered for the analysis while assuming a power-law function variation of the material properties in the thickness direction. The governing equations are solved using a finite element method, where several new numerical results are presented to demonstrate the robustness and reliability of the proposed model. The compartive study shows that the proposed element model is: (a) accurate and comparable with the literature; (b) of a faster rate of convergence to the reference solution; (c) excellent in terms of numerical stability; (d) valid for both symmetric and non-symmetric FG-CNTRC beams. Results also show the validity of the proposed formulation for both thin and thick FG-CNTRC beams. In addition, the effect of various material and geometric parameters such as the CNTs volume fraction, distribution patterns of CNTs, boundary conditions, and the length-to-thickness ratio is investigated on the bending and buckling responses of FG-CNTRC beam structures. Several new referential results are also reported for the first time, which will serve as a benchmark for future studies in a similar direction. [ABSTRACT FROM AUTHOR]

The lattice structures use has increased in several sectors due to the potential for mass reduction without significant rigidity loss. In this paper, an isogrid tube multi-objective optimization considering six objectives is presented. The finite element method was applied to develop a numerical model for this complex structure, and a new optimization algorithm called the Multi-objective Lichtenberg Algorithm was used to find all the best possible designs. The optimizations were made considering two methodologies: (i) using a surrogate model derived from the design of experiments considering the response surface model and (ii) finite element updating, a direct link between the meta-heuristic and the numerical model. The latter is unprecedented in the literature for isogrid tubes and proved to be the best methodology, besides not even needing explicit equations. It discovered isogrid tube designs using TOPSIS that reduced at least 45.69% of the mass, 18.4% of the instability coefficient, 61.76% of the TW, and increased the natural frequency by at least 52.57%. The results show that optimizations via finite element updating associated with meta-heuristics not only allow the true interpretation of complex problems nature through real Pareto fronts, but can also deliver innovative results. [ABSTRACT FROM AUTHOR]

This study aims to examine the effect of the diameter, number, and location of the circular cutout on the free vibration response and buckling loads of the laminated composites. Eigen-buckling and free vibrations analyses are performed for the laminated composite plates by using the finite element software ANSYS. Numerical results obtained by the finite element method are compared to the experimental ones. In the numerical analyses, the effect of the delamination around the cutout on the buckling load and the natural frequency is also examined. The critical buckling load and first natural frequency values obtained by both numerical and experimental studies are used to create a prediction model using the artificial neural networks. The Levenberg–Marquardt backpropagation algorithm is used as the training method. It is observed that both the number and location of the cutout affect the critical buckling load and first natural frequency values. Numerical and experimental results are presented together with the ANN prediction results. [ABSTRACT FROM AUTHOR]

A first endeavor is made in this paper to explore new analytic buckling solutions of moderately thick rectangular plates by a straightforward double finite integral transform method, with focus on typical non-Lévy-type fully clamped plates that are not easy to solve in a rigorous way by the other analytic methods. Solving the governing higher-order partial differential equations with prescribed boundary conditions is elegantly reduced to processing four sets of simultaneous linear equations, the existence of nonzero solutions of which determines the buckling loads and associated mode shapes. Both numerical and graphical results confirm the validity and accuracy of the developed method and solutions by favorable comparison with the literature and finite element analysis. The succinct but effective technique presented in this study can provide an easy-to-implement theoretical tool to seek more analytic solutions of complex boundary value problems. [ABSTRACT FROM AUTHOR]

The hysteretic capacity of reinforced concrete (RC) structures depends to a large extent on the hysteretic behavior of steel bar to sustain many cycles of high plastic deformations without obvious degradation of strength and stiffness. It is important to develop an accurate and computationally efficient model of steel bar in the nonlinear response analysis of RC structures subjected to cyclic loads. The high strength and ultra-high-strength (UHS, yield strength above 1000 MPa) steel bars are becoming more and more popular in concrete construction, which is beneficial for materials saving and reduction of steel bar congestion. In order to investigate the cyclic behaviors of UHS steel bars and to propose a hysteretic model for this kind of steel bars including buckling, a total of 54 specimens with nine slenderness ratios were carried out under compressive and cyclic loadings. The modified stress–strain curve model of UHS steel bars with different slenderness ratio was developed based on the experimental data, which can take buckling and fatigue-induced reduction of stress into account. This study offers a solid database for researches on the mechanical properties of UHS steel bars. And the proposed empirical model can easily be implemented in the finite element analysis of RC elements with UHS steel bars under cyclic loadings. [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]

This paper presents the results of standard test results and Finite Element numerical modelling for a thermally insulated log-house timber wall loaded in compression and exposed to fire. A key aspect in the design of log-house systems, being susceptible to possible local failure mechanisms and buckling phenomena, is represented by geometrical details like the cross-section of logs (typically characterised by depth-to-width ratios in the order of two or more) and the corner joints features. This is also the case of log-house structures exposed to fire, were the premature collapse due to combined thermo-mechanical loads should be properly prevented. In this context, insulation claddings can markedly delay the fire propagation and temperature increase in the timber components, as to increase their overall fire resistance. Such an aspect is important especially for commercial buildings or accommodation facilities, according to international design requirements. To this aim, the paper reports on a full-scale, ≈ 3 m × 3 m and 90 mm thick, thermally insulated log-house wall specimen ('W90-insulated') loaded in compression (RN = 0.13 the ratio, as in a 2-storey building) and exposed to fire, in accordance to the EN/ISO temperature-time standard curve. The most important test results are commented, including comparisons towards an unprotected wall with identical nominal geometry ('W90′), which was previously tested in the same facility. It is shown, in particular, that the insulation package can extend the fire resistance of the wall up to more than 150 min (with limited charring and deformations of logs), that is three times the unprotected sample. The furnace experiment herein presented, even in presence of intrinsic limitations for the testing method, emphasises the need of a wide set of instruments to properly capture the key temperature and deformation results of log-house assemblies, as well as the lack in design standards of specific performance parameters. The W90-insulated test predictions are hence explored in the paper via FE numerical models, where major advantages for the timber components are derived from past literature efforts and special care is spent for the thermal insulation package. Even in presence of well known simplifications (i.e., thermo-mechanical boundaries/loads and thermo-physical properties of materials), as shown, the FE method can offer interesting correlation with the full-scale predictions, for more than 100 min of exposure. In addition, the crucial role of cladding layers on the fire resistance and failure time/mechanism of log-house walls is further assessed, based on FE parametric studies of technical interest, inclusive of different configurations for the thermal insulation layers. [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 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]

A computational method is proposed for the analysis and prediction of instability (wrinkling or necking) of multilayered compressible plates and sheets made by metals or polymers under plane strain conditions. In previous works, a basic assumption (or a physical argument) that has been frequently made is that materials are incompressible to simplify mathematical derivations. To account for the compressibility of metals and polymers (the lower Poisson's ratio leads to the more compressible material), we propose a combined semi-numerical algorithm and finite element method for instability analysis. Our proposed algorithm is herein verified by comparing its predictions with published results in literature for thin films with polymer/metal substrates and for polymer/metal systems. The new combined method is then used to predict the effects of compressibility on instability behaviors. Results suggest potential utility for compressibility in the design of multilayered structures. [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]

In order to avoid using C interpolation functions in finite element implementation of the previous zig-zag theories, artificial constraints, in which the first derivatives of transverse displacement will be replaced by the assumed variables, are usually employed. However, such assumption will violate continuity conditions of transverse shear stresses at interfaces. Differing from previous work, this paper will propose a C-type zig-zag theory for buckling analysis of laminated composite and sandwich plates with general configurations. The first derivatives of transverse displacement have been taken out from a displacement field of the proposed zig-zag theory. Thus, the C interpolation functions are only required in finite element implementations of the proposed model. Without use of any artificial constraints, an eight-node quadrilateral element based on the proposed model is presented by incorporating the terms associated with the geometric stiffness matrix. In order to verify performance of the proposed model, several buckling problems of sandwich plates with soft core have been analyzed. Numerical results show that the proposed model is able to predict accurately buckling loads of the soft-core sandwich plates with varying fiber orientations of face sheets. [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 numerical study was conducted using the finite element method to determine the effects of square and rectangular cutouts on the buckling behavior of a 16-ply quasi-isotropic graphite/epoxy symmetrically laminated rectangular composite plate. The square/ rectangular cutouts were subjected to uniaxial compression loading. This study addresses the effects of the size of the square/rectangular cutout, orientation of the square/rectangular cutout, plate aspect ratio (a/b), and plate length/thickness ratio (a/t) on the buckling behavior of the symmetrically laminated rectangular composite plate under uniaxial compression loading. Buckling loads were computed for seven different quasi-isotropic laminate configurations [0°/+45°/−45°/90°], [15°/+60°/−30°/−75°], [30°/+75°/−15°/−60°], [45°/+90°/0°/−45°], [60°/−75°/+15°/−30°], [75°/−60°/+30°/−15°], [90°/−45°/+45/°0°]. Results showed that the magnitudes of the buckling loads decrease with increasing cutout positioned angle as well as c/b and d/b ratios for plates with a rectangular cutout. The symmetrically laminated quasi-isotropic [0°/+45°/−45°/90°] composite plate is stronger than all other symmetrically analyzed laminated quasi-isotropic composite plates. The magnitudes of the buckling loads of a rectangular composite plate with square/rectangular cutout decrease with increasing plate aspect ratio (a/b) and plate length/thickness (a/t) ratio. [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]

This paper investigates the existence of the critical force chain length and the buckling of unconfined grain columns in dense granular materials. Tests on assemblies of flat pentagon photoelastic particles were first carried out to demonstrate the maximum length of force chains. Then, the theoretical buckling analysis and distinct element method (DEM) simulations for grain columns composed of mono-sized elliptical particles were performed. The results revealed the existence of critical column length, which is generally affected by the particle shapes, the rotational resistance at particle contact points and the end constraints to the grain columns. The interparticle friction does not have explicit effect on the critical force chain length, but it has significant influence on the grain column's curvature when collapse takes place. The thickness of shear band in granular soils can be determined as the critical length of grain columns by appropriately imposing the constraints on the boundaries, as confirmed by DEM simulations and experimental results. [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]

By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudo-symplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory. [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]

Three-dimensional finite element analysis is applied to verify mechanical behavior of spot welds for one, three and five spot welds under tensile and compressive loading conditions. The elastic-plastic stress distribution at edge of hot spot weld is used for strength calculations. To obtain exact and reliable results for finite element analysis of spot welds, which are generally very small relative to other dimensions, sub-modeling technique is applied. The proposed numerical calculation scheme allows one to take into account the material parameters and geometrical non-linearity effects related to a gap between thin plates, buckling, etc. We provide the analysis of elastic and elastoplastic behavior of specimens with various configuration of spot welds subjected to tensile and compressive axial loads. [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]