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This article considers a bidirectional functionally graded (BDFG) beam with various distributions of volume fraction. The impact of these distributions on the buckling and bending response of BDFG beam with general boundary conditions is investigated via a quasi-3D solution. It is assumed that the beam is exposed to a set of in-plane varying compressive loads and there mechanical characteristics change in both directions. Also, the BDFG beam is considered to be exposed different external mechanical loads. Hamilton's principle is employed to derive the governing equations, which are then solved using analytical solution to obtain buckling and bending characteristics. The precision of the current formulation is investigated via a comparison with available data in literature. Some numerical results are presented and discussed to assess the effect of different parameters such type of volume fraction, boundary condition, varying load, and beam geometry on the buckling and bending of BDFG beam. [ABSTRACT FROM AUTHOR]

Fragility and the presence of a poisonous substance (lead) are the two major issues with traditional piezoceramics and structures that include them. This work suggests an active structure that is lightweight, flexible, and eco-friendly such that a polymeric foam plate is sandwiched between two piezoelectrically activated nanocomposite layers. A combination of a polymer and piezoelectric nanowires (NWs) of zinc oxide (ZnO) is used in the nanocomposite layers. For the proposed active structure, two types of void distributions and functionally graded (FG) distributions of the NWs have been assumed in each corresponding layer. The buckling characterization of the proposed eco-friendly active sandwich plate (EFASP) under biaxial mechanical loads has been conducted using an extended meshless solution based on a third-order theory. An in-depth parametric study on the EFASPs' biaxial buckling resistance revealed that increasing NW content considerably enhances buckling resistance, with this enhancement strongly reliant on the distribution profile of the NWs. Moreover, it was observed that embedding voids in the substrate layer can lead to a large structural weight reduction while only marginally lowering the buckling performance of suggested EFASPs. [ABSTRACT FROM AUTHOR]

An analytical investigation on buckling behavior of thick functionally graded shells with nearly cylindrical shapes and porosities under mechanical loads is presented in this paper. Loading conditions considered are that axial compressive load, lateral pressure and combined mechanical loads in thermal environments. Porosities are evenly or unevenly distributed within the shell. Governing equations are established based on a higher order shear deformation theory taking into account interaction between the shell and surrounding elastic medium. Two-term form of deflection is assumed to satisfy simply supported boundary conditions and Galerkin method is applied to derive closed-form results of buckling loads. [ABSTRACT FROM AUTHOR]

Thermo-mechanical buckling analysis of laminated spherical shells bounded with the piezoelectric actuator layers has been presented in this article. Applied loads are a combination of thermal, mechanical and electrical loads. Derivations of equilibrium and stability equations are based on the classical laminated shell theory and Sanders's nonlinear kinematic relations. The analysis employs the Galerkin method to achieve closed-form formulas for the buckling loads of the piezo-laminated spherical shell. Effects of applied actuator voltage, voltage sign, geometrical parameters of the shell (length, diameter, and thickness), material properties, and layout of composite layers on the buckling strength are investigated. Analytical solutions are obtained for three types of thermal loading, and one thermo-mechanical loading condition. The results are validated by the known data in the literature. [ABSTRACT FROM AUTHOR]

The high temperature environment makes the buckling of composite laminated plate happen earlier. Further weight savings can be achieved once the plate has a favorable postbuckling stiffness. This study aims to address this issue by developing a ROM-driven lamination optimization to maximize the buckling and postbuckling performance of compressed plates under initial temperature field. The reduced-order model(ROM) constructed using the improved Koiter theory is reformulated to be suitable for thermal-mechanical buckling problems. A linear subspace of the force space is represented to be the span of the mechanical load, the thermal load and a set of predefined perturbation loads. The thermal load related to the initial temperature field is constant during the increase of in-plane compressive load. An independently additional degree of freedom corresponding to the thermal load is implemented into the construction of the reduced-order model. The buckling and postbuckling performance can be extracted from the solution of reduced-order model, and then subsequently selected as inputs to achieve the optimal laminate. The main novelty of this work is to achieve the thermal-mechanical buckling and postbuckling optimization, benefitting from the highly efficient single run of thermoelastic geometrically nonlinear analysis. Various numerical examples have been selected to validate the performance of the proposed method, considering the influences of length-to-width ratio, α1/α2, ply number and nonuniform temperature field. [ABSTRACT FROM AUTHOR]

This article presents the axial buckling analysis of polymer-CNT-fiber nanocomposite annular system (PCFCAS) resting on Winkler-Pasternak substrates under various temperature gradients. With the aid of Hamilton's principle and the higher-order shear deformation theory (HSDT), the governing equations are derived. For developing an accurate solution approach, a generalized differential quadrature method (GDQM) is finally employed. Various geometrically parameters are taken into account to investigate the axial buckling analysis of the PCFCAS subjected to a high-temperature environment. Finally, the presented results demonstrate that different parameters such as outer to inner radius ratio (Ro/Ri), patterns of temperature increase, volume fraction and orientation angle of the carbon fibers (CFs), weight fraction and distribution patterns of carbon-nanotubes (CNTs), and other geometrical and physical parameters have an important role in the axial buckling load of the current structure. The fundamental and golden results of this paper could be that when the PCFCAS is in an environment with sinusoidal, and uniform temperature change, the structure encounters with the highest axial buckling load. In contrast, the lowest buckling load occurs for the uniform temperature change. Also, when the effect of the Winkler and Pasternak foundation is considered, there is a sinusoidal effect from the Ro/Ri parameter on the axial buckling load of the disk, and this matter is true for all boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear time history response and dynamic-buckling of functionally graded material (FGM) shell structures in thermal environments with temperature-dependent material properties is studied. An implicit conservative/decaying time integration scheme and a curved 8-node degenerated shell element are used for time and spatial discretization respectively. Numerical results show that the developed shell element formulation with the implicit time integration scheme is capable of solving nonlinear dynamic-buckling and large displacement dynamic problems of FGM shells in severe thermal environments. Th influence of material constituents, power-law indexes and thermo-mechanical loadings on the transient dynamic response and dynamic-buckling phenomena are considered. [ABSTRACT FROM AUTHOR]

This article aims to investigate the post-buckling behavior of plates and cylindrical panels made of functionally graded materials (FGM) and carbon-nanotubes reinforced composites (FG-CNTRC) under mechanical loads. Unlike the other high order shear deformation theories, the proposed formulation is elaborated within a double directors finite shell element which allows a parabolic distribution of the transverse shear strains, guarantee the zero condition of the transverse shear stresses on the extreme surfaces of the shell and introduces large deformations and finite rotations through a non-linear framework. Newton-Raphson with arc length control solution strategy is used to resolve the equilibrium paths. A power-law distribution and the extended rule of mixture are used to determine the effective material properties of functionally graded materials and carbon-nanotubes reinforced composites. The effectiveness and the accuracy of the formulation is checked via several comparisons with published results in the literature. Especially, some complex post-buckling curves of FGM and FG-CNTRC curved panels and plates with different mechanical loadings are provided that could be useful for future references. The effects of various parameters are also reported. [ABSTRACT FROM AUTHOR]

The buckling of slender columns with functionally graded microstructures is studied. In such columns, the flexural modulus is varied in a controlled manner along the column length. The objective is to identify microstructures that maximize (and minimize) the critical buckling load when compared to a reference homogeneous column. Several microstructures are examined and a constraint is imposed so that the volume averaged flexural modulus remains the same in all columns. The buckling load is determined using both the linear perturbation analysis as well as the Rayleigh–Ritz method. A relationship between the material distribution and the corresponding mode shape is established. [ABSTRACT FROM AUTHOR]

A complex finite strip method was used to study the buckling of functionally graded plates (FGPs) under thermal and mechanical (longitudinal, transverse, and shear in-plane) loading. The mechanical characteristics of FGPs were assumed to vary through the thickness, according to power law distribution. The nonlinear temperature distribution in the direction of the plate thickness was assumed according to thermal conduction steady state conditions. In complex finite strip method, the polynomial Hermitian functions were assumed in the transverse direction and the complex exponential functions were used in the longitudinal direction to evaluate the standard and geometric stiffness matrices that have the ability of calculating the critical shear stress in contrast to trigonometric shape functions. The solution was obtained by the minimization of the total potential energy and solving the corresponding eigenvalue problem. In addition, numerical results for FGPs with different boundary conditions were presented and compared with those available in the literature and the interaction curves of mechanical and thermal buckling capacity of FGPs were obtained. [ABSTRACT FROM PUBLISHER]

By using a three-dimensional (3D) space-frame-like model, a molecular mechanics (MM) approach is proposed for determination of the buckling loads, effective Young's modulus and Poisson's ratio of the nanosheets, using a proper unit cell. The governing equations are derived based on the 3D kinematics of deformations and the principle of minimum total potential energy. The unit-cell-based results are employed for the space-frame-like finite element model of the nanosheet. The nonlinear MM equations are solved by representing bonds of the boron nitride nanosheet (BNNS) by beam elements to extract the local characteristics. These properties are employed in modelling of the nanosheet, as a space-frame-like finite element structure. The force field constants are chosen according to the Morse, AMBER, UFF and DREIDING models to determine the buckling strength, and effective Poisson's ratio and in-plane rigidity of the whole graphene and BNNSs. Silicon Carbide nanosheets are analysed based on different force constants. These results are concordant with the results available in the literature. The comparisons reveal that the DREIDING force field usually gives the most accurate predictions. [ABSTRACT FROM AUTHOR]

In this article, the framework of the Flügge's shell theory, the transfer matrix approach, and the Romberg integration method have been employed to investigate the buckling analysis of a radial loaded oval cylindrical shell with parabolically varying thickness along its circumference. Trigonometric functions are used to form the modal displacements of the shell and Fourier's approach is used to separate the variables. The mathematical analysis is formulated to overcome the difficulties related to mode coupling of variable curvature and thickness of the shell. Using the transfer matrix of the shell, the buckling equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate and rewritten in a matrix form and solved numerically. The proposed model is adopted to get the critical buckling loads and the corresponding buckling deformations for the symmetrical and antisymmetrical modes of buckling. The influences of the shell geometry, orthotropic parameters, ovality parameter, and thickness ratio on the buckling parameters and the bending deformations are presented for different type-modes of buckling. [ABSTRACT FROM AUTHOR]

In this article, the thermal effects on buckling and free vibrational characteristics of functionally graded (FG) size-dependent nanobeams subjected to various types of thermal loading are investigated by presenting a Navier-type solution for the first time. Temperature-dependent material properties of FG nanobeams vary continuously along the thickness according to the power-law form. The small-scale effect is taken into consideration based on Eringen's nonlocal elasticity theory. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying an analytical solution. It is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams. [ABSTRACT FROM PUBLISHER]

This article presents the buckling analysis of laminated composite stiffened plates subjected to partial in-plane edge loading. The finite element method is used to carry out the analysis. The eight-noded isoparametric degenerated shell element withC0continuity and first-order shear deformation and a compatible three-noded curved beam element are used to model the plate skin and the stiffeners, respectively. The eigen value analysis is carried out to track the buckling load. The convergence study is performed for some specific problems and the results are compared with the available results in the literature. It is observed that the convergence of results is very fast for this finite element model. Effect of different parameters like orientation of fibers, number of layers, and loading types are considered in the present investigation. It is also observed that all these parameters have significant effect on the buckling response of the composite stiffened plate. [ABSTRACT FROM AUTHOR]

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The material properties of FGM plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are solved analytically for a plate with simply supported boundary conditions. Resulting equations are employed to obtain the closed-form solution for the thermal force resultant for each loading case. Numerical examples covering the effects of the plate aspect ratio, side-to-thickness ratio and gradient index on thermal force resultant are discussed. [ABSTRACT FROM PUBLISHER]

In the present work, buckling analysis of orthotropic thin rectangular plates with uniform thickness resting on Pasternak foundation are investigated for eight types of boundary conditions: SSSS, CCCC, SCSC, SSSC, SSCC, CCCF, SSFC, and CFCF. Based on classical plate theory, governing differential equation in buckling are solved numerically using generalized differential quadrature method (GDQM) to obtain critical buckling loads and corresponding modes. The kinds of nonlinear loading are presented in six cases including symmetrical and unsymmetrical distribution. In addition, the effects of aspect ratio, orthotropic moduli ratio and coefficients of foundation on the buckling load are illustrated. The present work is the first attempt to consider the influence of the nonlinearity of distributed in-plane bi-directional loading in determination of buckling load and representation of the corresponding shape modes. Some numerical examples are provided to demonstrate good accuracy of the GDQ method to evaluate the critical buckling load in case of nonlinear distributed bi-directional compressive loads. As shown, profile of distributed in-plane loading plays an important role on buckling behavior of the rectangular plate. [ABSTRACT FROM AUTHOR]

This article presents the exact elastic buckling of annular plates with elastically restrained edges against rotation and translation at inner and outer periphery. The classical plate theory is used to derive the governing differential equation for annular plate with elastically restrained edge support system. The buckling mode may not be axisymmetric as previously assumed. In certain cases, an asymmetric mode would yield a lower (critical) buckling load. This is due to switching of mode. This work presents the critical buckling load parameters for axisymmetric and asymmetric buckling modes. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of rotational and translational restraints, Poisson's ratio and other boundary conditions on the buckling of uniform isotropic annular plates. The numerical results obtained are in good agreement with the previously published data. In this article, the characteristic equations are exact; therefore, the results can be calculated to any accuracy. [ABSTRACT FROM AUTHOR]

In this work, the influence of uniaxial and biaxial nonuniform edge loads on buckling characteristics of composite laminates with and without cutout is investigated by using a finite element method. Furthermore, this investigation addresses the effects of different degree of edge restraints on buckling analysis. Regarding this, a nine node heterosis plate element has been adapted by employing the effects of shear deformation and rotary inertia. The influence of different parameters, such as ply-orientations, nonuniform edge loads, boundary conditions, and cutout sizes, has been considered and studied in detail. It is clearly illustrated that cutout sizes under different loading conditions have remarkable effects on buckling behavior of composite laminates. [ABSTRACT FROM AUTHOR]

Over a period of more than 45 years, an extensive research program has allowed a series of very simple propositions, relating to the safe design of shells experiencing imperfection sensitive buckling, to be recast in the form of a series of lemmas. These are briefly summarized and their practical use is illustrated in relation to the prediction of safe lower bounds to the imperfection sensitive buckling of axially loaded, fiber reinforced polymeric, laminated cylinders. With a fundamental aspect of the approach, sometimes referred to as the reduced stiffness method, being the delineation of the various shell membrane and bending stiffness (or perhaps more appropriately energy) components contributing to the buckling resistance, the method will be shown to also provide a powerful way of making rational design decisions to optimize the use of fiber reinforcement. [ABSTRACT FROM AUTHOR]

Structural elements with complex geometries, boundary conditions and load patterns cannot be designed against buckling using empirical formulae because of uncertain elastic buckling moments or unknown buckling effective lengths, which are basic parameters for these equations. This article proposes a shell finite element procedure for buckling design of metal beams of complex configurations with codified initial imperfections assumed in the Perry-Robertson formula. The advantage of the proposed method lies in the use of elastic buckling moment with empirical design formulae for determination of design moment capacity of a beam; thereby eliminating the uncertainty of modelling initial imperfections. More importantly, the moment modification factor and assumption of effective length can be avoided because all second-order and yield effects have been considered in the computer model. Numerical examples demonstrate that the simplified method has a high level of accuracy, versatility and flexibility for the design of complex beams. [ABSTRACT FROM AUTHOR]

The presence of in-plane loading may cause buckling of stiffened panels. An accurate knowledge of critical buckling load and mode shapes is essential for reliable and lightweight structural design. This paper presents parametric studies on simply supported laminated composite blade-stiffened panels subjected to linearly varying in-plane edge/compressive loading. Studies are carried out by changing the panel orthotropy ratio, stiffener depth, pitch length (number of stiffeners), smeared extensional stiffness ratio of stiffener to that of the plate and load distribution parameter. Based on the studies, a few important parameters influencing the buckling behavior are identified and their significance is discussed. Further, the interaction equations for combined loadings are validated by carrying out numerical studies. [ABSTRACT FROM PUBLISHER]

By using the Ritz energy method and finite element method, buckling behaviors of combined-loaded functionally graded cylindrical shells are investigated. The combined loads are composed of axial, lateral, and torsional loads. Results show that the contribution of lateral pressure to buckling is more significant than that of axial compression or torsion and the contributions of axial compression and torsion are almost the same. Also, a practical method is proposed in this article to determine the load-dominant bound between the single buckling mode due to one dominant load and the mixed buckling mode due to interaction of the two loads. [ABSTRACT FROM AUTHOR]

The present work aims to study the elastoplastic buckling, postbuckling, and failure behavior of perforated Ni/Al2O3functionally graded material (FGM) plate with various shaped cutouts (i.e., circular, square, diamond, and elliptical) of various sizes under thermomechanical loading conditions using finite element method (FEM). The nonlinear FEM formulation is based on the first-order shear deformation theory and von Kármán’s nonlinear kinematics in which the material nonlinearity is incorporated. The nonlinear temperature-dependent thermoelastic material properties of FGM plate are varied in the thickness direction by controlling the volume fraction of the constituent materials (i.e., ceramic and metal) as per a power law, and Mori–Tanaka homogenization scheme is applied to evaluate the properties at a particular thickness coordinate of FGM. In accordance with the Tamura–Tomota–Ozawa model (TTO model), the ceramic phase of FGM is considered to be elastic, whereas the metal phase is assumed to be elastoplastic. Further, the elastoplastic analysis of FGM is assumed to followJ2plasticity with isotropic hardening. After validating the present formulation with the results available in the literature, various numerical studies are conducted to examine the effects of material inhomogeneity, thermal loading, cutout shape, and size on the elastoplastic buckling, postbuckling, and failure behavior of perforated FGM plate. It is observed that for smaller cutout sizes, the FGM plate with square shape cutout possesses maximum value of ultimate failure load; however, for larger cutout size, the FGM plate with diamond cutout depicts highest ultimate failure load. Furthermore, for all cutout shapes, the ultimate failure load of FGM plate decreases with an increase in cutout size. It is also revealed that irrespective of shape and size of cutout, the material plastic flow has considerable effect on postbuckling path of FGM plate, and under thermomechanical loading conditions, the FGM plate shows destabilizing response after the point of maximum postbuckling strength. [ABSTRACT FROM AUTHOR]

In the present paper, the shear buckling analyses of adhesively bonded plates including an orthotropic material were performed. The adherends were selected as isotropic homogenous materials and a single adhesive was used in the overlap region. In the adhesive layer, an orthotropic material was located as an inclusion and its shape was assumed with an elliptical geometry. Three different orthotropic inclusions were selected: glass/epoxy, graphite/epoxy, and boron/epoxy. The effects of the inclusion shape and properties on the shear buckling were investigatedviafinite element analyses. The finite element analyses were verified according to an analytical solution having a full homogeneous isotropic adhesive layer. The analysis results showed that the maximum buckling loads were obtained when using the boron/epoxy inclusion compared to the glass/epoxy and graphite/epoxy inclusions. In addition, the possibility of delamination in the vicinity of the inclusion was examined. By this means, the influences of the delamination shape and magnitude on the critical buckling load were investigated. The greatest effect was obtained when the delamination shape was close to a circle and its magnitude was the largest. [ABSTRACT FROM PUBLISHER]

A size-dependent finite element (FE) formulation including surface free energy effect is developed in this article to study the post-buckling behavior of nanofilms under the action of thermal loads. The Gurtin-Murdoch surface elasticity theory is utilized to consider the surface effects. Moreover, the principle of virtual work is used so as to derive the equilibrium equations. The proposed FE formulation is based on the first-order shear deformation theory (FSDT). The von Kármán nonlinear relations are also employed to take the geometric nonlinearity into account. After deriving the FE equations, the resulting set of parameterized non-linear equations is solved using the pseudo arc-length continuation algorithm, and bifurcation diagrams of nanofilms are obtained. Selected numerical results are presented for the influences of surface stress on the thermal post-buckling characteristics of nanofilms subject to different types of boundary conditions. [ABSTRACT FROM PUBLISHER]

As part of the Network of Excellence on Marine Structures (MARSTRUCT), a series of studies has been carried out into the buckling of glass-fibre-reinforced polymer plates with in-plane compression loading. The studies have included fabrication and testing of square, laminated panels with various thicknesses and initial geometrical imperfections, material testing, advanced finite element modelling studies and finally parametric studies covering a range of slendernesses and imperfection amplitudes. The paper provides an overview of the studies, which involved several participants in the Network. [ABSTRACT FROM AUTHOR]

Design of pile foundations in seismically liquefiable soils involves identifying the appropriate failure mechanisms. Piles in liquefiable soils are conventionally designed against bending failure due to lateral loads arising from inertia and/or lateral spreading. This is strong evidence that there is another mechanism, which the code does not consider, that may govern the failure of these foundations. In this paper, the response of a single end bearing pile in liquefied soil with and without the effect of axial load has been presented. The effect of liquefaction is incorporated in the pile-soil interaction through nonlinear analysis using the finite difference program Fast Lagrangian Analysis of Continua (FLAC). The method of analysis is carried out using the well documented failure of Showa Bridge piles which failed during the 1964 Niigata earthquake. The response of the pile is also evaluated using dynamic analysis. The need for proper identification of failure mechanisms as well as design guidelines is highlighted. [ABSTRACT FROM AUTHOR]

The article comments on the paper, entitled "Buckling Behaviour of Single Pile and Pile Bent in the Scotch Road Bridge," by Y. Khodair and S. Hassiotis. The estimation of critical buckling load of embedded piles in soil was analyzed adequately by the authors. Several issues concerning the numerical modeling of pile buckling were not addressed adequately in the paper and which can be misleading.

Offshore installations are exposed to hydrocarbon explosions and/or fire accidents. Especially, explosions lead to serious damages to human, safety, and environment. To minimise and prevent the damage from explosions, blast walls are generally installed in oil and gas production structures. Typical blast walls are classified into flat, corrugated, and stiffened types. Among them, corrugated blast walls are frequently used for reasons such as construction, cost, and energy absorption. However, it has been known that a corrugated type of blast wall buckles between the web and flange under the explosion loads, and loses its stiffness. It means that the buckling phenomenon of a blast wall is closely related to the structural strength. This study investigates on the structural characteristics of a blast wall under quasi-static and dynamic (explosion) loads with or without a flat-plated stiffener. Finally, it can be concluded that the flat type of stiffeners are located at the buckling region to delay the buckling and improve the strength of blast walls. [ABSTRACT FROM AUTHOR]

The buckling and collapse problems of reinforced thermoplastic pipe (RTP) caused by the combined bending and external pressures were investigated in this paper. Based on the model initially proposed by Kyriakides et al., a 2D theoretical model was developed which takes into account the transverse shear deformation, the mean radius change, the wall thickness change and the pre-buckling deformation. By means of numerical calculation, the predicted collapse envelopes of different loading paths are presented. Two kinds of failure modes during the loading paths were also experimented on. A 3D finite element model was established by ABAQUS to confirm the accuracy of the theoretical model. The compared results were proven to agree. The effects of different loading paths and the ratio of diameter to thickness were also discussed and useful conclusions were drawn for RTP's marine engineering application. [ABSTRACT FROM PUBLISHER]

Present investigation deals with the snap-through phenomenon in a thermally pre-buckled or post-buckled reinforced composites beam. Composite laminated beam is reinforced with graphene platelets (GPLs) where the weight fraction of GPLs may vary in each layer. The governing equations of the beam are obtained by means of the first order shear deformation beam theory and the von-Kármán type of kinematic assumptions. The conventional Ritz method with Chebyshev polynomials is used to discretize the governing equations and establish a set of non-linear equations dealing with the response of a beam under the action of thermal and mechanical loads. Furthermore, the case of uniform temperature elevation in the beam and uniform lateral pressure is considered. At first, the response of the beam under uniform temperature elevation is obtained. Depending on the magnitude of temperature rise, beam may remain flat or undergo thermal post-buckling. Using the displacement control strategy, the non-linear eigenvalue problem is solved. After that the response of the pre-buckled or post-buckled beam subjected to uniform lateral pressure in large deflection is evaluated. Due to the possibility of snap-through phenomenon, the cylindrical arch-length technique is employed. At first, two comparison studies are provided to assure the validity and efficiency of the developed formulation. After that, novel numerical results are given to discuss the effects of temperature change, weight fraction of GPLs, distribution pattern of GPLs and boundary conditions. It is shown that the limit loads of the snapping phenomenon and the intensity of the snap-through phenomenon are highly dependent to the mentioned factors. [ABSTRACT FROM AUTHOR]

In this paper, the mechanics of shear deformable micro beams is investigated via finite element analysis, and a machine learning technique (Deep Learning Neural Network (DLNN)). DLNN is provided for the first time to accurately model and predict this behavior. Using the Finite Element Method (FEM), the obtained coupled equations of motion for shear deformable micro-scale beams are solved using a combination of Timoshenko beam theory and the modified couple stress theory (MCST). The results are compared with literature for each analysis to show the accuracy and the proposed finite element model. After presenting the mechanical model, by using Finite Element Analysis (FEA), a deep learning neural network model is developed for small-scale structures and the capability of this model in predicting different mechanical behavior under thermo-mechanical loading is investigated. It is shown that the presented model has great accuracy in predicting both static and dynamic behavior of small-scale structures with a significant reduction in the computational cost. The application of DLNN for modeling the machines of small- scale structures is a step forward for predicting the behavior of Nano/Micro Electro Mechanical Systems (NEMS/MEMS). [ABSTRACT FROM AUTHOR]

This article presents the instability of a variable-arc-length elastica where one end is attached on the hinged joint and the other end is placed on the sleeve support. The friction is also introduced at the sleeve end. At the hinged end, the concentrated moment is applied to turn the elastica around the joint. The system of governing differential equations is obtained from equilibrium equations, constitutive equation and nonlinear geometric relations. To extract the behaviour of this problem, the system of differential equations needs to be integrated from one end to the other and satisfied boundary conditions. In this problem, we utilise the Runge–Kutta scheme as an integration tool and the shooting method plays a vital role to compute the results. The results are interpreted by using the load-deflection diagram where the stiffness of the system can be observed. From the results, it can be found that there are two equilibrium points for a given end moment that is less than its critical value. This results from the non-monotonic load-deflection curves. There is a limit load point (buckling load) for each value of frictional coefficient. Beyond the buckling load, the elastica can lose its stability. Moreover, we discovered that, with presence of the friction (i.e. dry friction), the elastica shows more stable behaviour than its counterpart without friction since the buckling load increases when the frictional coefficient increases. [ABSTRACT FROM AUTHOR]

A simplified variational model for the formation of convoluted accommodation structures, as seen in the hinge zones of larger-scale geological folds, is presented. The model encapsulates some important and intriguing nonlinear features, notably: infinite critical loads, formation of plastic hinges, and buckling on different length-scales. An inextensible elastic beam is forced by uniform overburden pressure and axial load into a V-shaped geometry dictated by formation of a plastic hinge. Using variational methods developed by Dodwell et al., upon which this paper leans heavily, energy minimisation leads to representation as a fourth-order nonlinear differential equation with free boundary conditions. Equilibrium solutions are found using numerical shooting techniques. Under the Maxwell stability criterion, it is recognised that global energy minimisers can exist with convoluted physical shapes. For such solutions, parallels can be drawn with some of the accommodation structures seen in exposed escarpments of real geological folds. [ABSTRACT FROM AUTHOR]

This study performs the inelastic static and dynamic stability analyses of a column subjected to a nonconservative force using the finite element method. Based on the tangent modulus theory, the nonlinear compressive stress-strain and tangent modulus-stress relationships of an inelastic column are derived from the column strength curves given in two design codes. The extended Hamilton principle is employed to obtain the mass, elastic stiffness, and geometric stiffness matrices. Evaluation procedures for the critical values of buckling and flutter of the nonconservative systems are briefly introduced. In numerical examples, the influence of various parameters on the inelastic static and dynamic stability of the nonconservative systems is addressed as follows: (1) the effect of the nonconservativeness parameter on the critical buckling and flutter loads of the column for the inelastic stability analysis from the characteristic curves, (2) the variation of the effective length factor (K-factor) for inelastic columns with respect to the nonconservativeness parameter. [ABSTRACT FROM AUTHOR]

Finding new efficient connectors or improving existing ones are important issues in timber construction. This research investigates an innovative large-diameter dowel-type connection by using a finite elements model calibrated with experimental results. This connection is made of a large-diameter single dowel reinforced by means of a steel plate with a vulcanised rubber layer. The steel plate shape, thickness and dimensions, the rubber stiffness, the steel mechanical properties, etc., are parameters that may influence the critical load of the plate. The joint load-bearing capacity is also highly depending on the load direction to the grain. Those parameters are investigated using FE modelling and discussed in order to propose design recommendations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the use of Schifflerised angle sections for triangular-based lattice communication towers. The torsional-flexural buckling properties of conventional 90°, 60° and schifflerised angles are compared. The experimental results obtained from the compression tests conducted on three different sizes of schifflerised angle sections are compared with the analytical results predicted from finite element analysis and with the capacities predicted from the procedure given in the literature. The capacity of schifflerised angles are underestimated by the methods suggested in the literature. The FE model non-linear analysis predicts the failure loads closer to the test results with a variation of −3 to 10%. The strength of schifflerised angles is 5 to 20% higher compared to conventional 90° angles. The behaviour of 60 m high three-legged triangular communication tower with schifflerised angles for leg members and conventional equal angles for all other members tested at Tower Testing and Research Station, CSIR-Structural Engineering Research Centre, Chennai is presented. NE-NASTRAN, a finite element software, is used to model the tower using beam column and plate shell elements for predicting the behaviour. The analytical and test results are compared with the codal provisions. [ABSTRACT FROM PUBLISHER]

In this article, geometric and material nonlinear analyses of planar and space trusses subjected to thermo-mechanical loads are performed using the Total Lagrangian formulation. The material properties are Thermally InDependent (TID). By obtaining the equilibrium path of these structures, their buckling and post-buckling behaviors are predicted under thermal and mechanical loads. To consider material nonlinearity, a mixed isotropic–kinematic hardening criterion is developed in this formulation. The behavior of material is assumed to be bilinear. To solve nonlinear equations iteratively, the Generalized Displacement Control Method (GDCM) is used. The authors' scheme is general and can be employed for different types of planar and spatial truss structures having complicated geometries and behaviors. Several popular benchmarks are considered to show the accuracy and correctness of the proposed formulation. Corresponding equilibrium paths and stress–strain curves are reported for each problem. [ABSTRACT FROM AUTHOR]

The authors of this article investigate the nonlinear stability of axisymmetric functionally graded annular spherical shells with temperature-dependent material properties subjected to thermo-mechanical loads and resting on elastic foundations. Equilibrium and compatibility equations are derived by using the classical thin shell theory in terms of the shell deflection and the stress function. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain the closed-form of load–deflection paths. An analysis is carried out to show the effects of material and geometrical properties and combination of loads on the stability of the shells. [ABSTRACT FROM PUBLISHER]

In this article, the prediction of free vibration characteristics of various initially compressively loaded structural members is given in the form of a master formula. These structural members are optimised for the strength criteria and are subjected to high initial compressive loads (or stresses). These initial compressive loads have to be considered when the free vibration characteristics are evaluated. The standard method is to solve the differential equation considering the term corresponding to these loads. Though this is possible for simple structural members, it is often difficult while dealing with complex structural members with complicated effects. Under these circumstances, the popular approximate continuum and numerical methods like the Rayleigh-Ritz and finite element methods are used to obtain reliable and accurate solutions to the initially loaded free vibration characteristics of these structural members. However, these approximate methods are also having their inherent difficulties. To avoid this, a simple but accurate formula is developed, which is very useful for the design engineers while dealing with structural members used in missiles and rockets. The use of master formula for the first mode and also higher modes of vibration has been shown for typical structural members. [ABSTRACT FROM AUTHOR]

To better understand the mechanics of coiled tubing working within the risers connected to Floating liquefied natural gas (FLNG), this paper studied a specific marine ‘pipe-in-pipe’ system with a low diameter ratio. The experimental results showed that the axial load on the inner pipe of an unfixed system increased with the increase in injected length. In this case, the ‘force-in’ was always larger than the ‘force-out’. The changing trend of force-in and force-out within the unfixed system was essentially found to be stable after a sinusoidal buckling of the inner pipe. Even though the magnitudes of force-in and force-out did not increase a lot, the injected length increased significantly. Relationship of force-in, as well as force-out, between fixed and unfixed system when the pipe was buckled sinusoidally and helically was found. The results help in working of a coiled tubing within small diameter marine risers. [ABSTRACT FROM AUTHOR]

To reach an optimal design solution for the composite layup of large-scale wind turbine blades, subjected to various design load conditions, while, fulfilling numerous design requirements, is a challenging task to accomplish. Since, a large-scale blade is a slender beam structure, therefore, its thin composite layup can be assumed to be under plane stress condition. Consequently, a parametric study of the skin laminates used in the blade composite layup, is conducted to explore and identify the possible design improvements. The results show that the use of off-axis fiber angles of the skin laminate lower than the conventional 45° are more favorable to achieve higher laminate stiffness, strength, bucking stability, fatigue resistance, and bend-twist coupling value, thereby, demonstrating the potential improvements to the existing composite layup design of large-scale wind turbine blade. [ABSTRACT FROM AUTHOR]

In a thermal environment, using the formulations of the refined shear deformation theory, the flexion of the functionally graduated rectangular plates (P-FGM) based on nonuniform elastic foundations is presented. The layers resting on nonuniform elastic foundation are subjected to symmetrical distributed loads. Nonlinear variations in the in-plane displacements through the thickness of the plate are based on the choice of the displacement field of the present theory. Without including shear correction factor, the present theory satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate. The present refined shear deformation theory contains only four unknowns. According to a power law of the volume fraction, the properties of the materials of this plate vary continuously across the thickness. Comparisons with other results have been made nonuniform foundation. The effects of the index and the dimensions of the P-FGM plate and of the elastic foundation parameters on the thermomechanical behavior are studied. Numerical results show accuracy comparable to other theories in the literature. [ABSTRACT FROM AUTHOR]

In order to determine the stress–strain response of buried pipelines under the ground load, the pipeline–soil coupling finite element model was established. The mechanical behaviours of buried pipelines in the soil stratum and the rock stratum, as well as the effects of surrounding soil's elasticity modulus, Poisson's ratio and cohesion on stress and strain of buried pipelines were investigated. The results show that the maximum von Mises stress, high stress area, axial strain and plastic strain increase with the increasing ground load. Buried pipeline in the soil stratum is more prone to failure than in the rock stratum under the same ground load. The maximum axial compressive strain appears at the bottom of buried pipelines when there is no buckling, and the maximum tensile strain appears on the two sides. High stress area, the axial strain, the plastic strain and the plastic area decrease with the increase of the soil's elasticity modulus and cohesion. But the surrounding soil's Poisson's ratio has a small effect on the stress and strain of buried pipelines under the ground load. The results can provide a theoretical basis and reference for safety evaluation, repair and maintenance of buried pipelines. [ABSTRACT FROM PUBLISHER]

The use of tubes as energy absorption structures has been prevalent for many decades and numerous studies have been done on metal and composite tubes of varying thickness, length and section geometry. This paper extends the work to hybrid tubes and presents the results of experimental work pertaining to the collapse modes and crashworthiness characteristics of hybrid tubes that were subjected to quasi-static axial compressive loading. The hybrid specimens were featured by inner mild steel tube wrapped by a material combination of glass fibres in the form of reinforcing direct roving fabric in thermosetting polyester resin. Tubes were cut at different lengths of the same circular cross-section that encompassed both classical progressive buckling and the global bending modes of failure. Particular attention was paid to the investigate effect of tube length on crashworthiness parameters and critical length to avoid global bending during quasi-static crushing of thin-walled tubes. At first, similar work was done on steel tubes to compare results obtained by hybrid tubes with plain counterparts. [ABSTRACT FROM PUBLISHER]

Steel plate shear walls are lateral load resisting systems, especially against earthquake excitation. They are constructed with or without stiffeners. Stiffened walls are more ductile than those without stiffeners. In this research a numerical study using finite element analysis via a finite element program is conducted. Nine thin steel plate shear wall models were considered in three groups of 5-storey, 10-storey and 15-storey walls. In each group different yield point steel for the infill plate was used. The yield points of infill plates were assumed to be 160, 200 and 240 MPa. The results showed that using low yield point (LYP) steel will increase energy dissipation of models by up to 63%. Using LYP steel also decreases the lateral displacement of models by up to 16%. [ABSTRACT FROM AUTHOR]

The needle-punching machine is used for producing nonwoven fabrics. The needle is considered to be a very important member in the machine. The failure of the needle (simple or compound) during punching under the effect of the compressive force causes fabric defects and delays in production. In this paper, a theoretical approach is applied to calculating the load above which the needle loses its elastic stable equilibrium. It is shown that the coefficient of the elastic stable equilibrium, n, is 1.4706 for the compound needle and 1.1116 for the simple needle. The calculations were made by the use of an mz-80K personal computer. [ABSTRACT FROM AUTHOR]

A test set-up in intermediate scale was conceived to investigate the structural integrity of materials under fire. The task was to develop a realistic test scenario targeting component-like behaviour. Carbon-fibre-reinforced sandwich specimens (500 × 500 × 20 mm) were used to examine failure mechanisms, times to failure and critical failure loads under compression. Fire tests were performed with fully developed fire applied to one side of the specimen by an oil burner. In a first test series, the applied load was varied, but the fully developed fire remained unchanged. In general, times to failure were short. Decreased load levels resulted in prolonged times to failure and led to a different failure mechanism. Results obtained in the test series were compared with a bench-scale study (150 × 150 × 20 mm) investigating identical material. The comparison clearly revealed the influence of size on the time to failure and the load-bearing capacity. [ABSTRACT FROM PUBLISHER]

The capability of nonlinear analysis methods in tracing the equilibrium path depends on how to return to static status. In this paper, some residual factors existed in the iteration steps are employed. By setting the residual load parameter to zero, minimizing its factor and the residual displacement parameter, three novel constraint equations are obtained. The new formulas are proved by numerical examples. All obtained results illustrate the minimum residual load scheme's robustness in comparison with the cylindrical arc-length algorithm and other previous strategies. Moreover, the capacities of new procedures in tracing the load and displacement limit points are assessed. [ABSTRACT FROM AUTHOR]

The paper is concerned with the tension field action in webs of steel-concrete composite plate girders. A three-dimensional finite element model has been used to carry out nonlinear analyses on composite plate girders. The results obtained from the finite element analyses are compared with those from experiments. It is observed from the comparative study that the proposed nonlinear finite element model is capable of predicting the ultimate load behaviour of steel-concrete composite plate girders to an acceptable accuracy. Results are presented to explain the development of the tension field action in the webs and to illustrate a measure of the contribution by the concrete slab acting compositely with the girder to the changes in tension field compared to a plain steel girder. [ABSTRACT FROM AUTHOR]