Search

Abstract This paper was dealt with buckling and post-buckling behavior of short thin-walled Z-columns made of a carbon-epoxy laminate, subjected to eccentric compressive load. The buckling mode and the buckling load of real structures versus load eccentricity were discussed. The study involved both experimental tests were carried out on real laminated structures and numerical simulations by the finite element method. The buckling load of real structures was determined by approximation methods on the basis of experimental and numerical post-buckling equilibrium paths of the structure. Additionally, in numerical simulations, the bifurcation load value was determined by solving an eigen problem. In all cases, experimental findings and numerical results show high agreement. The study determined the quantitative influence of the direction and value of compressive load eccentricity on the buckling load and rigidity of the structure in the post-buckling state. [ABSTRACT FROM AUTHOR]

Abstract Repair of a composite laminate with delamination using micro-bolts is studied parametrically. The effects on compressive buckling load of delamination crack length, bolt material, bolt diameter and arrangement, and bolt–laminate clearance are considered. For 45- and 65-mm crack lengths, buckling load recovery rates using brass bolts are 90% and 73%, respectively. Using steel increases the rate by 6.6% compared to the intact specimen. Tests are performed fixing the number of steel bolts for bolt diameters of 0.6, 1.0, and 1.2 mm. The buckling load recovery rate using 1.2- versus 0.6-mm bolts increases by 6.8%. Finite element analysis confirms the effect of the bolt–laminate gap: 27% larger buckling load for no clearance than for a 0.1-mm gap. 18% higher buckling load, which is 97% of intact-specimen buckling load, is obtained for a 1.2-mm-diameter bolt repair by gluing bolts and holes and then tightening them compared with using bolts alone. [ABSTRACT FROM AUTHOR]

Abstract The present paper deals with the description of the stability loss and postbuckling for multilayered composite structures. Both, the experimental results and theoretical predictions are presented and discussed. The wide literature review is also pointed out considering the issue of both experimental and theoretical buckling analyses for composite rectangular plates and shells. A special attention is focused on the buckling and postbuckling behaviour od structures with cutouts and reinforcement. [ABSTRACT FROM AUTHOR]

Abstract In this work, a formulation for buckling and geometrically nonlinear analysis of functionally graded plates under thermo-mechanical loading is presented. The influence of high temperature environment on deflections due to mechanical loading as well the deflections produced by thermal loads acting alone or combined with mechanical loads is analysed. The implemented finite element model is based on a non-conforming triangular flat plate/shell element, with three nodes and eight degrees of freedom per node, associated with a higher order shear deformation theory. The solutions of some illustrative examples are evaluated involving the variation of volume fractions of constituent materials, temperature range and material combinations, which have significant impact on the deflections of plates. The numerical results obtained with the present model are presented and compared with alternative solutions. [ABSTRACT FROM AUTHOR]

Abstract Cylindrical lattice structures are types of lightweight structures and can utilize the orthotropy of fiber-reinforced composite materials. Maximization of the buckling loads is important because they dominate the strength of the structures. On the basis of the fact that a hyperboloidal shape deviation increases the buckling loads of cylindrical homogeneous shells, the changes in the buckling loads of cylindrical lattice structures with a hyperboloidal shape deviation are discussed. Further, the buckling loads of both conventional cylindrical lattice structures and shape-deviated hyperboloidal lattice structures with respect to the compressive, bending, and torsional loads are calculated using a finite element method. The results show that the shape deviation decreases the buckling loads, while the change in mass is negligible. The effects of the shape deviation on the buckling loads differ between homogeneous shell structures and lattice structures. [ABSTRACT FROM AUTHOR]

A general analytical procedure is proposed to design tapered laminated composite structures. It is based on: 1) the introduction of two variables representing a laminate configuration, 2) the analytical determination of the lower bound of the number of layers in each of the segments constituting the construction, 3) the definition of the reference sublaminate which configuration is transferred to all segments/parts of the construction, 4) the gradual building of configurations for symmetric balanced laminates having odd or even number of plies. The solution is verified by the comparison with results existing in the literature for both inner and outer tapers. A multi-panel composite structure is considered to demonstrate the applicability of the proposed method. As usual, in a such class of problems, the whole construction is divided into segments/panels. The individual segments are subjected to the simultaneous action of in-plane, tensile or compressive and shear loads. The present results demonstrate the simplicity and effectiveness of the method and non-uniqueness of solutions. The paper intends to clarify the physical sense of the discussed problem. [ABSTRACT FROM AUTHOR]

Elastoplastic buckling behaviors of rectangular plates made from functionally graded materials (FGMs) are investigated in this paper. The elastoplastic material properties are assumed to vary smoothly through the thickness of the plates. The three dimensional material constitutive relation of FGMs is found by introducing the material homogenization method, named Tamura-Tomota-Ozawa(TTO) model, into J 2 deformation theory or J 2 flow theory. The uniform strain hypothesis helps to simplify the prebuckling state and derive the analytical expression of the position of the material elastoplastic interface. The buckling governing equations and the buckling critical condition of the structures are formulated under the framework of the classical plate theory. An iterative algorithm is designed to obtain the elastoplastic buckling critical load, a converging result between the prebuckling and the buckling critical internal forces. ABAQUS simulation well verifies the present theoretical predictions from J 2 flow theory, and is resorted to investigate the postbuckling behaviors of FGM plates. Discussions are addressed for the effects of the constituent distribution, the material plastic flow, the preloaded states of the plates, and the regions of buckling types are plotted as well. [ABSTRACT FROM AUTHOR]

A solution of the buckling problem for a shear loaded composite anisogrid lattice plate with the clamped edges based on the Galerkin method is presented in this paper. The lattice plate is modelled as an equivalent continuous orthotropic plate with effective stiffness parameters. The deflection of buckled plate is presented in the form of a double series containing clamped–clamped beam functions. The critical in-plane shear load is found solving the generalised eigenvalue problem for a homogeneous system of algebraic equations in which the unknowns are the coefficients of the double series. Based on this solution, the effects of the plate dimensions and parameters of lattice structure on the value of critical load are investigated and analysed. Results of these analyses are successfully verified using the finite element method. An approximate analytical expression providing fast and reliable way of calculation of the critical buckling load is obtained for the lattice plate composed of the ribs made of the same composite material and with the same size of their cross-sections. [ABSTRACT FROM AUTHOR]

Grid-stiffened composite structures not only allow for significant structural weight reduction but also are competitive in terms of structural stability and damage tolerance compared with conventional stiffened candidates. As the development of Automated Fibre Placement (AFP) technology matures, a unitized construction of skin and stiffeners is easily manufacturable. In this paper, a curved stiffener layout is optimized to enhance the structural buckling resistance. A linear variation of stiffener angles is used, resulting in the formation of a locally rhombic lattice pattern. Due to the spatial variation of angle and spacing induced by the use of curved stiffeners, analytic solutions for the responses are not generally applicable. Thus, global and local buckling loads are calculated based on finite element models by a previously-developed global/local coupled strategy. Since the stiffeners are not explicitly modelled in the finite element calculations, a fixed mesh is used for gradient-based optimization. Both parametric design and optimization are performed in order to find the optimal curved grid pattern, whose practical performances are assessed by post-buckling analysis. A comparison between the performances of structures with curved stiffeners, with straight stiffeners, and variable-stiffness skins with curved fibres, demonstrates the potential of curved stiffener configurations in improving the structural efficiency. [ABSTRACT FROM AUTHOR]

As a first attempt, optimum stacking sequences of thick laminated composite plate is obtained to maximize its buckling load via employing the finite element (FE), genetic algorithms (GAs) and particle swarm optimization (PSO) methods. The higher-order shear deformation theory (HSDT) is used to obtain governing equations of the plate. The finite element method (FEM) is employed to solve these equations and to gain buckling load of the plate. The FEM solution is linked with a developed optimization algorithm which is a mix of genetic algorithms (GAs) and particle swarm optimization (PSO) techniques. Some examples are solved to show applicability and usefulness of the proposed hybrid method for maximizing buckling load of the plate via finding optimum stacking sequences of the plate. Also, influences of different parameters on the optimum stacking sequences of the thick plate are studied. [ABSTRACT FROM AUTHOR]

In the present paper, the post-buckling behavior of a simply supported piezoelectric hybrid microplate subject to thermal, electrical and mechanical loads is studied. The size effect in the mechanical behavior of the microplate is captured by using the modified couple stress theory. The Mindlin plate theory is adopted to describe its deflection behavior with the von Karman’s geometric nonlinearity taken into account. Based on these assumptions and the principle of minimum potential energy, the equilibrium equations of the microplate and associated boundary conditions are derived. By applying the Galerkin method to the equilibrium equations, closed-form solutions for the critical thermal/mechanical buckling load and the load–displacement relation in the post-buckling stage are obtained. Furthermore, the effects of the material length scale parameter to thickness ratio, the applied electric field and in-plane boundary conditions on the buckling and post-buckling behavior of the piezoelectric hybrid microplate are discussed in detail. [ABSTRACT FROM AUTHOR]

Research is limited with respect to load-deflection behavior of slender concrete columns internally reinforced with Fiber Reinforced Polymer (FRP) spirals and longitudinal bars. An analytical buckling model based on numerical integration is presented to predict the load versus deflection performance of slender concrete columns reinforced with FRP spirals and longitudinal bars, subjected to eccentric loads. The model can be used to predict the behavior of slender concrete columns with various configurations including FRP and/or steel reinforcement, single or double spiral, and number of longitudinal bars. The longitudinal bars considered include steel, FRP, or hybrid reinforcement consisting of steel and FRP bars. The model is found to predict the experimental performance of slender concrete columns reinforced with Glass FRP longitudinal bars and spirals with satisfactory accuracy. The model is used to create interaction diagrams for FRP spiral-confined circular concrete columns with various slenderness ratios, reinforced with steel, FRP or hybrid reinforcement. [ABSTRACT FROM AUTHOR]

The buckling response and load carrying capacity of thin-walled open cross-section profiles made of Fibre Metal Laminates, subjected to static axial compression loading are considered. These include thin-walled Z-shape and channel cross-section profiles adopting a 3/2 FML lay-up design, made of 3 aluminium layers. The objective of the investigation is the comparison of standard thickness Fibre Reinforced Plastic layers versus thin-ply material technology. Whilst thin ply designs differ only by the layer thickness, they offer an exponential increase in stacking sequence design freedoms, allowing detrimental coupling effects to be eliminated. The benefit of different hybrid materials are also considered. The comparisons involve semi-analytical and finite element methods, which are validated against experimental investigations. [ABSTRACT FROM AUTHOR]

The purpose of this paper was to study the effect of I-shape stiffener stiffness on the buckling and post-buckling, up to collapse behavior of stiffened composite panel under the uniform uniaxial compression load. Six stiffened composite panel configurations, which were orthogonally designed with two skin configurations and three I-shape stiffener configurations, were took into account in the experimental investigation. Three specimens for each configuration (18 specimens in total) were manufactured for test. Before tests, the key dimensions of I-stiffener and skin were measured. Furthermore, all the specimens were also inspected visually and detected by the ultrasonic C-scan system. No initial delamination or debonding area was found on all the specimens according to their C-scan images. The experimental results show that the equivalent compression stiffness of I-shape stiffener has great influence on the buckling load and failure mode of stiffened panel, but a little effect on the failure load of stiffened panel. The skin thickness has great impact on the buckling load and the final failure load. [ABSTRACT FROM AUTHOR]

Stiffened cylindrical shells are widely used in modern engineering structures, especially in aircraft, oil-transmitting pipeline, spacecraft industry and ocean engineering. Due to the increasing demands for high structures performances, this paper presents the effect of stiffeners on the nonlinear buckling of cylindrical shells with functionally graded (FG) coatings under torsional load. The cylindrical shell is reinforced with external axial stiffeners. The material properties are assumed to vary continuously through the thickness direction. Equilibrium and stability equations for cylindrical shells are derived by using the classical shell theory (CST) with von-Karman nonlinear kinematic relations. Using analytical approach, Galerkin procedure, and the Airy stress function, the resulting equations are employed to obtain the closed-form expression for the critical buckling loads and load–deflection relation. The influences of the number of stiffeners, volume fraction exponent, the thickness of the metal layer, and geometric parameters on the nonlinear buckling behavior of the cylindrical shell with FG coatings are examined in details. [ABSTRACT FROM AUTHOR]

Buckling analysis of nanobeam is significantly important for design of nano-electro-mechanical systems (NEMS), especially for those under non-uniform temperature induced commonly by the operation of NEMS. In this work, such issue is investigated with the aids of size-dependent model, i.e. nonlocal thermoelasticity, and size effect of heat conduction on buckling property is considered for the first time. Euler–Bernoulli beam is adopted and reformulated within nonlocal theory. Analytical solution to critical load for various boundary conditions, e.g. SS, CF, CS and CC, is obtained using eigenvalue method. And the temperature distribution is determined using nonlocal heat conductive law. The effect of elastic and thermal nonlocal parameter on the critical load is systematically discussed. It is observed that classical models over-predict the critical load, which may be dangerous in practical applications. The present work is expected to be helpful for design of nanobeam-based devices and systems. [ABSTRACT FROM AUTHOR]

Unstiffened cylindrical shells are very sensitive to geometric imperfections such as production-related deviations from the ideal geometry (conventional imperfections) as well as imperfect boundary conditions, material and wall thickness imperfections (non-conventional imperfections). The load carrying capability of unstiffened shells is reduced significantly by those imperfections. The NASA SP-8007 design guideline from 1968 is currently used for shell design. This guideline provides knock-down factors for the buckling loads and is based on experimental data of isotropic and orthotropic test specimen. Therefore the structural behavior of composite material is not considered adequately. Based on the single-perturbation load approach (SPLA), this paper introduces a new physical based approach, to determine a lower bound for the buckling load of unstiffened composite cylindrical shells with respect to conventional and non-conventional imperfections, the constant single-buckle imperfection (CSBI) principle. The CSBI principle is based on the theory of the metastability of the geometric imperfect cylindrical shell which is introduced within this paper. The results indicate that the CSBI principle has the potential to provide an improved shell design in order to reduce weight and cost of thin-walled shells. [ABSTRACT FROM AUTHOR]

The present study is concerned with an analysis of load and frequency interaction effects in the dynamic buckling of sandwich plates and shells with a soft, transversely flexible core. The analysis is based of a general geometrically nonlinear soft-core sandwich model presented and a corresponding extended Galerkin solution strategy presented earlier. In the present study, the formalism is adopted and transformed into an eigenvalue problem. Assuming large transverse average displacements but small amplitudes for the vibration problem, a partially decoupled problem is obtained where in a first step the static buckling and face wrinkling problems can be addressed without consideration of the dynamic problem. In a second step, the dynamic eigenvalue problem can be solved, using the static solution as input parameters. The model is applied in parametric studies on the vibration response of plane and doubly curved sandwich panels with rectangular projection. In all cases, strong interaction effects between the external static preload and the natural frequencies are observed. The development of overall buckling or local face wrinkling instabilities enabled due to the transverse flexibility of the core result in distinct drops of the first natural frequency. [ABSTRACT FROM AUTHOR]

Practical applications such as airplane wings are usually subjected to combined thermal and mechanical loads, and they hence are prone to buckling failure. Preceding works on the buckling of advanced materials, e.g., functionally graded materials, under combined thermal and mechanical loads are rather rare in literature. In this paper, we report new numerical results of thermal-mechanical buckling of functionally graded rectangular and skew plates (FGPs) under combined thermal and mechanical loads. The numerical responses of buckling are computed using isogeometric analysis (IGA) based on the first-order shear deformation plate theory (FSDT) without shear-locking effect. We present formulations and then provide validation of numerical results computed by the proposed formulation against reference existing solutions. Parametric study is also performed to explore insight into the effects of various numerical aspect ratios such as gradient index, plate aspect ratio, loading type, skew angle, and boundary condition, etc. on mechanical response of FGPs. The stability diagrams are also presented. [ABSTRACT FROM AUTHOR]

The free vibration and buckling behaviors of foam-filled composite corrugated sandwich plates under thermal loading are investigated theoretically. A refined shear deformation theory is extended incorporating two different combinations of hyperbolic and parabolic shear shape functions. Equivalent thermoelastic properties of the foam-filled corrugation are obtained using the method of homogenization based on the Gibbs free energy. Based on hyperbolic-polynomial variation of all displacements across the thickness of both face sheets and sandwich core, the shear plate theory accounts for both transverse shear and thickness stretching effects. The theoretical predictions are validated against existing results as well as finite element simulations. The effects of geometric and material parameters on natural frequency and critical temperature change for buckling are systematically investigated. The proposed theory is not only accurate but also simple in predicting the free vibration and thermal buckling responses of composite sandwich plates with foam-filled corrugated cores. [ABSTRACT FROM AUTHOR]

This paper presents a unified nonlinear analytical solution of bending, buckling and vibration for the temperature-dependent functionally graded (FG) rectangular plates subjected to thermal load. Geometric nonlinearity resulted from mid-plane stretching is considered. Material properties of FG plates are assumed to vary with temperatures and the volume fractions of the constituents. Newly proposed higher order shear deformation theories in present available literature are sorted out and given a unified application. Three types of mathematical models, P-FG, S-FG and E-FG models, describing effective material properties of functionally graded materials (FGMs) are discussed. Finally, based on the unified nonlinear analytical solution, influences of material heterogeneity, thermal load, and plate geometry on bending, buckling and vibration of FG plates are studied. Outcomes reveal that the nonlinear solution exhibits better accuracy in calculation of shear stress in bending responses. The thermal load plays an important role in determining the bending, buckling and vibration of the FG plate. In addition, the characteristics of these three types of mathematical models to simulate effective material properties of FGMs are numerically compared and discussed. [ABSTRACT FROM AUTHOR]

An approximate analytical solution of the buckling problem formulated for a composite sandwich cylindrical shell subjected to a uniform external lateral pressure is presented in the paper. Both ends of the shell of finite length are fully clamped. The problem is solved using the Galerkin method. The analytical formula for the critical load has been obtained and verified by comparison with a finite-element solution. Based on this formula buckling analyses of sandwich pipes with different types of core materials normally used in underwater applications have been performed. Applications of the formula to the solutions of design problems have been demonstrated for the clamped–clamped sandwich pipes considering constraints imposed on the value of critical pressure. [ABSTRACT FROM AUTHOR]

In this paper, a re-look into the upper and lower bound solution to the buckling of composite columns is presented in details and this includes the complete derivation of the expressions for the kinematical compatibility conditions. Included in this contribution are also the results of the current finite element simulation together with the results of the experiments. Moreover, further investigations are conducted to test whether the proposed three methods of calculating the effective flexural stiffness can be employed in cooperation with the developed mathematical model to form the desired upper and lower bounds for the buckling loads of both the perfect and single-delaminated fiber-reinforced composite beams for the various parameters that are studied. In these analyses, single-delaminated fiber-reinforced composite beams which consist of random ply-orientations and stacking sequences are employed to put up a stringent test on the generalness and applicability of these three methods. It is observed that for all the cases that were examined, these three means of evaluating the effective bending modulus of a fiber-reinforced composite beam pass are validated. [ABSTRACT FROM AUTHOR]

Morphing aircraft aim to increase the performance of aircraft over multiple flight conditions, by enabling shape changes in flight in order to optimise their aerodynamic properties for the current conditions. The skin of a morphing aircraft is a critical component. It must be compliant in degrees of freedom that are required for actuation, to minimise the actuation loads. However, it must also carry structural loads, and therefore be stiff in load bearing degrees of freedom. This leads to a requirement for extremely anisotropic material systems. A common solution is the use of a corrugated panel. However, previous work on corrugations has not addressed the problem of compressive buckling loads. This work analyses the performance of corrugated panels under buckling loads, and optimises corrugation patterns for the objectives of weight, buckling performance, and actuation compliance. Simplified analytical models that derive properties equivalent to conventional plates are used to obtain approximate estimates of the buckling loads. Furthermore a new mode of buckling, that occurs entirely in-plane and is unique to panels with extreme anisotropy is analysed. The simple models allow optimisation to be performed, and both a single-objective and a multi-objective approach are demonstrated. The results are compared to Finite Element Analysis. [ABSTRACT FROM AUTHOR]

In practice, voltage would be stored in actuators due to applied mechanical loads or voltage specified as input to them. The effect of stored voltage in actuators on buckling analysis has not been studied so far. This article addresses fully coupled electromechanical buckling analysis of active laminated composite thin to thick plates using partial hierarchical Rayleigh–Ritz solution. The formulation is derived from variational principle with consideration for shear deformation plate theory. Another major contribution is to postpone the initiation of buckling of a laminated plate by increasing its flexural stiffness using feedback piezoelectric control. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution for the buckling and free vibration analysis of laminated beams by using a refined and generalized shear deformation theory which includes the thickness expansion. The eigenvalue equation is derived by employing the Rayleigh quotient, and the Ritz method is used to approximate the displacement field. The functions used in the Ritz method are chosen as either a pure polynomial series or a hybrid polynomial-trigonometric series. The hybrid series is used due to the superior convergence and accuracy compared to conventional pure polynomial series for certain boundary conditions. The boundary conditions are taken into account using the penalty method. Convergence of the results is analyzed, and numerical results of the present theory are compared with other theories for validation. Nondimensional natural frequencies and critical buckling loads are obtained for a variety of stacking sequences. The effect of the normal deformation on the fundamental frequencies and critical buckling loads is also analyzed. [ABSTRACT FROM AUTHOR]

Bio-inspired helicoidal carbon fiber reinforced polymer composite (CFRPC) laminates are one of the novel composite structures that have potential applications in many engineering fields. The optimization design of helicoidal layups with linear, nonlinear Recursive, Fibonacci, Exponential and their combination-form arrangements are carried out using ABAQUS and ASA algorithm on Isight platform. Two cases of the compressive postbuckling under uniaxial compression and the thermal postbuckling under uniform temperature rise of helicoidal CFRPC laminated plates stacked with optimal layups are performed and the secondary buckling and mode jumping in the postbuckling region are examined for the first time. Numerical investigations are carried out for 16-ply symmetrical helicoidal laminated plates with various width-to-thickness ratios under different boundary conditions and are compared with quasi-isotropic counterparts. The results show that the bio-inspired helicoidal CFRPC laminated plates can enhance the buckling load and the buckling temperature as well as the compressive and the thermal postbuckling strength. In some cases, the secondary buckling and mode jumping may occur for rectangular helicoidal laminated plate in the postbuckling region. [ABSTRACT FROM AUTHOR]

In this paper, the thermal effect on buckling and free vibration characteristics of functionally graded (FG) size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution for the first time. Material properties of FG nanobeam are supposed to be temperature-dependent and vary continuously along the thickness according to the power-law form. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on Timoshenko beam theory through Hamilton’s principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as thermal effect, material distribution profile, small scale effects, beam thickness and mode number on the critical buckling temperature and normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the thermal buckling and vibration behavior of a FG nanobeams is significantly influenced by these effects. [ABSTRACT FROM AUTHOR]

This paper presents a method for the determination of the buckling loads of symmetrically laminated composite plates under uniaxial compressive load with explicit consideration of bending–twisting-coupling (BTC). The plates under consideration are assumed to be thin and balanced with a symmetric stacking sequence and consist of layers with ply orientations of {0°/±45°/90°}, but otherwise arbitrary lamination schemes. The characteristic laminate quantities are described in a non-dimensional notation in order to capture all combinations of material and stacking sequences that are physically possible. Plates with rectangular planforms in the framework of Classical Laminate Theory (CLT) under several different sets of boundary conditions are considered, and the buckling problem of such composite laminated plates is solved in an approximate manner by using the classical Rayleigh–Ritz method. Several combinations of the boundary conditions ‘simply supported’ and ‘clamped’ are analyzed, and the obtained results are compared with finite-element simulations for verification purposes. Based on the computed data, two different design equations for sufficiently long plates are developed which allow for a rapid and closed-form analytical assessment of the buckling behavior of symmetrically layered composite plates under explicit consideration of bending–twisting coupling. It is found that the closed-form analytical analysis equations are simple in their application and yet still work with very satisfying accuracy which makes them very suitable for use in practical engineering work. [ABSTRACT FROM AUTHOR]

Abstract: A three-layered structure is composed by two external elastic beams that sandwich a viscoelastic core providing their shear coupling. The time-dependent bending of a simply-supported composite-beam of this type, axially-compressed and with an initial sag, are studied assuming a Maxwell–Wierchert constitutive model of viscoelasticity accounting for the memory effect. The phenomena of glassy-, rubber- and creep-buckling are examined for various values of the load. Comparisons are made with a quasi-elastic approximation that assumes a relaxed elastic shear modulus for the interlayer, parametrically dependent on time. The limits of this simplified approach are discussed. [Copyright &y& Elsevier]

Abstract: A new solution for analyzing of the symmetrical composite plate having two parallel edges simply supported and the remaining parallel edges being clamped (SS–C–SS–C plate) subjected to linear-varying in-plane loads is presented. Levy series are used to represent the displacement field of the plate and a numerical procedure is developed based upon finite-difference method. Convergence study is carried out as well. The proposed method has been validated for both isotropic and composite plates with various aspect ratios and load parameters through numerical examples. [Copyright &y& Elsevier]

Semi-analytical models for the linear buckling analysis of unstiffened laminated composite cylinders and cones with flexible boundary conditions are presented. The Classical Laminated Plate Theory and the First-order Shear Deformation Theory are used in conjunction with the Donnell’s non-linear equations to derive the buckling equations. Axial, torsion and pressure loads can be applied individually or combined in the proposed models. The stiffness matrices are integrated analytically and for the conical shells an approximation is proposed to overcome non-integrable expressions. Comparisons with the literature show that the classical base functions available for axial compression cannot capture the buckling modes for non-orthotropic laminates. For torsion loads these classical shape functions do not catch the buckling modes even when applying the assumption of pure orthotropy, and it is shown how the proposed models correlate well with experimental data from the literature and finite element results. The use of elastic constraints at the boundaries allows the simulation of different boundary conditions in a versatile way and it is shown how those constants can be adjusted in order to change from one type of boundary condition to another. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the buckling analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates under various in-plane mechanical loads, using the element-free kp-Ritz method. The first-order shear deformation plate theory is applied and a set of mesh-free kernel particle functions are used to approximate two-dimensional displacement fields. Effective properties of materials of the plates reinforced by single-walled carbon nanotubes (SWCNTs) are estimated through a micromechanical model based on either the Eshelby–Mori–Tanaka approach or the extended rule of mixture. Comparison study and numerical simulations with various parameters are conducted to assess efficacy and accuracy of the present method for analysis of buckling of SWCNT-reinforced composite plates. Results demonstrate that the change of carbon nanotube volume fraction, plate width-to-thickness ratio, plate aspect ratio, loading condition and temperature have pronounced effects on buckling strength of CNTRC plates as well as the boundary condition. [Copyright &y& Elsevier]

Abstract: The paper is concerned with the buckling analysis of the composite orthotropic cylindrical shell with clamped edges subjected to inertia loading. The problem is characterised by a non-uniform pre-buckling stress state. To address this, the relevant governing system of differential equations with variable coefficients has been derived and solved using Galerkin method. As a result, the problem of determining the critical acceleration causing the buckling of shell is reduced to the solution of the corresponding generalised eigenvalue problem. Using the proposed approach, the critical accelerations are calculated for the glass-fibre reinforced shells with various dimensional and stiffness parameters. Results of calculations are compared with those based on finite-element modelling and analysis. [Copyright &y& Elsevier]

Abstract: The analytical modelling of the local buckling failure mode for composite anisogrid lattice cylindrical shells with the typical system of hexagonal cells is here discussed. The aim is to complement the set of constraint equations that are associated with the preliminary design phase of such structures under axial compressive loads, and to prospectively improve the final solutions. The basic constraint equations for anisogrids without the skin are focused on the global buckling of the shell, the local buckling of helical ribs, and the material failure of these ribs. However, the local buckling of helical ribs is normally based on a simplified and qualitative approach. Conversely, the developed modelling, which is based on the Ritz method, accounts for the helical angle of the periodic cell, the stiffness of intersecting hoop and helical ribs, and the positive effect of the prebuckling tensile force in hoop ribs. This model has been verified with the aid of finite-element analysis, demonstrating a noteworthy accuracy. Thanks to the comparison with the parallel study on anisogrid shells with triangular cells, the effect of hoop rib positioning on the local buckling strength (i.e., hexagonal or triangular system of cells) is finally assessed. [Copyright &y& Elsevier]

Abstract: In this paper an analysis of dynamic response of thin-walled composite columns with opened stiffened cross-sections was described. The columns were subjected to an in–plane pulse loading and three different stability criteria were applied: the Budiansky–Hutchinson, the Kleiber–Kotula–Saran and the phase-plane one. A pulse loading of rectangular shape was concerned. The columns were assumed to be simply supported at the ends. Additionally, an attention was paid to an influence of the tracking time of dynamic response on critical values of dynamic load factors. A plate model was adopted in the analysis. Differential equations of motion were obtained from the Hamilton’s Principle, taking into account all components of inertia forces. The discussed problem of dynamic buckling was solved with a numeric method. Special attention was given to a coupled buckling of various global buckling modes. [Copyright &y& Elsevier]

Abstract: Analytical relations between the critical buckling load of a functionally graded material (FGM) Timoshenko beam and that of the corresponding homogeneous Euler–Bernoulli beam subjected to axial compressive load have been derived for clamped–clamped (C–C), simply supported–simply supported (S–S) and clamped–free (C–F) edges. However, no such relation is found for clamped–simply supported (C–S) beams. For C–S beams, the transcendental equation has been derived to find the critical buckling load for the FGM Timoshenko beam which is similar to that for a homogeneous Euler–Bernoulli beam. For the FGM beams Young’s modulus, E, and Poisson’s ratio, ν, are assumed to vary through the thickness. The significance of this work is that for the C–C, S–S and C–F FGM Timoshenko beams, the critical buckling load can be easily found from that of the corresponding homogeneous Euler–Bernoulli beam and two constants whose values depend upon the through-the-thickness variations of E and ν. For the C–S FGM Timoshenko beam the transcendental equation for the determination of the critical buckling load is similar to that for the corresponding homogeneous Euler–Bernoulli beam. [Copyright &y& Elsevier]

Abstract: The concept of variable angle tow (VAT) placement is explored for enhancing the buckling resistance of composite plates subjected to axial compression loading. The problem is relatively difficult to solve because of varying stiffness properties and requires prior prebuckling analysis to determine the non-uniform stress variation followed by the buckling analysis of VAT plates. A stress function formulation for in-plane analysis and displacement formulation for buckling analysis was employed to derive the governing differential equations of VAT plates based on classical laminated plate theory. The Differential Quadrature Method (DQM) is applied to solve the differential equations. The novel aspect of the present work is the use of Airy’s stress function to model the prebuckling analysis of VAT plates which considerably reduces the problem size, computational effort and provides generality to model pure stress and mixed boundary conditions. DQM was applied first to solve the prebuckling problem of VAT plates subjected to cosine distributed compressive load/ uniform end shortening. Then, DQM was applied to solve the buckling problem of rectangular VAT plates subjected to axial compression under different plate boundary conditions. Results were validated with detailed finite element analysis and the relative accuracy and efficiency of the DQM approach is discussed. [Copyright &y& Elsevier]

Abstract: The paper deals with a refined analytical model for the local buckling failure modes of composite anisogrid lattice cylindrical shells made of a regular system of triangular cells. Such structures are preliminarily designed with the aid of closed-form solutions specifying the minimum mass and the corresponding optimal design variables under a set of formulated constraint equations. These equations address the main failure mechanisms that can be typically experienced by the structure due to axial compressive loads, namely, the global buckling of the shell, the local buckling of helical ribs, and the material failure of helical ribs. However, the local buckling of helical ribs is normally based on a simplified and qualitative approach. Thus, the scope of the present work is to improve the prediction of this failure mode by means of a rather accurate modelling which accounts for the interaction of intersecting hoop and helical ribs, the influence of the number of hoop sections of the shell, and the effect of the prebuckling tensile force in hoop ribs. The proposed model – that has been verified with the aid of finite-element analysis – lastly suggests the possibility to improve the preliminary design solution with respect to the fully analytical approach. [Copyright &y& Elsevier]

Abstract: In this paper, buckling behaviors of composite cylindrical shells made from functionally graded materials (FGMs) subjected to pure bending load were investigated. The material properties were assumed to be graded along the thickness. The non-uniform bending force on the shell section was considered in the buckling government equation of FGM cylindrical shells based on the Donnell shallow shell theory. The prebuckling deformation of the FGM cylindrical shells was neglected and the buckling mode was assumed to occur non-uniformly in local district along the shell circumferential direction. The eigenvalue method was used to obtain the buckling critical condition. The theoretical results were in excellent agreement with those of ABAQUS code. Results show that the inhomogenity of the materials is significant for buckling of FGM cylindrical shells. [Copyright &y& Elsevier]

Abstract: The paper presents the solution of the buckling problem for an orthotropic rectangular plate having two parallel edges simply supported, one edge clamped and the remaining edge free (the SSCF plate). The plate considered is subjected to a linearly varying in-plane load that can take the form of uniform compression, combination of in-plane bending and uniform compression, or pure in-plane bending. The solution technique involves reduction of the relevant variational buckling equation to a one-dimensional form using the Kantorovich procedure and subsequent application of the generalised Galerkin method. The buckling problems are solved for isotropic and orthotropic plates with various aspect ratios. The analytical solution is verified using the finite-element analysis. The comparisons of computational results demonstrate the appropriateness and efficiency of the approach developed in this work for the calculation of critical loads of composite SSCF plates with various dimensional and stiffness parameters. [Copyright &y& Elsevier]

Abstract: The onset of buckling in square laminated multi-layered composite plates, subject to unidirectional in-plane loads, is investigated within the framework of a generalized higher-order shear deformation theory suitable to capture significant transverse shear and thickness-wise deformation effects. The displacement field is expanded in a Taylor series of the thickness coordinate with arbitrary polynomial degree; in turn, the series coefficients, expressed as a superposition of admissible functions, are determined according to the Rayleigh–Ritz method. Truly higher-order polynomial terms, along with a sufficient number of in-plane admissible functions, are shown to be necessary for convergence towards the fundamental buckling load multiplier. As a by-product, reduced-order models are identified for various plate geometries and lamination schemes. The sensitivity of the lowest buckling load with respect to the nondimensional parameters (the thickness ratio, the ratio between the elastic moduli, the ply angle) is investigated. In particular, the attention is focused on the cross-over phenomenon between the lowest two buckling eigenvalues in multi-layered composite square plates with different lamination schemes. The presented results shed light onto the buckling behavior of thick shear-deformable multi-layered plates. [Copyright &y& Elsevier]

Abstract: Solution of the buckling problem for the CCFF orthotropic plate subjected to in-plane pure bending is presented. The two parallel clamped edges of the plate are loaded by linearly distributed in-plane loads statically equivalent to the in-plane bending moments. The problem is solved using method of lines for partial differential equations and Galerkin’s method. The buckling problems are solved for isotropic, orthotropic and multilayered CFRP composite plates with various aspect ratios. Results of calculations of critical loads are compared with those based on finite-element modelling and analyses. The comparisons demonstrate efficiency of the proposed approach to the buckling analysis of composite CCFF plates with various dimensional and stiffness parameters. [Copyright &y& Elsevier]

Abstract: The paper deals with the solution of the buckling problem for a rectangular orthotropic plate with two parallel free edges. The other two parallel simply supported opposite edges of the plate are loaded by a linearly distributed in-plane load which is equivalent to the pure in-plane bending. Buckling analysis is performed using the Levy-type solution and subsequent finite-difference approximation of the boundary-value problem. Solution of the corresponding eigenvalue problem yields the critical buckling coefficient and critical load. The problem is solved for isotropic and orthotropic composite plates. The design chart has been obtained for the isotropic plates with various aspect ratios from which the corresponding critical loads can be found. Critical buckling coefficients are determined for composite plates with various aspect ratios and angles of the reinforcement orientation. The optimum material reinforcement structure providing the maximum value of critical load is determined. [Copyright &y& Elsevier]

Abstract: This study investigates the applicability of scaled models for predicting the buckling behavior of delaminated composites. Such a study is important since it provides the necessary scaling laws, and the factors which affect the accuracy of the scale models. Employment of similitude theory to establish similarity among structural systems can save considerable expense and time, provided that the proper scaling laws are found and validated. In this study a number of parametric studies are performed. The limitations and acceptable intervals of all parameters and corresponding scale factors are investigated. Particular emphasis is placed on the case of delamination buckling of orthotropic plates. Both complete and partial similarities are discussed. This study indicates that models with a different delamination size, depth and number of delaminations than those of the prototype are capable of predicting buckling loads of the prototypes with good accuracy. [Copyright &y& Elsevier]

Abstract: In this paper, the effects of the delaminations size on the critical buckling load and compressive failure load of E-glass/epoxy composite laminates with multiple large delaminations are studied. A numerical and experimental study is carried out to determine the buckling load of rectangular composite plates. For the experiments (0°/90°/0°/90°)s oriented cross-ply laminated plates with multiple large delaminations and without delamination are produced by using hand lay-up technique. The experimental buckling loads of plates are found by clamping from the two edges and then these results are compared with the results obtained by ANSYS11.0 package. In addition, the compressive failure loads of composite laminates containing multiple large delaminations are found by compression test fixture. It is found that the longest and near-surface delamination size influences the buckling load and compressive failure load of composite laminates. However, the size of beneath delaminations has no significant effect on the buckling load and compressive failure load of composite laminates. [Copyright &y& Elsevier]

Abstract: The purpose of this study is to investigate the cutout shape effects on the buckling behavior of 1×1 rib knitting glass/epoxy laminated plates in three different knitting tightness levels as low, medium and high. The composite plate is produced five plies as [0°]5Course by using hand lay-up technique. In order to investigate the shape effects, five different plates are used such as, without cutout (W-C), central circular/elliptical cutout (C/E-C), central square/rectangular cutout (S/R-C), edge semi-circular/semi-elliptical cutout (SC/SE-C), and edge semi-square/semi-rectangular cutout (SS/SR-C). In addition, circular/elliptical diameter-to-plate width ratio and square/rectangular length-to-plate width ratio effects on buckling load of 1×1 rib knitting glass/epoxy plates are also investigated. The experimental buckling loads of plates are obtained by clamping from two edges and then these results are compared with the results calculated from the numerical analysis. ANSYS 10 commercial software is used for numerical study. A good agreement was obtained between finite element method and experimental measurements. Results are showed that the buckling loads depend on the cutout area and the level of tightness. [Copyright &y& Elsevier]

Abstract: Dynamic buckling analysis of FGM plates has not been accomplished so far. In the present paper, vibration and dynamic buckling of FGM rectangular plates with surface-bonded or embedded piezoelectric sensors and actuators subjected to thermo-electro-mechanical loading conditions are investigated. A finite element formulation based on a higher-order shear deformation theory is developed. Both initial geometric imperfections of the plate and temperature-dependency of the material properties are taken into account. Dynamic buckling of plates already pre-stressed by other forms of loading conditions is assumed to occur under suddenly applied thermal or mechanical loads. A nine-node second order Lagrangian element, an efficient numerical algorithm for solving the resulted highly non-linear governing equations, and an instability criterion already proposed by the author are employed. A simple negative velocity feedback control is used to actively control the dynamic response of the plate. Results show that generally, initial geometric imperfections lead to an increased fundamental bending natural frequency and decreased buckling loads. Furthermore, buckling mitigation due to utilizing integrated piezoelectric sensors and actuators is mainly achieved in extremely high gain values. Therefore, the piezoelectricity effect on the buckling load is small in applicable voltages. It is also noticed that the temperature-dependency and initial geometric imperfections remarkably affect the buckling loads. [Copyright &y& Elsevier]

Abstract: Dynamic buckling of piezolaminated plates under thermo-electro-mechanical loads has not been investigated so far. In the present paper, effects of the thermo-piezoelasticity on the dynamic buckling under suddenly applied thermal and mechanical loads are investigated for imperfect rectangular composite plates with surface-bonded or embedded piezoelectric sensors and actuators. A finite element formulation based on a higher-order shear deformation theory is developed. Both the initial geometric imperfections of the plate and the temperature-dependency of the material properties are taken into account. Complex dynamic loading combinations include in-plane mechanical loads, heating, and electrical actuations are considered. A nine-node second order Lagrangian element, an efficient numerical algorithm for solving the resulted highly nonlinear governing equations, and an instability criterion already proposed by the author are employed. A simple negative proportional feedback control is used to actively control the transient response of the plate. Results show that buckling mitigation due to utilizing integrated piezoelectric sensors and actuators is mainly achieved in extremely high gain values. It is also noticed that in many cases, effects of the control voltage on the results may be ignored compared to the temperature-dependency of the material properties and initial geometric imperfections effects. [Copyright &y& Elsevier]

Cutouts are always located in aerospace composite structures to meet specified requirements on the service and functions. The presence of cutout, especially large-sized cutout, would result in a significant stress concentration, and consequently a complicated failure mechanism. This paper presents an experimental and numerical study on the post-buckling damage process of high-performance carbon fiber reinforced polymer (CFRP), T800/X850, multidirectional composite laminated specimen. The simply supported specimen is with a central large-sized elliptical cutout and subjected to shearing load. In the numerical analysis, a damage model incorporating both advanced strain softening schemes and cross-coupling effect between the failure mechanisms is constructed for the damage simulation. Regularizations are implemented for coupling the damage variables to address the deficiencies of the existing model and access the real physical damage behavior of laminated composites. The strain invariant failure theory is employed for evaluation of delamination. To assess the objectivity of the present numerical model, the numerical predictions are compared with experimental data. The predicted damage and propagation patterns show good agreement with experiment results. [ABSTRACT FROM AUTHOR]