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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 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]

Buckling loads of laminated panels calculated by analytical approaches are usually based on the assumptions that the panels are subjected to uniform in-plane edge loads without cutouts, despite of the fact that real structural components are subjected to various kinds of non-uniform in-plane edge loads along with different sized cutouts. The main objective of this paper is to study the effects of reinforced/unreinforced circular cutouts and non-uniform in-plane edge loads on the buckling behavior of composite panels with different ply-orientations by the finite element technique. Furthermore, it addresses the effects of different boundary conditions and thickness of panels. To carry out the analyses, a nine-noded heterosis plate element and a compatible three-noded beam element are developed, including the effect of shear deformation and rotary inertia for both the plate and the stiffeners. In structural modeling, the plate and the stiffener elements are treated separately, with their displacement compatibility maintained using transformation matrices. It has been illustrated in this study that presence of larger-sized reinforced cutouts predominantly increases the buckling strength of the panel as compared to those with smaller sized cutouts. [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]

This work presents a study of the behavior, performance and failure of thinwalled composite channel section columns. The study is carried-out using nonlinear finite element models of laminated columns, including geometric imperfections and material failure, as well as approximate analytical solutions based on the Classical Lamination Theory. The accuracy of the numerical model is assessed using experimental results available in the literature and very good results were obtained. The results show the influence of the column layup and wall thickness on the structural behavior of laminated columns, including the buckling mode and ultimate failure load. Finally, the numerical model is used to assess the accuracy of approximate closed-form expressions for evaluation of the local buckling loads of composite channel section columns. [ABSTRACT FROM AUTHOR]

In the present work, an innovative approach is developed and employed to investigate the buckling load of composite laminated plates using polar representation of the fourth-order flexural stiffness tensor. Based on the Rayleigh-Ritz method for calculating the buckling load of orthotropic uncoupled laminates, a new approach is proposed for calculating the critical buckling load as a function of fiber orientation and the number of layers. A new formula is also represented for measuring the possible numbers of buckling modes based on the length-to-width ratio of the plate. Moreover, the new methods make it easy to handle buckling problems, optimization and design of laminated plates subjected to in-plane loads. The efficiency and precision of this method are proved by numerical examples. The anisotropic parts of the buckling load are calculated, and their polar variations are investigated. [ABSTRACT FROM AUTHOR]

A numerical study is carried out using finite element method, to examine the effects of square and rectangular cutout on the buckling behavior of a sixteen ply quasi-isotropic graphite/epoxy symmetrically laminated rectangular composite plate [0°/+45°/-45°/90°] subjected to various linearly varying in-plane compressive loads. Further, this paper addresses the effects of size of square/rectangular cutout, orientation of square/rectangular cutout, plate aspect ratio(a/b), plate length/thickness ratio(a/t), boundary conditions on the buckling bahaviour of symmetrically laminated rectangular composite plates subjected to various linearly varying in-plane compressive loading. It is observed that the various linearly varying in-plane loads and boundary conditions have a substantial influence on buckling strength of rectangular composite plate with square/rectangular cutout. [ABSTRACT FROM AUTHOR]

This work presents a metamodel strategy to approximate the buckling load response of laminated composite plates. In order to obtain representative data for training the metamodel, some laminates with different stacking sequences are generated using the Latin hypercube sampling plan. These stacking sequences are converted into lamination parameters so that the number of inputs of the metamodel becomes constant. The buckling load for each laminate of the training set are computed using finite elements. In this way the inputs-outputs metamodel training pairs are the lamination parameters and the corresponding bucking load. Neural network and support vector regression metamodels are employed to approximate the buckling load. The performances of the metamodels are compared in a test case and the results are shown and discussed. [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]

In this study, a buckling analysis was performed on square plates made of composite material with and without elliptical notch using the finite element method. The boron/epoxy laminated plates were asymmetrically orderly arranged into the following way [(θ/−θ)]. The resistance to buckling of the laminated plates subjected to mono-axial compression is highlighted according to the fiber orientations, the degree of anisotropy, size and the orientation of the notch. Results show that the minimum buckling load obtained corresponds to the largest ratio a/b =1 (circular notch), while maximum buckling loads correspond to the smallest ratio of the geometric defect a/b. More the size of the geometric defect is important less the buckling load will be. Thus, the amplification factor N ∗ grows with the increase of the ply thickness. When φ =0° and the angle of orientation of fibers is θ =0°, N ∗ is of the order of 5 and doubles when θ =90°. While for φ =90°, the maximum amplification is of the order of 4% for θ =45° corresponding to the minimum value of the first case where φ =0° and θ =0°. [ABSTRACT FROM AUTHOR]

Critical buckling loads of composite laminates are usually calculated using analytical solutions based on the assumption of uniform in-plane loads, despite of the fact that real structures are often subjected to various nonuniform loads. The present work is focused on the buckling behavior of composite laminates, with and without cutouts, subjected to various nonuniform in-plane loads. The effect of the size of the cutouts, on the buckling behavior, has been studied using finite element method. Furthermore, parametric studies on the effects of plate aspect ratio, location of the cutout and the application of a nonuniform load combined with a shear load have also been studied. Higher buckling loads were observed in pure in-plane bending compared to uniformly/nonuniformly distributed loads. Consequently, it is important to consider nonuniformly distributed loading whenever applicable, to utilize complete strength of the composite laminate and to avoid premature failure of the composite laminate due to structural instability. [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]

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]

Buckling and postbuckling behavior of symmetric laminated composite plates with surface mounted and embedded piezoelectric actuators subjected to mechanical, thermal, electrical, and combined loads is studied. Formulation is based on the classical laminated plate theory with von-Karman non-linear kinematic relations. Initial geometrical imperfections are also accounted, and finally applying Galerkin procedure, the resulting equations are solved to obtain closed form expressions for non-linear equilibrium paths. Temperature dependency of thermo-mechanical properties is considered. Three cases of simply supported boundary conditions are investigated. Effects of in-plane compressive loading, temperature dependency and independency of properties, electrical loading, lay-up configuration, and geometric imperfection are discussed. Results for various states are verified with the known data in the literature. [ABSTRACT FROM AUTHOR]

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]

The conventional approach to analysis the buckling of rectangular laminates containing an embedded delamination subjected to the in-plane loading is to simplify the laminate as a beam-plate from which the predicted buckling load decreases as the length of the laminate increases. Two-dimensional analyses are employed in this paper by extending the one-dimensional model to take into consideration of the influence of the delamination width on the buckling performance of the laminates. The laminate is simply supported containing a through width delamination. A new parameter β defined as the ratio of delamination length to delamination width is introduced with an emphasis on the influence of the delamination size. It is found that (i) when the ratio β is greater than one snap-through buckling prevails, the buckling load is determined by the delamination size and depth only; (ii) as the ratio β continues to increase, the buckling load will approach to a constant value. Solutions are verified with the well established results and are found in good agreement with the latter. [ABSTRACT FROM AUTHOR]

Abstract: A closed-form solution is obtained to determine the buckling and post-buckling behavior of elastically restrained composite panels under compressive loading. The approach allows to study the response of stiffened panels undergoing local buckling modes, taking into account the restraints provided by the stiffeners to the rotation of the skin edges. The panels are modeled as thin plates referring to Marguerre type equations together with classical lamination theory. The equations are written in non-dimensional form, allowing for the study of a wide class of orthotropic laminates. The problem is formulated in terms of out of plane displacement, represented with a single-mode approximation, and Airy stress function. The compatibility equation is solved exactly, while the method of Galerkin is applied to impose the equilibrium. The buckling load, the out of plane displacement at different load levels, and the post-buckling stiffness are derived and compared with finite element analyses, revealing good accuracy. Sensitivity analyses are also performed obtaining design charts. [Copyright &y& Elsevier]

In this study, the influence of nonuniformity of eccentricity of stringers on the general axial buckling load of stiffened laminated cylindrical shells with simply supported end conditions is investigated. The critical loads are calculated using Love's First-order Shear Deformation Theory and solved using the Rayleigh-Ritz procedure. The effects of the shell length-to-radius ratio, shell thickness-to-radius ratio, number of stringers, and stringers depth-to-width ratio on the buckling load of nonuniformly eccentric shells, are examined. The research demonstrates that an appropriate nonuniform distribution of eccentricity of stringers leads the buckling load to increase significantly. [ABSTRACT FROM AUTHOR]

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: Buckling analysis of symmetrically laminated rectangular plates with parabolic distributed in-plane compressive loadings along two opposite edges is performed using the Rayleigh–Ritz method. Classical laminated plate theory is adopted. Stress functions satisfying all stress boundary conditions are constructed based on the Chebyshev polynomials. Displacement functions for buckling analysis are constructed by Chebyshev polynomials multiplying with functions that satisfy either simply supported or clamped boundary condition along four edges. Methodology and procedures are worked out in detail. Buckling loads for symmetrically laminated plates with four combinations of boundary conditions are obtained. The proposed method is verified by comparing results to data obtained by the differential quadrature method (DQM) and the finite element method (FEM). Numerical example also shows that the double sine series displacement for simply supported symmetrically laminated plates having bending–twisting coupling may overestimate the stiffness, thus providing higher buckling loads. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with the theoretical prediction of buckling loads for symmetric angle-ply and cross-ply laminated flat composite columns, consisting of two portions of different widths connected by fillets. The buckling loads of the column under axial compression were obtained for the following end conditions: simply supported, simply-clamped, clamped-clamped, and clamped free. Based on the first order shear deformation theory (FSDT), finite elements method (FEM) with FORTRAN computer language was exploited to obtain the critical buckling loads. The effects of orientation angles, fillet radius, column thickness and wideness, and modulus ratios on the buckling load were investigated. The results were presented in both graphical and tabular forms. [ABSTRACT FROM AUTHOR]

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]

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]

As a first attempt, finite element (FE), genetic algorithm (GA) and particle swarm optimization (PSO) methods are mixed to maximize buckling load of stiffened laminated composite plate via finding optimum fibers orientation of the plate. The FE method is used to solve the higher-order shear deformation based equations of the plate. To improve the performance of genetic algorithms for solving the problem, the particle swarm optimization technique is added as an operator of the GA. Accuracy, convergence and applicability of the proposed approach are shown. Effects of the dimensions of the plate, the cross section shapes of the stiffener(s), number of layers of the plate and boundary conditions on the optimum results are investigated. [ABSTRACT FROM AUTHOR]

Abstract: The design problem of maximizing the buckling load factor of laminated multi-material composite shell structures is investigated using the so-called Discrete Material Optimization (DMO) approach. The design optimization method is based on ideas from multi-phase topology optimization where the material stiffness is computed as a weighted sum of candidate materials, thus making it possible to solve discrete optimization problems using gradient based techniques and mathematical programming. The potential of the DMO method to solve the combinatorial problem of proper choice of material and fiber orientation simultaneously is illustrated for multilayered plate examples and a simplified shell model of a spar cap of a wind turbine blade. [Copyright &y& Elsevier]

Buckling strength is the most important design criterion for laminated composite structures subjected to compressive loading. The aim of the present work is to introduce an explicit procedure in designing laminated composite plates for maximum buckling load subjected to strength and stiffness constraints using the polar formalism, which relates stiffness to the critical buckling load in order to simplify the calculation and optimization of the buckling load. The polar representation of plane elasticity is effectively used in this work in order to introduce a unified optimization method. Design for maximum flexural stiffness as well as laminate effective elastic modulus was developed in order to achieve the optimal orientation of the layers giving the maximum buckling strength. Three optimization procedures were proposed. The first one is unconstrained optimization and the two other cases are constrained optimization subjected to the flexural stiffness and the elastic modulus constraints. The quasi-homogeneous laminates, which have been used as a special class of laminate stacks, were proposed as the general solution for the optimal stacking sequence of the layers. [ABSTRACT FROM AUTHOR]

This paper proposes a novel numerical optimization procedure with mixed integer and continuous design variables for optimal design of laminated composite plates subjected to buckling loads. In the present optimization problem, the objective function is to maximize the buckling load factor. The design variables are fibre orientation angles and thickness of layers, in which the fibre orientation angles are integer variables and thickness are continuous variables. The constraints include the limitation of variables and the total thickness of the plate. For analyzing the buckling behavior of laminated composite plates, a recently proposed smoothed finite element method named the cell-based smoothed discrete shear gap method (CS-DSG3) is employed. For solving the current optimization problems which contain both integer and continuous variables, an improved different evolution algorithm, named mixed-variable different evolution (mDE) is proposed. In the mDE, the mutation and selection phases of the original DE are replaced by an adaptive mutation mechanism and an elitist selection technique, respectively. These improvements not only help balance effectively the global and local search abilities of the DE, but also help deal with integer and continuous design variables. The reliability and effectiveness of the proposed optimization procedure are investigated through some numerical examples for optimal design of laminated composite plates with 2, 3, 4 and 10 layers subjected to buckling loads. Additionally, the influence of different loading and boundary conditions on the optimal solution is also investigated. [ABSTRACT FROM AUTHOR]

Abstract: Buckling of composite annular plates under uniform internal and external radial edge loads have been investigated using energy method. Trefftez rule is used in the stability equations. The symmetric buckling of symmetric cross-ply laminates is considered. In this paper, buckling behavior for the three laminates (90/0)2s , (90/02/90) s and (902/02) s are studied. Influence of some parameters such as thickness, stacking sequence, type of supports and the ratio of hole to sheet radius on buckling loads and modes are investigated. The results of the energy method are compared with the results of numerical method. Based on the results, in the plates with clamped boundary conditions the symmetric buckling assumption is not accurate, contrary to other boundary conditions. [Copyright &y& Elsevier]

The paper deals with the effect of moisture and temperature on the buckling response of a laminated composite plate subjected to hygrothermomechanical loadings. Mechanical loading consists of uniaxial, biaxial, and shear. The distribution of temperature and moisture on the surface is considered to be uniform. The degradation in material properties due to moisture and temperature is taken into account using a micromechanical model. The mathematical formulation is based on higher order shear deformation theory and von Karman's nonlinear kinematics. A C0 finite-element method based on higher-order shear deformation plate theory is used for deriving the standard Eigenvalue problem. ATaylor series based mean-centered first-order perturbation technique is used to find out the second-order statistics of the hygrothermal buckling loads. The effects of temperature rise, moisture concentration, fiber-volume fraction, and plate parameters on buckling response of the plate are presented. [ABSTRACT FROM AUTHOR]

Abstract: Post-buckling strength and the critical buckling load parameter of laminated composite cylindrical/hyperboloid shell panel subjected to uniform temperature field is investigated in this paper. The mathematical model is developed taking into account the full nonlinearity effect in stiffness matrices in Green–Lagrange sense based on the higher order shear deformation theory. Governing equations are derived by minimizing the total potential energy of the system. The panel is represented with the nonlinear finite element model. The system equations are solved by a direct iterative approach to find out the thermal post-buckling equilibrium path. Influence of different parameters such as lamination scheme, modular ratio, amplitude ratio, thickness ratio, curvature ratio, aspect ratio and various support conditions have been examined in details. The results are compared with those available in literature. [Copyright &y& Elsevier]

The present work uses a finite-element approach to study vibration, buckling, and dynamic instability characteristics in damaged cross-ply and angle-ply curved panels. The panels are subjected to nonuniform, centrally, and edge-distributed follower loading. First order shear-deformation theory was used to model the doubly curved panels and was formulated in accordance with Sanders' first approximation. An anisotropic damage formulation was used to model damage. An analysis was carried out on plate and shallow shells to obtain vibration, buckling, and static instability (i.e., divergence) and dynamic instability (i.e., flutter) behavior. The effects of load type, load width, damage, and damage location on natural frequency, buckling load, divergence load, flutter load and flutter frequency were studied. The effect of curvature to improve the stability characteristics of panels is discussed. The desirable position of damage on a panel is discussed on the basis of different stability behavior. Results indicate that narrow edge loading is undesirable in most cases. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the buckling and vibration analysis of isotropic and laminated plates by a first-order shear deformation theory. The numerical approach is based on collocation with radial basis functions. The model allows the analysis of arbitrary boundary conditions and irregular geometries. It is shown that the present method, based on a first-order shear deformation theory produces highly accurate natural frequencies and modes of vibration, as well as critical loads and modes. [Copyright &y& Elsevier]

This paper presents a unified Lévy-type solution procedure for the buckling analysis of both thin and thick composite plates under biaxial loads. The plates are simply-supported at two opposite edges, while the two remaining sides are subjected to any combination of simply-supported, clamped and free conditions. The problem is formulated in the context of a variable-kinematic approach, offering the advantage of automatically handling theories of various order. Both layerwise and equivalent single layer theories are considered. The governing equilibrium equations are derived analytically from the Principle of Virtual Displacements (PVD), and are solved exactly referring to the Lévy-type procedure. The accuracy of the predictions is demonstrated by comparison with results available in literature, including exact 3D solutions. A comprehensive set of benchmark results is provided for plates subjected to different loading and boundary conditions and characterized by various width-to-thickness ratios. [ABSTRACT FROM AUTHOR]

In the present study, the buckling behaviour of laminated composite skew plates with different boundary conditions subjected to linearly varying in-plane loads are presented. The skew plate is modelled based on higher order shear deformation theory, which accurately predicts the buckling behaviour for the thick plate. The in-plane stress distribution within the skew plate due to linearly varying in-plane load is equal to the applied in-plane edge load in the pre-buckling range. Using these in-plane stress distributions, the total potential energy functional is formulated. Total potential energy is a function of the total strain energy of skew plate and potential energy due to in-plane stress distributions. The total strain energy of skew plate contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total potential energy functionals mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Using a Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total potential energy functional is converted into sets of algebraic equations. Finally, these algebraic equations are rearranged as a linear eigenvalue problem, which is solved to obtain the critical buckling loads. The numerical results are presented for different skew angles, boundary conditions, length to thickness ratios, aspect ratios and in-plane loadings. It is observed that the critical buckling load increase with the increase of skew angle as well as change in the mode shape at a lower aspect ratio with the increase of skew angle. [ABSTRACT FROM AUTHOR]

Abstract: This article presents to study the stability of laminated orthotropic cylindrical and truncated conical shells resting on elastic foundations and subjected to combined loads with the clamped and simply supported boundary conditions. Here, axial tensile loads separately applied to the small and large bases of a laminated truncated conical shell, respectively. The basic relations, the modified Donnell type stability and compatibility equations have been obtained for laminated orthotropic truncated conical shells on the Pasternak type elastic foundation. Applying Galerkin method, the critical combined loads of laminated orthotropic conical shells on the Pasternak type elastic foundation with different boundary conditions are obtained. The appropriate formulas for single-layer and laminated cylindrical shells on the Pasternak type elastic foundation made of orthotropic and isotropic materials are found as special cases. Finally, influences of the boundary conditions, the elastic foundation, the number and ordering of the layers and variations of the shell characteristics on the critical combined loads are investigated. The results are compared with their counterparts in the literature. [Copyright &y& Elsevier]

Abstract: A semi-analytical method is developed for pre-buckling and buckling analyses of thin, symmetrically laminated composite panels with an elliptical cutout at an arbitrary location and orientation under general thermo-mechanical loading conditions. Both the pre-buckling and buckling analyses are based on the principle of stationary potential energy utilizing complex potential functions and complete polynomials. The complex potential functions capture the steep stress gradients and local deformations around the cutout, and the “complete” polynomials improve the global buckling response of the laminate. The complex potential functions in the pre-buckling state automatically satisfy the in-plane equilibrium equations, thus reducing the first variation of the total potential energy in terms of line integrals only. Because the complex potential functions for out-of-plane displacements are augmented by the “complete” polynomials, the area integral terms in the second variation of the total potential energy, referred to as the Treftz criterion, are retained in the buckling analysis. The kinematic boundary conditions are idealized by employing extensional and rotational springs (elastic restraints) with appropriate stiffness values. Based on the numerous validation problems, this analysis is proven credible for predicting the buckling load of rectangular and non-rectangular panels with a cutout. [Copyright &y& Elsevier]

Abstract: Stiffness tailoring of laminated composite structures using steered fibre tows is a design method that maximally uses the directional properties of composite materials. Cylindrical structures usually have circular cross sections while some application, geometric or aerodynamic requirements can necessitate other cross sections, e.g. elliptical. Circumferential tailoring can increase the buckling load of thin cylinders by compensating for non-uniform sectional loading such as bending and/or varying radius of curvature in general cylinders. Here, strength constraints are considered in maximum buckling load design, to ensure that the failure load is greater than the buckling load. A two-step optimisation framework is used to separate the theoretical and manufacturing issues in design. A computationally cheap semi-analytical finite difference method is used to solve the linear static and buckling problems. Conservative failure envelopes based on Tsai-Wu failure criterion are used for strength evaluation. To avoid repetitive analyses, successive convex approximation method is used. For demonstration, circumferential tailoring framework is applied to a circular cylinder under bending and an elliptical cylinder under axial compression. The improvements in buckling capacity of variable over constant stiffness designs are shown and verified using nonlinear buckling analysis in the commercial FEM software Abaqus TM , and the mechanisms of improvements are investigated. [Copyright &y& Elsevier]

Abstract: This paper deals with multiobjective optimization of symmetrically angle-ply square laminated plates subjected to biaxial compressive and uniform thermal loads. The design objective is the maximization of the buckling load for weighted sum of the biaxial compressive and thermal loads. The design variable is the fiber orientations in the layers. The performance index is formulated as the weighted sum of individual objectives in order to obtain optimal solutions of the design problem. The first-order shear deformation theory (FSDT) is used in the mathematical formulation of buckling analysis of laminated plates. The modified feasible direction (MFD) method is used for optimization routine. For this purpose, a program based on FORTRAN is used. Finally, the effect of different weighting factors, number of layers, aspect ratios, load ratios and boundary conditions on the optimal design is investigated. [Copyright &y& Elsevier]

The nonlinear buckling response of laminated composite cylindrical shells reinforced with graphene nanoplatelets (GNPs) is studied in this paper. The functionally graded (FG) shell reinforced by GNPs is analytically studied under external pressure and uniform temperature rise loadings. It is also assumed that the GNP-reinforced laminated composite shell is in contact with an elastic foundation. Various types of profiles are employed for the GNP distribution patterns in the shell thickness including 10 nanocomposite layers. The nonlinear strain-displacement relations of the shallow cylindrical panel are established utilizing the third-order shear deformation shell theory. Governing equilibrium equations of the laminated GNP-reinforced composite shell are formulated employing the principle of virtual displacement. The coupled system of nonlinear differential equations is solved analytically for the hinged–hinged and fixed–fixed boundaries of the shell using a perturbation-based technique. Correctness of presented formulations and obtained solutions is proved by comparisons with results from previous studies for an isotropic cylindrical shell. Novel numerical results reveal that the material properties, geometrical characteristics and load parameters significantly affect on the buckling behavior of laminated composite cylindrical shells. [ABSTRACT FROM AUTHOR]

Abstract: The objective of the present work is to study the effects of flexural boundary conditions on buckling and postbuckling behavior of axially compressed quasi-isotropic laminate, (+45/−45/0/90)2 s with various shaped cutouts (i.e., circular, square, diamond, elliptical–vertical and elliptical–horizontal) of various sizes using the finite element method. The FEM formulation is based on first order shear deformation theory and von Karman’s assumptions are used to incorporate geometric nonlinearity. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. It is observed that the laminates clamped and simply supported on all edges have the highest and lowest buckling and postbuckling strength, respectively, irrespective of cutouts shape and size. It is also noted that a fully clamped laminate with large size elliptical–vertical cutout can take higher compressive buckling load than the laminate without cutout for same boundary condition. [Copyright &y& Elsevier]

Abstract: Optimal design of laminated composite stiffened panels of symmetric and balanced layup with different number of T-shape stiffeners is investigated and presented. The stiffened panels are simply supported and subjected to uniform biaxial compressive load. In the optimization for the maximum buckling load without weight penalty, the panel skin and the stiffened laminate stacking sequence, thickness and the height of the stiffeners are chosen as design variables. The optimization is carried out by applying an ant colony algorithm (ACA) with the ply contiguous constraint taken into account. The finite strip method is employed in the buckling analysis of the stiffened panels. The results shows that the buckling load increases dramatically with the number of stiffeners at first, and then has only a small improvement after the number of stiffeners reaches a certain value. An optimal layup of the skin and stiffener laminate has also been obtained by using the ACA. The methods presented in this paper should be applicable to the design of stiffened composite panels in similar loading conditions. [Copyright &y& Elsevier]

Abstract: This paper reports the result of an investigation into the local buckling for the delimitation of an elliptic shape near the surface of piezoelectric laminated shells, where local delaminated sub-shells may be monolayer and multiplayer, and the geometrical axes of elliptically delaminated sub-shells are inconsistent with the geometrical main axes of piezoelectric laminated base-shells. From example calculations, the effects of the geometrical and physical parameters, stacking models of piezoelectric laminated base-shells, elliptically laminated sub-shells, and coupled electric and thermal loads on the local buckling for elliptically delaminated sub-shells near the surface of piezoelectric laminated base-shells are described and discussed. [Copyright &y& Elsevier]

The aim of this study was to determine how the change of glass laminate fibres to flax fibres will affect the stability of thin-walled angle columns. Numerical analyses were conducted by the finite element method. Short L-shaped columns with different configurations of reinforcing fibres and geometric parameters were tested. The axially compressed structureswere simply supported on both ends. The lowest two bifurcation loads and their corresponding eigenmodes were determined. Several configurations of unidirectional fibre arrangement were tested. Moreover, the influence of a flange width change by ±100% and a column length change by ±33% on the bifurcation load of the compressed structure was determined. It was found that glass laminate could be successfully replaced with a bio-laminate with flax fibres. Similar results were obtained for both materials. For the same configuration of fibre arrangement, the flax laminate showed a lower sensitivity to the change in flange width than the glass material. However, the flax laminate column showed a greater sensitivity to changes in length than the glass laminate one. In a follow-up study, selected configurations will be tested experimentally. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this paper is to study the interaction curves along with buckling and postbuckling responses of a quasi-isotropic laminate with a centrally placed circular cutout of various sizes under uni-axial compression combined with in-plane shear loads (positive and negative). The present study is carried out using finite element method. The finite element formulation is based on the first order shear deformation theory and von Karman’s assumptions to incorporate geometric nonlinearity. The resulting nonlinear algebraic equations are solved by Newton–Raphson method. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. It is observed that pure compression- buckling, -first-ply failure and -ultimate failure strengths of the quasi-isotropic laminate with and without circular cutout decreases with increasing accompanying shear load. In addition, it is also noted that for a given uni-axial compression load, a quasi-isotropic laminate with and without a cutout can sustain higher negative shear load in comparison to the positive shear load. [Copyright &y& Elsevier]

Abstract: The aim of present investigation is to study the buckling and postbuckling response and strengths under positive and negative in-plane shear loads of simply-supported composite laminate with various shaped cutouts (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) of various sizes using finite-element method. The FEM formulation is based on the first order shear deformation theory which incorporates geometric nonlinearity using von Karman’s assumptions. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. The effect of cutout shape, size and direction of shear load on buckling and postbuckling responses, failure loads and failure characteristics of quasi-isotropic [i.e., (+45/−45/0/90)2s] laminate has been discussed. In addition, the effect of composite lay-up [i.e., (+45/−45/0/90)2s, (45/−45)4s and (0/90)4s] has also been reported. It is observed that the cutout shape has considerable effect on the buckling and postbucking behaviour of the quasi-isotropic laminate with large size cutout. It is also observed that the direction of shear load and composite lay-up have substantial influence on strength and failure characteristics of the laminate. [Copyright &y& Elsevier]

The critical loads for a layered material compressed by a surface load are determined numerically using the three-dimensional linearized theory of stability and the piecewise-homogeneous material model. Symmetry conditions on the lateral sides of a layered composite sample are assumed. It is shown that internal loss of stability in the layered composite is microbuckling near the loaded surface manifested as end crushing. The buckling modes decay with distance from the end. The effect of the inhomogeneity of the initial state induced by the load on the buckling modes is studied. The inhomogeneity of the initial state has a strong effect on the amplitudes of the buckling modes and the area of their localization [ABSTRACT FROM AUTHOR]

This paper studies a closed-form solution for the nonlinear postbuckling behavior of long unsymmetrical rotationally-restrained laminated composite plates subjected to shear load. The analysis method described can be applied to the postbuckling behavior of stiffened plates under limitations of the local buckling mode, in which the portion of panel with two stiffeners is modeled as a thin plate with two edges restrained with torsion springs. Nondimensional parameters are introduced in order to cover a wide class of material properties and laminate configurations. An appropriate mode shape function is proposed for the postbuckling process, under the assumption that the buckling mode remains unchanged as the deflection increases. Substituting the shape function into the governing equations, an precise closed-form solution for the load–deflection relationship is derived using the Galerkin method. To conclude, stiffened composite plates with representative unsymmetrical laminate configurations are used as analytical models for a comparison of the closed-form solution. The finite element simulation demonstrates the closed-form solution’s ability to predict postbuckling behavior with high computational efficiency. [ABSTRACT FROM AUTHOR]