Special Issue on Stability of Composite Structures

Buckling of composite members;

Plate buckling;

Buckling and vibration of thin-walled structures;

Shear and large displacement analysis;

Interactive buckling and nonlocal mechanics;

Shear effects for in-plane and out-of-plane analyses;

Inelastic buckling;

Anisotropic effects, microstructured materials, and stability problems;

Buckling of sandwich structures;

Stability of partially composite members and delamination effects;

Postbuckling; and

Dynamic buckling.

In “Local Buckling Analysis of Restrained Orthotropic Plates under Generic In-Plane Loading,” Qiao et al. investigated analytically and numerically the local buckling of composite orthotropic plates under generic in-plane loading and with rotationally restrained boundary conditions. They used both semianalytical and finite-element method (FEM) numerical approaches to characterize the stability behavior of laminated plates or panels of fiber-reinforced plastic structural shapes. The approximated semianalytical solution is obtained from the variationally based Rayleigh-Ritz method, and it is successively compared with available results published in the literature.

In “Modeling of Interactive Buckling in Sandwich Struts with Functionally Graded Cores,” Yiatros et al. studied the interactive buckling in sandwich struts with functionally graded cores. The postbuckling behavior is analyzed for this sandwich column composed of two Euler-Bernoulli extensible columns connected with a shear functionally graded core. Linearized and nonlinear analyses are presented for this nonlinear elastic structural problem, and the possibility of capturing secondary bifurcations for such nonlinear systems is numerically shown. This nonlinear model is compared successively to some FEM results based on two-dimensional analyses for the core behavior.

In “Buckling Loads of Two-Layer Composite Columns with Interlayer Slip and Stochastic Material Properties,” Schnabl et al. presented an efficient stochastic buckling model for studying the structural reliability of layered composite columns with interlayer slip between the layers and random material and loading parameters. The deterministic model is composed of two connected elastic columns with the shear effect neglected for each column. The nonderterministic approach is based on the exact buckling model, response surface method, and Monte Carlo simulations. The probability of failure for this stochastic buckling problem is computed, and it is shown to be very sensitive to loading and material distribution parameters.

In “Effect of Fiber Orientation on Buckling and First-Ply Failures of Cylindrical Shear-Deformable Laminates,” Cagdas and Adali investigated the effect of fiber orientation on buckling and first-ply failures of cylindrical shear-deformable laminates using an 8-node shell finite element (FE). The best ply angle is optimized for each stacking sequence to maximize the failure load. They identified that the rotational restraints at the curved edges have a pronounced effect on the failure load.

In “Thermal Postbuckling of Shear Deformable FGM Cylindrical Shells Surrounded by an Elastic Medium,” Shen incorporated the additional effect of an elastic medium on the thermal postbuckling of shear deformable functionally graded material (FGM) cylindrical shells. The surrounding elastic medium is modeled as a Pasternak foundation. The nonlinear governing equations are solved using a singular perturbation technique. The numerical results show that in some cases the FGM cylindrical shell with an intermediate volume fraction index does not have an intermediate buckling temperature and thermal postbuckling strength. In the case of heat conduction, the nonlinear equilibrium path for geometrically perfect FGM shells with simply supported boundary conditions is no longer of the bifurcation type.

In “Generalized Beam Theory to Analyze the Vibration of Open-Section Thin-Walled Composite Members,” Silvestre and Camotim extended a generalized beam theory (GBT) formulation to analyze the vibration of open-section thin-walled composite members. The effects of cross-section in-plane deformation, geometric and material couplings, primary and secondary warping, and rotary inertia are accounted for in the formulation. As an example, the local and global vibrations of lipped channel members are analyzed to illustrate the capabilities of the GBT-based methods for thin-walled composite structures.

In “Shear Deformable Generalized Beam Theory for the Analysis of Thin-Walled Composite Members,” Silvestre and Camotim also included the first-order shear deformation effect in the GBT formulation for both the shear deformation and buckling analysis of thin-walled composite members. They aimed to present a unified GBT formulation to account for all the specific behaviors associated with shear deformation. The lipped channel columns were used as examples to illustrate the shear deformation effects obtained by the improved and unified GBT.

In “Nonlinear Constitutive Model for Axisymmetric Bending of Annular Graphene-Like Nanoplate with Gradient Elasticity Enhancement Effects,” Yu and Lim developed a gradient elasticity approach to capture some small-scale effects for the axisymmetric bending of annular graphemelike nanoplates. After introducing a strain gradient–based internal energy, the Ritz approximation method is used based on a power series solution and a linear algebra problem is then solved. It is shown that the gradient elasticity approach leads to the stiffening phenomenon as a result of the small-scale parameters; i.e., the small length scale parameters tend to decrease the bending deflection of the nanoplate.

In “Out-of-Plane Buckling of Microstructured Beams: Gradient Elasticity Approach,” Challamel and Ameur analyzed the out-of-plane behavior of a small-scale or microstructured beam within the gradient elasticity theory. The lateral-torsional buckling of the gradient elasticity beam under a uniform bending moment is analytically investigated. Some analytical solutions are provided, including the eventual prebuckling effects. Some energy arguments are also presented for the higher-order out-of-plane boundary conditions. The stiffening property of the gradient elasticity approach is confirmed for such a simple structural case. It is also shown that the warping phenomenon can be typically cast in the framework of gradient elasticity for usual engineering practices.

In “Lateral-Torsional Buckling of Partially Composite Horizontally Layered or Sandwich-Type Beams under Uniform Moment,” Challamel and Girhammar developed a three-dimensional (3D) beam theory that accounts for the possible planar interlayer slip, with possible applications in the field of horizontally layered or sandwich-type beams. The lateral-torsional buckling of this partially composite beam under uniform moment is analytically and numerically investigated. It is shown that the theoretical buckling problem has to be solved from a system of linear differential equations with nonuniform coefficients. The Rayleigh-Ritz approach is used to derive a simple engineering formula, and it appears to be quite efficient with respect to the exact numerical results obtained from the resolution of the direct differential equations.

In “Buckling Behavior of Sinusoidal Web for Composite Wood I-Joist with Elastically Restrained Loaded Edges under Compression,” Chen et al. conducted some analytical, numerical, and experimental analyses of the buckling behavior of a sinusoidal web for a composite wood I-joist with elastically restrained loaded edges under compression. Wood I-joists are efficient and lightweight structural members that are well suited for long-span floor and rafter applications. The structural problem can be described as the buckling of a sinusoidal shell with two rotationally restrained loaded edges in compression. The analytical approach is based on the Rayleigh-Ritz method with polynomial approximation functions. Some FE results are performed to validate the analytical method. Compression tests show the increase of the buckling capacities for the sinusoidal web when compared to a flat web.

In “Comparison of Variational, Differential Quadrature, and Approximate Closed-Form Solution Methods for Buckling of Highly Flexurally Anisotropic Laminates,” Wu et al. compared the efficiency of variationally based methods, differential quadrature methods, and other numerical methods for buckling of highly flexurally anisotropic laminates. Such strong anisotropic plates are difficult to analyze because of localized gradients in the mode shapes. The interest of using Lagrange multipliers in the Rayleigh-Ritz method is shown, especially for extreme anisotropic cases. The differential quadrature method as well as the Hellinger-Reissner variational principle is presented for such a problem. The advantages of each method are discussed. All methods are compared with numerical FE analysis results. In addition, a simple closed-form solution is given for the case of a flexurally anisotropic laminate plate with three sides simply supported and one long edge free.

In “Analytical Solution for Initial Postbuckling Deformation of the Sandwich Beams Including Transverse Shear,” Yu et al. developed some new analytical methods for the characterization of the initial postbuckling behavior of sandwich columns including transverse shear behavior. This problem can be considered as the Haringx elastica for the specific shear modeling. The clamped-clamped boundary condition is treated as an example of the approximated method. By coupling MacLaurin series expansion and orthogonal Chebyshev polynomials, the sinusoidal nonlinearity of the exact shear beam equations is approximated by a cubic nonlinearity. Analytical approximations are established by combining the method of Newton linearization with the method of harmonic balance. The approximation method is shown to be more efficient than other usual asymptotic methods already available for this engineering problem for small or even large rotation angles.

In “Buckling of Generic Higher-Order Shear Beam/Columns with Elastic Connections: Local and Nonlocal Formulation,” Challamel et al. studied the buckling of generic higher-order shear beams/columns with elastic connections in a unified and variationally consistent framework. It is shown that most higher-order shear beam models available in the literature can be classified as gradient elasticity Timoshenko models. The concept of a generalized connection for this higher-order shear beam problem is developed. Analytical solutions are presented for the generalized elastically connected columns. The validity of the engineering formula is also discussed for such kinds of boundary conditions. The buckling equations are finally extended to include the Eringen-based nonlocal elasticity constitutive law to account for small-scale effects. Variational arguments and a simple engineering formula are also given for the nonlocal case.

In “Buckling of Stiffened Antisymmetric Laminated Plates,” Sun and Harik analytically and numerically investigated the buckling of stiffened antisymmetric thin cross-ply and angle-ply laminated plates with bending-extension coupling using the finite strip method. It is shown that the associated system of three equations of equilibrium can be reduced to a single eight-order partial differential equation of the displacement function. This equation is then solved analytically using Ferrari’s method, and the in-plane buckling load can be calculated in a semianalytical format. The effect of various parameters including the plate aspect ratio, plate material orthotropy ratio, and bending-extensional coupling are extensively discussed. Finally, some numerical FE analyses are performed for such a problem, and the semianalytical results are compared very well with the FE modeling.

In “Buckling of Asymmetrically Delaminated Three-Dimensional Twisted Composite Beam: Exact Solution,” Kroflič et al. analytically studied the buckling of asymmetrically delaminated 3D twisted composite columns. The extensional and shear effects are rigorously included in the delaminated columns. The system of homogeneous linearized differential equations with nonconstant coefficients is solved with a power series method with the help of the theory of analytic differential systems. A parametric study is presented, in which the effects of slenderness, the length of delamination, the asymmetry position of the delamination area, and the transverse shear effect on the buckling load are investigated.

In “Free Vibrations and Stability of a New Slender System Subjected to a Conservative or Nonconservative Load,” Tomski and Uzny studied the free vibrations and stability of a new theoretical slender system subjected to a conservative or nonconservative load. The elastic column is loaded by nonconservative follower forces of the Beck type, coupled with a conservative loading system. The specific feature of the loading system is the introduction of a rotational spring between the connected rigid elements at the column extremity. The critical loads, both divergence and flutter loads, the regions of divergence and flutter instabilities, and the characteristic curves in the plane load-natural frequency are determined for this undamped structural problem. Numerical computations are performed for various values of the loading parameter.