Free vibration of composite rectangular plates with rectangular cutouts

A simple numerical method based on the Rayleigh principle is presented for predicting the natural frequencies of composite rectangular plates which exhibit special and general orthotropy. The method is illustrated for simply-supported rectangular plates having central rectangular cutouts and double square cutouts. The results are compared with the reported finite element and analytical results.     

Collapse analysis of composite cylindrical panels with small cutouts

A finite element study was conducted to determine the effects of notches on the load bearing capability and radial displacements of axially loaded composite cylindrical panels. The panel considered assumed that eight symmetrically placed graphite/epoxy plies were used. A mesh refinement in the vicinity of the cutout was conducted in order to study the non-linear collapse analysis. In addition, the effect of different size cutouts with aspect ratios (axial dimension of cutout divided by circumferential dimension) of 2·0 and 0·5 was studied. The findings indicated that as the surface area of the cutout increased, the buckling load decreased. Cutouts with aspect ratios of 2·0 appeared to be capable of carrying higher loads than notches with an aspect ratio of 0·5.     

Finite element dynamic stability analysis of laminated composite skew plates containing cutouts based on HSDT

The finite element dynamic stability analysis of laminated composite skew structures subjected to in-plane pulsating forces is carried out based on the higher-order shear deformation theory (HSDT). The two boundaries of the instability regions are determined using the method proposed by Bolotin. The numerical results obtained for square and skew plates with or without central cutout are in good agreement with those reported by other investigators. The new results for laminated skew plate structures containing cutout in this study mainly show the effect of the interactions between the skew angle and other various parameters, for example, cutout size, the fiber angle of layer and thickness-to-length ratio. The effect of the magnitude of the periodic in-plane load on the dynamic instability index is also investigated.     

Thermomechanical postbuckling of multilayered composite panels with cutouts

The results of a study of the detailed thermomechanical postbuckling response characteristics of flat unstiffened composite panels with central circular cutouts are presented. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. The postbuckling displacements, transverse shear stresses, transverse shear strain energy density, and their sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the post-buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical postbuckling response and its sensitivity to changes in panel parameters.     

Tailoring for strength of composite steered-fibre panels with cutouts

A large number of composite parts include cutouts to accommodate windows, doors, and bolted joints. These regions are hot-spots in terms of design because they concentrate stresses, hence becoming critical in terms of the structural integrity of the part.A traditional approach to the problem of stress concentrations around cutouts is to locally increase the laminate thickness in order to improve the strength margins. Often this practice attracts more loads to the cutout besides increasing part weight. A more effective solution is to tailor the panel in-plane stiffness by means of fibre-steered laminates, and avoid the stress concentrations altogether.The present research demonstrates that it is possible to design and manufacture composite panels whose buckling and first-ply failure responses are insensitive to the existence of a central hole. Moreover, it is shown that the structural performance of these designs more than doubles that of straight-fibre configurations.     

Eigen analysis of fiber-reinforced composite plates

Composites plates of various orientation and thickness with fiber-reinforced plastics (FRP) find increasing applications in aerospace and automotive structures (due to their high strength, stiffness to weight ratios, and high damping characteristics). Determination of the dynamic characteristics and the investigation of such structures are essential not only in the design but also in manufacture development.

In the present paper, the eigen analysis of laminated square plates with various fiber orientations, various boundary fixations, and different stacking sequences has been presented and discussed. The experimental analysis and finite element techniques are utilized to study the effect of fiber orientation and boundary conditions on the dynamic characteristics of frequency and mode shapes. The vibrational system technique is utilized for experimental measurements. The results show agreement between experimental and theoretical investigations. Also, these results show a close connection between damping and stiffness characteristics in glass-fiber composites.     

Stress analysis of perforated composite plates

Thin-walled plates and panels of various constructions find wide use as primary structural elements in simple and complex configuration. In aerospace structures, panels with variously shaped cutout are often used. The understanding of the effects of cutout on the load bearing capacity and stress concentration of such plates is very important in designing of complex structures. An analytical investigation is used to study the stress analysis of plates with different central cutout. Particular emphasis is placed on flat square plates subjected to a uni-axial tension load. The results based on analytical solution are compared with the results obtained using finite element methods. The main objective of this study is to demonstrate the accuracy and simplicity of presented analytical solution for stress analysis of composite plates with central cutout. The effect of cutout geometry (circular, square, or special cutouts), material properties (isotropic and orthotropic), fiber angles, and cutout curvature are considered. The results presented herein, indicated that the presented method can be used to determine accurately the stresses and stress concentration in composite plates with special shape cutouts.     

Aerothermoelastic analysis of composite laminated plates

The flutter behavior of a thermally buckled composite laminated plate is investigated in the frequency and time domains using the finite element method. Von Karman large deformation assumptions and quasi-steady aerodynamic theory are employed for the analysis. The effects of temperature gradient, panel length-to-width ratio, fiber orientation, and stacking sequence on aerothermoelastic behavior of the plate are studied in detail. The flutter boundary, buckling boundary, time history response, and phase plane plots of cross-ply and angle-ply laminates are presented. The numerical results show that temperature gradient induces thermal moments and increases the overall stiffness of the plate, and thus may increase the flutter boundary significantly. When the buckle pattern of the plate changes, the eigenvalues of the natural modes are changed suddenly and the sequence of the natural modes may be altered. Therefore, the change in the buckle pattern postpones the coalescence and the flutter boundary may increase. The change in the coalescence pair may also postpone the coalescence and increase the flutter boundary.     

Hygrothermal analysis of woven-fabric composite plates

The elastic properties of glass/epoxy woven-fabric composites under hygrothermal loading were predicted by using three analytical models originally developed for the prediction of room-temperature elastic properties of woven-fabric composites. In this analysis, the dry and wet bulk resin properties tested at similar temperatures as the composites were used to predict the overall elastic properties of glass/epoxy plates. It is assumed that the fibres are not affected by both temperature and moisture. It was found that the predicted elastic properties of both satinweave and unidirectional fabric composites are in good agreement with experimental values.     

Finite element vibration analysis of composite skew laminates containing delaminations around quadrilateral cutouts

The free vibration analysis of laminated composite skew plates with delamination around a centrally located quadrilateral cutout is carried out based on the high-order shear deformation theory (HSDT) in this study. In the finite element formulation for the delamination around cutout, the seven degrees-of-freedom per each node are used with transformations in order to fit the displacement continuity conditions at the delamination region. The numerical results obtained for the rectangular plates are in good agreement with those of other preceding investigations. The new results for skew plates in this study mainly show the effect of the interactions between the skew angle and other various parameters, for example, cutout size, delamination area, and length-to-thickness ratio. Key observation points are discussed and a brief design guideline is given.     

A meshless local radial point collocation method for free vibration analysis of laminated composite plates

In this paper, a meshless local radial point collocation method based on multiquadric radial basis function is proposed to analyze the free vibration of laminated composite plates. This method approximates the governing equations based on first-order shear deformation theory using the nodes in the support domain of any data center. Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, and material properties are computed by present method. The choice of shape parameter, effect of dimensionless sizes of the support domain on accuracy, convergence characteristics are studied by several numerical examples. The results are compared with available published results which demonstrate the accuracy and efficiency of present method.     

Postbuckling strengths of composite laminate with various shaped cutouts under in-plane shear

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.     

Vibration analysis of symmetric laminated composite plates with attached mass

In this study, vibration of symmetrically laminated composite plates with attached mass is studied. The Ritz method with algebraic polynomial displacement field is used. The plates with at least two adjacent free edges are considered in the formulations. The effect of various parameters (number of layers, ratio of attached mass to the plate mass, position of attached mass, fiber orientation) upon the frequencies and mode shapes is investigated. It is found that attachment of a mass has important effects on the vibration characteristics of composite laminated plates.     

Nonlinear static analysis of composite laminated plates with evolving damage

Considering geometric nonlinearity and damage evolution, the static response characteristics of laminated composite plates subjected to uniformly distributed loading are investigated using finite element approach based on the first-order shear deformation theory. The damage evolution is modeled employing generalized macroscopic continuum theory within the framework of irreversible thermodynamics. The governing nonlinear equations are solved using Newton–Raphson iterative technique. The resulting finite element-based continuum damage model enables to predict the progressive damage and failure load. A detailed parametric study is carried out to investigate the influences of damage evolution, boundary conditions, span-to-thickness ratio, and lamination scheme on the static response of laminated plates undergoing moderately large deformation. It is revealed that the in-plane stretching forces owing to geometric nonlinearity significantly influence the failure load, damage, and stress distribution for immovable thin laminates.     

Interlaminar stresses analysis for laminated composite plates based on a local high order lamination theory

To evaluate the interlaminar stresses in composited laminates, a local high order lamination theory is proposed in this paper. The local displacement fields are expanded in terms of high order polynomial series through thickness within each ply. The displacement continuity constraints at the interface between layers are introduced into the potential energy functional by Lagrange multiplier method. Euler-Lagrange's equations and appropriate boundary conditions associated with the modified potential energy functional are derived. An infinite symmetric cross-ply laminate under cylindrical bending is examined to validate the credibility of the present theory.     

Materially nonlinear analysis of laminated composite plates

A materially nonlinear analysis of laminated composite plates is presented. The Reissner-Mindlin type plate theory and a fully three-dimensional elasticity theory of laminated composites are used to analyze the bending of plates under transverse loads. The modified Ramberg-Osgood relationship is used to compute the principal elastic moduli in each lamina. Results are also presented using the modified elastic-plastic criterion of Hill. The results agree well with those available in the literature. Many of the results presented here should serve as references for future investigations.     

Finite volume analysis of laminated composite plates

A numerical procedure for analysis of general laminated plates under transverse load is developed utilizing the Mindlin plate theory, the finite volume discretization, and a segregated solution algorithm. The force and moment balance equations with the laminate constitutive relations are written in the form of a generic transport equation. In order to obtain discrete counterparts of the governing equations, the plate is subdivided into N control volumes by a Cartesian numerical mesh. As a result, five sets of N linear equations with N unknowns are obtained and solved using the conjugate gradient method with preconditioning. For the method validation, a number of test cases are designed to cover thick and thin laminated plates with aspect ratio (width to thickness) from 4 to 100. Simply supported orthotropic, symmetric cross‐ply, and angle‐ply laminated plates under uniform and sinusoidal pressure loads are solved, and results are compared with available analytical solutions. The shear correction factor of 5/6 is utilized throughout the procedure, which is consistent with test cases used in the reviewed literature. Comparisons of the finite volume method results for maximum deflections at the center of the plate and the Navier solutions obtained for aspect ratios 10, 20, and 100 shows a very good agreement. Copyright © 2016 John Wiley & Sons, Ltd.     

Thermal postbuckling analysis of laminated composite plates

The thermal postbuckling behavior of graphite/epoxy multi-layered rectangular plates of various boundary conditions is studied using the finite element method. Temperature dependent thermal and elastic properties of the material are used in the analysis. The nonlinear finite element equations are solved as a sequence of linear eigenvalue problems to trace the thermal postbuckling paths of 15-layered symmetric angle-ply plates. The presence of secondary instability with an unsymmetric deformation mode has been identified for symmetric laminates under uniform temperature rise. In the case of linearly varying temperature rise through the thickness of the plate, the nonlinear equilibrium equations are solved by the modified Newton–Raphson technique to get the temperature-displacement curves.     

Progressive failure analysis for advanced grid stiffened composite plates/shells

A progressive failure methodology is developed to simulate the initiation and propagation of multi-failure modes for advanced grid stiffened (AGS) composite plates/shells on the basis of a stiffened element model. Failures of both skin and ribs are taken into consideration, which are matrix cracking, fiber failure, fiber–matrix shear failure, delamination in skin and fiber failure in rib. All these failures are defined using a set of 2-D stress-based polynomial failure criteria wherein the transverse shear stresses at centroid of the stiffened element are calculated by employing an integrated approach of finite element and finite difference method. Corresponding material and stiffness degradation behavior is introduced after the initiation of individual failure mechanisms. The progressive failure behavior of a composite orthotropic-grid curved panel with a centrally located cutout under compressive load is evaluated using the method.     

Finite element analysis of laminated composite plates

A finite element analysis technique for an arbitrarily laminated anisotropic plate is described. A superparametric quadratic plate element with five degrees-of-freedom per node is used in the analysis. A stress-strain relation is derived from a three-dimensional approach to the problem. The volume integration of the stiffness matrix is evaluated by numerical integration using the Gauss quadrature formula with 2 × 2 × 2 sampling points. A variety of laminated plate problems is solved and the results are compared with the exact solutions, which demonstrate the validity of the method.