Post-buckling behavior of composite laminated plates under end shortening and pressure loading, using two versions of finite strip method

Two different versions of finite strip method, namely spline and semi-analytical methods, are developed for analyzing the geometrically non-linear response of rectangular composite laminated plates of arbitrary lay-up to progressive end-shortening in their plane and to pressure loading. The plates are assumed to be thin so that the analysis can be carried out based on the classical plate theory. The in-plane lateral deflection υ is allowed at the loaded ends of the plate, whilst the lateral expansion of the unloaded edges is either free or completely prevented. Geometric non-linearity is introduced in the strain–displacement equations in the manner of the von Karman assumptions. The formulations of the finite strip methods are based on the concept of the principle of the minimum potential energy. A number of applications involving isotropic plates, symmetric and unsymmetric cross-ply laminates are described to investigate the effects of pressure loading. The comparison between the two sets of results obtained by different finite strip methods is very good. The study of the results revealed that the response of the laminates is significantly influenced by the application of the normal pressure loading. Particularly, the response of unsymmetric laminates is strongly affected by the sign of the normal pressure loading.     

Finite strip analysis of imperfect laminated plates under end shortening and normal pressure

The finite strip method is developed to predict the geometrically non-linear response of rectangular laminated plates subjected to progressive end shortening whilst initial imperfection and/or applied pressure loading are also present. The development is an extension of earlier work concerned with perfect, unpressurized laminates which have simply supported loaded ends at which lateral in-plane expansion is either allowed freely or is prevented completely. The analysis is conducted in the contexts of classical plate theory and first-order shear deformation plate theory, in turn. A number of applications involving both isotropic plates and laminated plates is described.     

Geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates

This research present the development of geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates. First-order, shear-deformable laminate composite plate theory is utilized in deriving the governing equations using a variational formulation. Geometric nonlinearity is accounted for in Von-Karman sense. A family of NURBS elements are constructed from refinement processes and validated using various examples. k-refined NURBS elements are developed to study thin plates. Isotropic, orthotropic and laminated composite plates are studied for various boundary conditions, length to thickness ratios and ply-angles. Computed center deflection is found to be in an excellent agreement with the literature. For thin plate analysis, linear and k-refined quadratic NURBS element is found to remedy the shear locking problem. k-refined quadratic NURBS element provide stabilized response to distorted, coarse meshes without increasing the order of the polynomial, owing to the increased smoothness of solution space.     

Vibration analysis of laminated composite plates: TV-holography and finite element method

An experimental and numerical investigation into the structural behaviour of symmetrically laminated carbon fibre-epoxy composite rectangular plates subjected to vibration. The laminated composite plates are composed on layers of Grafil XAS carbon fibres preimpregnated in 914C Fibredux epoxy resin and each plate was vibrated by a piezoelectric transducer (PZT) attached onto its surface. The specimens tested were of two different length to width ratios and of symmetric stacking sequence. In this study the short edges of the plate were of various combinations of clamp and free support conditions, and the long edges of the plate were of various combinations of free and simple support conditions. Experimental and finite element studies were carried out in parallel. The experimental vibrational response of the test plates were obtained using a TV-holography technique. The comparison between experimental results and finite element results are reasonably good in all the cases studied.     

Load increment procedure for post‐buckling analysis of laminated plates under in‐plane loads by finite strip method

A load increment procedure has been presented to integrate with the finite strip method for the post‐buckling analysis of laminated plates when subjected to uniform end shortening. In‐plane loads are introduced to reflect the end shortening effect. The Newton–Raphson procedure is implemented to attend a solution that satisfies the equilibrium condition and at the same time meets the loading requirements. Error associated with loading condition is minimised by adjusting the load factor to preserve the rate of convergence. The enhanced capability can be easily incorporated into the context of both classical and shear deformation plate theories. A range of application has been described. Convergence test and numerical results are presented for isotropic plate and laminates with general lay‐up arrangement. Copyright © 2000 John Wiley & Sons, Ltd.     

Stochastic nonlinear failure analysis of laminated composite plates under compressive transverse loading

This paper present the second ordered statistics of first-ply failure response of laminated composite plate with random material properties under random loading. The basic formulation is based on higher order shear deformation plate theory (HSDT) with the geometrically nonlinearity in the von-Karman. The direct iterative based C⁰ nonlinear finite element method combined with mean centered first order perturbation technique developed by the authors are extended and successfully applied nonlinearity for failure problem with a reasonable accuracy to predict the second order statistics (standard deviation) of first-ply failure response using Tsai-Wu and Hoffman failure criterion with macroscopic analysis. Typical numerical results for various combinations of boundary conditions, plate thickness ratios, aspect ratios, laminates scheme and layers, elastic modulus ratios have been presented to illustrate the application of developed procedure. Some new results are presented and examined which clearly demonstrated the importance of the randomness in the system parameters in the failure response of the structures subjected to transverse loadings.     

Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method

An isogeometric finite element method based on non-uniform rational B-splines (NURBS) basis functions is developed for natural frequencies and buckling analysis of thin symmetrically laminated composite plates based upon the classical plate theory (CPT). The approximation of the solution space for the deflection field of the plate and the parameterization of the geometry are performed using NURBS-based approach. The essential boundary conditions are formulated separately from the discrete system equations by the aid of Lagrange multiplier method, while an orthogonal transformation technique is also applied to impose the essential boundary conditions in the discrete eigen-value equation. The accuracy and the efficiency of the proposed method are thus demonstrated through a series of numerical experiments of laminated composite plates with different boundary conditions, fiber orientations, lay-up number, eigen-modes, etc. The obtained numerical results are then compared with either the analytical solutions or other available numerical methods, and excellent agreements are found.     

The effect of anisotropy on post-buckling behavior of laminated plates using semi-energy finite strip method

The effects of anisotropy (i.e. the ratio of longitudinal modulus of elasticity to transverse modulus of elasticity of a rectangular plate) on buckling and post-buckling performance of laminated plates under uniform end-shortening have been studied in this paper by implementing a Rayleigh–Ritz approach and a finite strip approach based on the concept of a rigorous post-buckling solution for composite plates and plate structures, namely the semi-energy approach. To validate the results, they are compared with those obtained from finite element method of analysis. The study of results has revealed that the buckling and post-buckling response of the laminates is significantly influenced by the changing of the anisotropy ratio.     

Vibration analysis of laminated composite plates with damage using the perturbation method

The present work focuses on vibration characteristics of damaged laminated composite plates. Damage is considered as a local reduction of anisotropic plate stiffness, and three damage factors (representing the damage severity, damage anisotropy, and damage location/area, respectively) are defined to describe damage status in the laminated composite plates. The analytical solutions are obtained by the perturbation method. A numerical analysis is conducted on the vibration of damaged laminated composited plates, and the effect of damage factors on the vibration characteristics is discussed. Results indicate that three damage factors have different influences on the vibration characteristics. Also, the modal curvatures and strain energy show higher damage sensitivity than the natural frequencies and displacement mode shapes. The perturbation-based vibration analysis developed in this study can be used to effectively evaluate the effect of damage on the vibration behavior of anisotropic plates and potentially identify the damage in the laminated plates.     

Nonlinear flexural analysis of laminated composite plates using RBF based meshless method

The paper presents the nonlinear flexural response of laminated composite plates. The mathematical formulation of the actual physical problem of the laminated composite plate subjected to mechanical loading is presented utilizing higher order shear deformation theory and von-Karman nonlinear kinematics. These nonlinear governing differential equations of equilibrium are linearized using quadratic extrapolation technique. A meshfree technique based on multiquadric RBFs is used for analysis of the problems. Isotropic, orthotropic and laminated composite plates with immovable simply supported and clamped edges are analyzed.     

Finite strip buckling and free vibration analysis of stepped rectangular composite laminated plates

A general spline finite strip method is presented which allows the spline knots to be located arbitrarily along the plate strip and also facilitates the use of analytical integration in evaluating strip properties. The development takes place in the contexts of first‐order shear deformation plate theory and of classical plate theory, and encompasses composite laminated material. The prediction of natural frequencies and buckling stresses of stepped rectangular plates is considered using the new approach in which refinement of knot spacings is used local to a step change. The superstrip concept is used as part of an efficient solution procedure. A number of applications demonstrate the validity and practicability of the developed method. Copyright © John Wiley & Sons, Ltd.     

Impact analysis of laminated composite plates and shells by super finite elements

A super finite element method that exhibits coarse-mesh accuracy is used to predict the transient response of laminated composite plates and cylindrical shells subjected to non-penetrating impact by projectiles. The governing equations are based on the classical theories of thin laminated plates and shells taking into account the von Karman kinematics assumptions for moderately large deflections. A non-linear Hertzian-type contact law accounting for curvatures of the colliding bodies is adopted to calculate the impact force . The theoretical basis of the present finite element model is verified by analysing impact-loaded laminated composite plate and shell structures that have previously been studied through analytical or other numerical procedures. The predictive capability of the present numerical approach is successfully demonstrated through comparisons between experimentally-measured and computed force-time histories for impact of carbon fibre-reinforced plastic (CFRP) plates. The current computational model offers a relatively simple and efficient means of predicting the structural impact response of laminated composite plates and shells.     

Buckling and free vibration finite strip analysis of composite plates with cutout based on two different modeling approaches

A Reddy type, third order shear deformation theory of plates is applied to the development of two versions of finite strip method (FSM), namely semi-analytical and spline methods, to predict the behavior of the moderately thick plates containing cutouts. The internal cutouts are modeled based on two different modeling approaches, and the effects of cutouts on the buckling critical stresses as well as natural frequencies are investigated.     

Closed form solutions for buckling and postbuckling analysis of imperfect laminated composite plates with piezoelectric actuators

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.     

Buckling analysis of composite laminates under end shortening by higher‐order shear deformable finite strips

A higher‐order shear deformable finite strip is developed and employed in the buckling analysis of laminated composite plates when subjected to uniform end shortening. This enables the transverse shear deformation to be accurately incorporated. The permitted laminate material properties are quite general, encompassing anisotropy and full coupling between in‐plane and out‐of‐plane behaviour. Results with respect to the number of plies, thickness of laminate and ratios of E₁₁/E₂₂ are presented for unsymmetric cross‐ply and angle‐ply lay‐ups and for laminates with arbitrary lay‐up arrangements. Copyright © 2002 John Wiley & Sons, Ltd.     

Linear and geometrically non-linear analysis of composite beams under transverse loading

The flexural analysis of fiber-reinforced composite beams based on a higher-order shear deformation theory is studied. The geometric non-linearity is incorporated in the formulation by considering the von Karman strains. The finite element method is used to solve the non-linear governing equations by direct iteration. Unlike conventional beam models, the present beam model accounts for y direction strains. It is observed that the solution obtained from the two approaches differ slightly in the case of cross-ply laminates, but there exists a considerable difference in the case of angle-ply laminates. The influence of boundary conditions, beam geometries, and ply orientations on the deflections and stresses of laminated beams is shown both in tabular and graphical form.     

Stress and failure analysis of laminated composites based on layerwise B-spline finite strip method

A layerwise B_k,k−1-spline finite strip method is developed for stress and failure analysis in fibre reinforced composite laminates. The composite laminates are divided into a number of numerical layers in the thickness direction. A linear variation of in-plane displacements are assumed across the thickness of each numerical layer to represent the sectional warping which can have significant effects on through thickness shear stresses. The development of B_k,k−1-spline finite strip method is presented. Material failure criteria and material degradation models for progressive failure are discussed and integrated in a progressive failure analysis for composite laminates. Numerical applications include a progressive failure analysis example are presented to verify the layerwise B-spline finite strip method developed for stress and failure analysis in composite laminates. Whenever possible the present predictions are compared with the existing analytical and numerical results.     

Reliability analysis of laminated composite structures using finite elements and neural networks

Saving of computer processing time on the reliability analysis of laminated composite structures using artificial neural networks is the main objective of this work. This subject is particularly important when the reliability index is a constraint in the optimization of structural performance, because the task of looking for an optimum structural design demands also a very high processing time. Reliability methods, such as Standard Monte Carlo (SMC), Monte Carlo with Importance Sampling (MC–IS), First Order Reliability Method (FORM) and FORM with Multiple Check Points (FORM–MCPs) are used to compare the solution and the processing time when the Finite Element Method (FEM) is employed and when the finite element analysis (FEA) is substituted by trained artificial neural networks (ANNs). Two ANN are used here: the Multilayer Perceptron Network (MPN) and the Radial Basis Network (RBN). Several examples are presented, including a shell with geometrically non-linear behavior, which shows the advantages using this methodology.