Reliability of fiber-reinforced composite laminate plates

Many engineering structures ranging from aircrafts, spacecrafts and submarines to civil structures, automobiles, trucks and rail vehicles, require less weight and more stiff and strong materials. As a result of these requirements, the use of composite materials has increased during the past decades. In fact during the past five years, we have witnessed exponential growth in research and field demonstrations of fiber-reinforced composites in civil engineering. Manufacturers and designers have now access to a wide range of composite materials. However, they face great problems with forecasting the reliability of composites materials. Due to the differences among the properties of materials used for composites, manufacturing processes, load combinations, and types of environment, the prediction of reliability of composites is a very complex task. In this study, the reliability of fiber-reinforced composite laminate plates under random loads is investigated. The background of the problem is defined, the failure criterion chosen is presented, and the probability of failure is computed by Monte Carlo simulation.     

Stochastic progressive failure analysis of laminated composite plates using Puck's failure criteria

The present work deals with second-order statistics of the progressive failure response of laminated composite plates subjected to in-plane uniaxial and bi-axial loadings with random system properties. A stochastic finite element method based on higher-order shear deformation theory combined with first- and second-order perturbation technique is used for solution of random progressive failure equation. A Puck failure criterion is used for the evaluation of first ply and last-ply failure load. The results obtained using the present solution approach are validated with the results available in the literature and Monte Carlo simulation.     

Prediction of reliability analysis of composite tubular structure under hygro-thermo-mechanical loading

The present paper focuses on reliability prediction of composite structure under hygro-thermo-mechanical loading, conditioned by Tsai-Wu failure criterion, where the Monte–Carlo method is used to estimate the failure probability(Pf). This model was developed in two steps: first, the development of a deterministic model, based on an analytical and numerical approach, and then, a probabilistic computation. Using the hoop stress for each ply, a sensitivity analysis was performed for random design variables, such as materials properties, geometry, manufacturing, and loading, on composite cylindrical structure reliability. The probabilistic results show the very high increase of failure probability when all parameters are considered.     

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.     

Material characterization of laminated composite plates via static testing

A minimization method for material characterization of laminated composite plates using static test results is presented. Mechanical responses such as strains and displacements are measured from the static tests of the laminated composite plates. The finite element method is used to analyse the deformation of the laminated composite plates. An error function is established to measure the differences between the experimental and theoretical mechanical responses of the laminated composite plates. The identification of the material elastic constants of the laminated composite plates is formulated as a constrained minimization problem in which the elastic constants are determined by making the error function a global minimum. A number of examples are given to illustrate the feasibility and applications of the proposed method.     

体积分数随机场作用下复合材料层合板固有振动特性不确定性分析

考虑复合材料层合板中每层体积分数空间不确定性的影响,采用指数型自相关函数模拟每层体积分数同空间位置的依赖关系,结合伽辽金-里兹正交多项式逼近和K-L展开方法,研究了体积分数随机场的自相关长度特征对材料属性随机场离散精度的影响;进而通过体积分数随机场作用下复合材料层合板的随机有限元模型,研究了T300碳纤维/QY8911...     

Non‐linear random response of laminated composite shallow shells using finite element modal method

This paper investigates the large‐amplitude multi‐mode random response of thin shallow shells with rectangular planform at elevated temperatures using a finite element non‐linear modal formulation. A thin laminated composite shallow shell element and the system equations of motion are developed. The system equations in structural node degrees‐of‐freedom (DOF) are transformed into modal co‐ordinates, and the non‐linear stiffness matrices are transformed into non‐linear modal stiffness matrices. The number of modal equations is much smaller than the number of equations in structural node DOF. A numerical integration is employed to determine the random response. Thermal buckling deflections are obtained to explain the intermittent snap‐through phenomenon. The natural frequencies of the infinitesimal vibration about the thermally buckled equilibrium positions (BEPs) are studied, and it is found that there is great difference between the frequencies about the primary (positive) and the secondary (negative) BEPs. All three types of motion: (i) linear random vibration about the primary BEP, (ii) intermittent snap‐through between the two BEPs, and (iii) non‐linear large‐amplitude random vibration over the two BEPs, can be predicted. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

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.     

Determination of optimum effective parameters on thermal buckling of hybrid composite plates with quasi-square cut-out using a genetic algorithm

ABSTRACT

The thermal buckling load on perforated composite plates is affected by several parameters, including design variables such as cut-out orientation, fibre angle, bluntness of cut-out corners, cut-out size to plate size ratio and stacking sequence. This study investigates the effect of these parameters on the thermal buckling load of a composite plate with a quasi-square cut-out. Optimal values of the parameters are determined using a genetic algorithm to achieve the maximum buckling load. The composite used herein is a four-layer laminated composite plate. The stacking sequences of the plate are also studied. Stability equations are obtained using first order shear deformation theory. The results showed that a plate with a quasi-square cut-out is more resistant to thermal buckling than one with a circular cut-out; thermal buckling of a composite plate is dependent on various parameters, and the maximum thermal buckling load can be achieved by appropriate selection of these parameters.     

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.     

Classical coupled thermoelasticity in laminated composite plates based on third-order shear deformation theory

A new mixed finite element formulation is proposed to analyze transient coupled thermoelastic problems. Coupled model of dynamic thermoelasticity is selected for a laminated composite and a homogeneous isotropic plate. For the particular finite element developed here, there are 15 degrees of freedom at each node. Two simply supported plates are considered subjected to sinusoidally distributed mechanical and thermal loading. It is seen, by comparing the present results with results from the NISA II FEM code, that they are in good agreement.     

The Green’s functions of a vertically inhomogeneous soil with a random dynamic shear modulus

This paper deals with the study of the Green’s functions of a layered soil with random characteristics. The dynamic shear modulus of the soil is modelled as a non-Gaussian random process that varies in the vertical direction and is characterized by a marginal probability density function and a correlation function. The stochastic finite element method is applied to a hybrid thin layer — direct stiffness formulation in order to obtain the stochastic system equations, which are solved by means of a Monte Carlo simulation. The influence of the variations of the dynamic shear modulus on the Green’s functions is illustrated for different excitation frequencies and receiver positions.     

Stochastic finite element analysis of a cable-stayed bridge system with varying material properties

Stochastic seismic finite element analysis of a cable-stayed bridge whose material properties are described by random fields is presented in this paper. The stochastic perturbation technique and Monte Carlo simulation (MCS) method are used in the analyses. A summary of MCS and perturbation based stochastic finite element dynamic analysis formulation of structural system is given. The Jindo Bridge, constructed in South Korea, is chosen as a numerical example. The Kocaeli earthquake in 1999 is considered as a ground motion. During the stochastic analysis, displacements and internal forces of the considered bridge are obtained from perturbation based stochastic finite element method (SFEM) and MCS method by changing elastic modulus and mass density as random variable. The efficiency and accuracy of the proposed SFEM algorithm are evaluated by comparison with results of MCS method. The results imply that perturbation based SFEM method gives close results to MCS method and it can be used instead of MCS method, especially, if computational cost is taken into consideration.     

Detection of stiffness degradation in laminated composite plates by filtered noisy impact testing

The purpose of this paper is to detect damage (stiffness degradation) of laminated composite plates from noisy impact response data. The combined finite element method (FEM) with five degrees of freedom (DOF) and the advanced noise filtering algorithm described in this paper may allow us not only to detect the deteriorated elements but also to find their locations and the extents. A first order shear deformation theory (FSDT) is used to predict the structural behavior and to detect damage of laminated composite plates. The filtering procedure is designed by means of a wavelet decomposition together with a selection of the measuring points, and the optimization criterion is constructed on an estimate of the probability of detection using genetic algorithms. All these techniques are applied for the first time to composites. The effects of filtered noise associated with the uncertainty of measurements due to the complex nature of composites are considered for different layup sequences, number of layers, and length–thickness ratios. Several numerical results show that the noise filtering system is computationally efficient in identifying stiffness degradation for complex structures such as laminated composites.     

In-plane free vibrations of single-layer and symmetrically laminated rectangular composite plates

This work presents accurate upper-bound solutions for free in-plane vibrations of single-layer and symmetrically laminated rectangular composite plates with an arbitrary combination of clamped and free boundary conditions. In-plane natural frequencies and modes shapes are calculated by the Ritz method with a simple, stable and computationally efficient set of trigonometric functions. Reliability of the method is assessed by comparison with known accurate solutions for isotropic plates and specially orthotropic single laminates. The extensive results presented here for the first time can be considered benchmark data against which other methods may be compared and validated in the future. Influence of fiber orientation, stacking sequence, degree of orthotropy, aspect ratio and boundary conditions upon the in-plane vibration behavior are also discussed.     

Multiscale analysis of laminated plates with integrated piezoelectric fiber composite actuators

This study is concerned with the detailed analysis of fiber-reinforced composite plates with integrated piezoceramic fiber composite actuators. A multiscale framework based on the asymptotic expansion homogenization method is used to couple the microscale and macroscale field variables. The microscale fluctuations in the mechanical displacement and electric potential are related to the macroscale deformation and electric fields through 36 distinct characteristic functions. The local mechanical and charge equilibrium equations yield a system of partial differential equations for the characteristic functions that are solved using the finite element method. The homogenized electroelastic properties of a representative material element are computed using the characteristic functions and the material properties of the fiber and matrix. The three-dimensional macroscopic equilibrium equations for a laminated piezoelectric plate are solved analytically using the Eshelby-Stroh formalism. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. The microscale stresses and electric displacement in the fibers and matrix are computed from the macroscale fields through interscale transfer operators. The multiscale analysis procedure is illustrated using two model problems. In the first model problem, a simply-supported sandwich plate consisting of a piezoceramic fiber composite shear actuator embedded between two graphite/polymer layers is studied. The second model problem concerns a cantilever graphite/polymer substrate with segmented piezoceramic fiber composite extension actuators attached to its top and bottom surfaces. Results are presented for the homogenized material properties, macroscale deformation, macroscale average stresses and microscale stress distributions.     

Optimization of laminated composite structure considering uncertainty effects

In this paper, the most conservative Tsai–Wu failure envelopes are obtained for laminated composite considering material as well as ply angle uncertainty. The uncertainty analysis is performed using Monte Carlo simulation (MCS). The obtained failure envelopes are then used as the constraint functions to perform the minimum weight design optimization problem using particle swarm optimization (PSO). Results show increase in weight of the laminate from the deterministic results and it varies from 4% to 50% depending upon the stacking sequence and loading condition. Substantial effects of uncertainty on the failure envelope and optimal design are quantified.     

Dynamic analysis of laminated composite plates traversed by a moving mass based on a first-order theory

The dynamic response of angle-ply laminated composite plates traversed by a moving mass or a moving force is investigated. For this purpose, a finite element method based on the first-order shear deformation theory is used. Stationary and adaptive mesh techniques have been applied as two different meshing schemes. The adaptive mesh strategy is then used to avoid off-nodal position of moving mass. In this manner, the finite element mesh is continuously adapted to follow and comply with the path of moving mass. A Newmark direct integration method is employed to solve the equations of motion. Parametric study is directed to find out how different parameters like mass of the moving object as well as the type of the angle-ply laminated composite plates affect the dynamic response. Numerical results show the significant effects of the stacking order on the dynamic responses of the composite structures under a moving mass. It is found that although [30/−60/−60/30] lamination shows the highest maximum vertical deflection but [−45/45/45/−45] lamination has the highest value of the dynamic amplification factor. The dynamic amplification factor for different stacking orders and mass velocities is less than 1.25.     

The structural intensities of composite plates with a hole

The structural intensities in isotropic and orthotropic laminae and composite laminated plates with and without a hole of different rim conditions are studied using the finite element method. Patterns of superposition among structural stress fields, intensity vectors, mode shapes and streamlines of energy flow are obtained for the various cases. It is found that the hole completely changes the distributions of the stress and energy flow path in plates. Despite its nature of mode dependent the pattern of energy flow may be different from each other despite having similar structural mode shapes, moreover the position of maximum stress is not corresponding to the position of maximum structural intensity.