Composite Quadrilateral Plates Research Articles

Panel flutter analysis of nano-hybrid laminated composite quadrilateral plates presuming curvilinear fibers

In the present article, the panel flutter behavior of nanocomposite hybrid laminated quadrilateral panel is studied. A three-phase carbon-nanotube (CNT)/polymer/fiber laminated composite is considered where the probable agglomeration of the CNT phase in the nano-matrix mixture is also addressed. Diverse use of fiber phase material in different plies is assumed in the context of hybrid laminated composite. A combination of nanocomposite polymer matrix, tow-steered curvilinear reinforcing fibers within the plies, and hybrid multi-material laminate is considered. The panel flutter behavior of the arbitrary quadrilateral hybrid laminated nanocomposite plate is formulated by a non-uniform rational B-splines-type isogeometric analysis method based on the first-order shear deformation plate theory. The nonideal mixture of the nanocomposite is also concerned about through applying a micromechanics approach. Representative results are obtained and compared with those available in the literature to demonstrate the quality of the proposed formulation. The effects of different parameters including the layup, mixture quality, boundary condition, geometry, and flow direction on the flutter behavior are investigated by performing parametric studies.

Optimization Design of Laminated Functionally Carbon Nanotube-Reinforced Composite Plates Using Deep Neural Networks and Differential Evolution

This study presents a new approach as an integration of deep neural networks (DNN) into differential evolution (DE) to give the so-called DNN-DE for frequency optimization of laminated functionally graded carbon nanotube (FG-CNT)-reinforced composite quadrilateral plates under free vibration. In the presented approach, the DNN is applied to predict the objective and constraints during the optimization process instead of using the time-consuming finite element analysis (FEA) procedures while the DE is used as an optimizer for solving the optimization problem. Several numerical examples are performed to illustrate the performance of the proposed method. Optimal results obtained by the DNN-DE are compared with those achieved by other methods in order to show the reliability and effectiveness of the proposed methodology. Additionally, the influence of various parameters such as the boundary condition, the carbon nanotube (CNT) volume fraction, the CNT distribution on the optimal results is also investigated. The obtained results indicate that the proposed DNN-DE is an effective and promising method in solving optimization problems of engineering structures.

Maximization of the fundamental frequency of the FG-CNTRC quadrilateral plates using a new hybrid PSOG algorithm

This research work presents the fundamental frequency optimization of the functionally graded carbon nanotube reinforced composite (FG-CNTRC) quadrilateral plates using an improved hybrid algorithm of the particle swarm optimization and genetic (PSOG) algorithm. The objective function is to maximize the fundamental frequency of the FG-CNTRC quadrilateral plates and the design variables are a set of the discrete values of the fiber orientations in the layers. The natural frequency of the plates is obtained by using the cell-based smoothed discrete shear gap method. The several comparative numerical examples are investigated to show the efficiency of the proposed hybrid PSOG algorithm. It is demonstrated in the numerical examples that this design method can provide with the accurate optimum solutions for the stacking sequences of the vibrating FG-CNTRC quadrilateral plates.

Multi-Objective Optimization of Laminated Functionally Graded Carbon Nanotube-Reinforced Composite Plates Using Deep Feedforward Neural Networks-NSGAII Algorithm

This paper proposes a novel and efficient DNN-NSGAII approach which is an integration of the deep feedforward neural network (DNN) and the nondominated sorting genetic algorithm II (NSGAII) to solve multi-objective optimization (MOO) problems of laminated functionally graded carbon nanotube-reinforced composite (FG-CNTRC) quadrilateral plates. The core idea of the proposed approach is to use the DNN as an analyzer to evaluate the objective and constraint functions instead of using the time-consuming finite element analysis methods (FEAMs) during the optimization process, while the NSGAII is employed to find a set of Pareto-optimal solutions of the MOO problems. Accordingly, the proposed DNN-NSGAII remarkably saves the computational cost, but still provides a high accurate optimal solution. The precision, efficiency, and capability of the proposed method are demonstrated through two different MOO problems of the FG-CNTRC quadrilateral plates. Obtained results of the DNN-NSGAII are compared with those of other methods to investigate the reliability and efficiency of proposed method. Moreover, the effects of various boundary conditions and carbon nanotube (CNT) distributions on the Pareto-optimal solutions of MOO problems are also examined.

Multiscale analysis on free vibration of functionally graded graphene reinforced PMMA composite plates

In this paper, a molecular dynamics (MD)-based multiscale analysis is employed to investigate the free vibration of graphene reinforced laminated composite plates from the atomic scale to the macroscopic behavior. The atomic models of graphene with different sizes, poly (methyl methacrylate) (PMMA) and graphene/PMMA composites with different graphene volume fractions are constructed, and Poisson's ratio as well as elastic moduli are in good agreements with the MD results. Then the efficiency parameters of the Young's and shear moduli of graphene/PMMA composites are derived at the micro scale via the extended Halpin-Tsai micromechanics model, and are employed subsequently to the vibration analysis at the macro scale. Based on the first order shear deformation theory and meshless method, the governing equation of functionally graded graphene reinforced composite (FG-GRC) quadrilateral plates is derived and discretized to analyze the vibration behavior. The effects of geometrical parameter, graphene volume fraction and distribution pattern are investigated on the dimensionless frequency of FG-GRC quadrilateral plates. The multiscale analysis in this paper combines the simulation of material properties at the atomic scale and the response of structure at the macro scale, which provides a feasible way to study the vibration behavior of composite structures.

Flutter analysis of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method

This paper investigates the flutter characteristics of graphene nanoplatelet (GPL) reinforced laminated composite quadrilateral plates using the element-free IMLS-Ritz method. The modified Halpin-Tsai model and rule of mixture are employed to predict the effective material properties including Young's modulus, mass density and Poisson's ratio. The energy functions of GPL reinforced composite (GPLRC) quadrilateral plates are obtained by the first-order shear deformation theory (FSDT) and first order piston theory. Based on the IMLS-Ritz approximation, the discrete dynamic equation of GPLRC quadrilateral plates is derived. The accuracy of the IMLS-Ritz results is examined by comparing the natural frequencies with those obtained from published values. A comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern, total number of layers, geometry and size of GPL reinforcements and geometric parameters of quadrilateral plates on the flutter boundary of GPLRC quadrilateral plates.

Thermal buckling analysis of temperature-dependent FG-CNTRC quadrilateral plates

The main objective of the present study is to analyze the thermal buckling of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) quadrilateral plates. Functionally graded patterns are introduced for the distribution of the carbon nanotubes (CNTs) through the thickness direction of the plate. The effective material properties of nanocomposite plate reinforced by CNTs are considered to be temperature-dependent (TD) and estimated using the micromechanical model. By the use of minimum total potential energy principle and based on the first-order shear deformation theory of plates, the stability equations are obtained. In order to use the generalized differential quadrature (GDQ) method and solve the stability equations, the irregular domain of quadrilateral plate is transformed into regular computational domain employing the mapping technique. The efficiency and accuracy of the proposed approach are first validated. Then, a comprehensive parametric study is presented to examine the effects of model parameters on the thermal buckling of FG-CNTRC quadrilateral plates. The results indicate that considering temperature dependency of the material properties plays an important role in the stability of the FG-CNTRC quadrilateral plates subjected to thermal loading.

Parametric instability behavior of tow steered laminated quadrilateral plates using isogeometric analysis

For the first time, the parametric instability regions of variable stiffness laminated composite quadrilateral plates subjected to uniform in-plane loadings are studied. The static as well as time-varying inplane loadings are assumed distributed throughout the whole geometry. The isogeometric analysis finite element formulation based on non-uniform rational B-splines is developed in order to address the dynamic instability of quadrilateral panels. The problem has been formulated by utilizing the principle of virtual work based on first order shear deformation plate theory. In terms of tow-steered reinforcements, the fiber orientations in every lamina is assumed to change linearly in the panel longitudinal direction. In order to demonstrate the capabilities of the developed formulation in predicting the structural parametric dynamic behavior, some representative results are obtained and compared with those available in the literature. The effects of geometry layout, loading frequency and amplitude, changes in curvilinear fiber orientations, and material orthogonality on the parametric instability regions are studied by applying Bolotin's first order approximation.

Geometrically nonlinear analysis of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method

This paper investigates the nonlinear bending of graphene nanoplatelet (GPL) reinforced laminated composite quadrilateral plates using the element-free IMLS-Ritz method. The effective material properties including Young's modulus, mass density and Poisson's ratio are determined by the modified Halpin-Tsai model and rule of mixture. The first-order shear deformation theory (FSDT) and the IMLS-Ritz approximation are employed to obtain the discrete nonlinear governing equation of quadrilateral plates with large deformation. The Newton-Raphson method is used to solve the nonlinear equation. The accuracy of the IMLS-Ritz results is examined by comparing with the published values. A comprehensive parametric study is carried out, with a particular focus on the effects of geometric parameters of quadrilateral plates and GPLs distribution pattern, weight fraction, total number of layers, and geometry and size of GPLs on the nondimensional deflection of GPLs reinforced laminated composite quadrilateral plate.

Vibration of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method

This paper investigates free vibration of graphene nanoplatelet (GPL) reinforced laminated composite quadrilateral plates using the element-free IMLS-Ritz method. The effective material properties including Young's modulus, mass density and Poisson's ratio are determined by the modified Halpin–Tsai model and rule of mixture. The first-order shear deformation theory (FSDT) is employed for formulation of the energy functional. Based on the IMLS-Ritz approximation, the discrete vibration equation of the laminated composite quadrilateral plates is derived. The accuracy of the IMLS-Ritz results is examined by comparing with the published values. A comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern, geometry and size of GPL reinforcements, total number of layers and geometric parameters of quadrilateral plates on the natural frequencies of GPL reinforced laminated composite quadrilateral plate.

Frequency optimization of laminated functionally graded carbon nanotube reinforced composite quadrilateral plates using smoothed FEM and evolution algorithm

The paper presents an efficient numerical optimization approach to deal with the optimization problem for maximizing the fundamental frequency of laminated functionally graded carbon nanotube-reinforced composite quadrilateral plates. The proposed approach is a combination of the cell-based smoothed discrete shear gap method (CS-DSG3) for analyzing the first natural frequency of the functionally graded carbon nanotube reinforced composite plates and a global optimization algorithm, namely adaptive elitist differential evolution algorithm (aeDE), for solving the optimization problem. The design variables are the carbon nanotube orientation in the layers and constrained in the range of integer numbers belonging to [−900 900]. Several numerical examples are presented to investigate optimum design of quadrilateral laminated functionally graded carbon nanotube reinforced composite plates with various parameters such as carbon nanotube distribution, carbon nanotube volume fraction, boundary condition and number of layers.

The IMLS-Ritz analysis of laminated CNT-reinforced composite quadrilateral plates subjected to a sudden transverse dynamic load

A first known study on the mechanical behavior of laminated CNT-reinforced quadrilateral composite plates due to a sudden transverse dynamic load is performed. In this study, a moderately thick plate is considered; therefore, the first-order shear deformation theory (FSDT) is employed in the formulation. The numerical analysis of the problem is carried out using the IMLS-Ritz method. The Newmark-β method is employed for the numerical time integration of the dynamic problem. The Mori-Tanaka approach is adopted for predicting the properties of CNT-composites. The numerical stabilities and accuracies of the IMLS-Ritz method are examined. The convergence properties are illustrated through solving an isotropic square plate and a laminated CNT-composite quadrilateral plate by varying their node numbers and support sizes. A comprehensive parametric study has been carried out to examine the dynamic behavior of symmetric and asymmetric CNT-composite plates.

Critical buckling load optimization of functionally graded carbon nanotube‐reinforced laminated composite quadrilateral plates

The effective method of transformed differential quadrature (TDQ) is improved for the buckling design optimization of functionally graded (FG) carbon nanotube‐reinforced laminated composite quadrilateral (FG‐CNTRCQ) plates with arbitrary straight‐sided based on the first‐order shear deformation theory. The laminated plates with both uniformly and FG distributions of single‐walled carbon nanotubes varied along the thickness of layers are considered. The TDQ method is used to directly discretize the governing differential equations for an arbitrary straight‐sided physical domain without any need to transform the equations to the computational domain. In the presented genetic algorithm, the orientation of fibers is considered as the design parameter to obtain the optimum critical buckling loads in terms of different parameters including distributions of the fibers, number of layers, stacking sequence, CNTs volume fraction, geometrical parameters, and boundary conditions. The edges of the plates can take arbitrary end supports of simply and clamped boundary conditions. The formulation is developed based on the invariant terms to provide a systematic procedure with minimum computational cost. Some parametric studies are conducted to examine the effectiveness of the model for the design purpose of the FG‐CNTRCQ plates. POLYM. COMPOS., 39:E853–E868, 2018. © 2017 Society of Plastics Engineers

Application of TW-DQ method to nonlinear free vibration analysis of FG carbon nanotube-reinforced composite quadrilateral plates

The differential quadrature (DQ) method in conjunction with the introduced transformed weighing coefficients (TW-DQ) is formulated to solve geometrically nonlinear free vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) quadrilateral plates. The methodology benefits from systematically development of approximating derivatives for an arbitrary straight-sided physical domain. The classical plate theory (CPT) together with von Karman’s strain-displacement assumptions are employed to derive the nonlinear governing partial differential equations with geometric nonlinearity. The vibrational behavior of quadrilateral plates with both uniformly and functionally graded symmetric distributions of carbon nanotubes through the thickness is investigated. The edges of the plates can take arbitrary end supports of immovable simply and clamped boundary conditions. The direct iteration method is used to solve the TW-DQ discretized form of the nonlinear governing equations. The fast rate of convergence of the present method is exhibited and comparison studies with the available solutions in literature are provided to examine its accuracy. Numerical results are also conducted to present the effects of carbon nanotubes volume fraction, amplitude ratio, aspect ratios, side angle, skew angle, graded distribution of nanotubes, and boundary conditions on the frequency ratio.

Free vibration analysis of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations using the IMLS-Ritz method

The vibration behavior was investigated of thin-to-moderately thick functionally graded carbon nanotube (FG-CNT) reinforced composite quadrilateral plates resting on elastic foundations. In the study, transverse shear and rotatory inertia were incorporated through first-order shear deformation theory. The improved moving least-squares-Ritz method was employed to derive the eigenvalue equation of the plate vibration. The study examined the effects of the elastic Winkler medium, CNT ratios, distributions of CNTs, boundary conditions, side angles, thickness-to-width ratios, and the relative plate aspect ratios on the vibration response of the FG-CNT reinforced composite plates. A set of vibration frequencies and mode shapes for the FG-CNT reinforced composite quadrilateral plates is presented. Additionally, a comprehensive parametric study and vivid mode shape plots demonstrate details of the vibration spectrum of the FG-CNT reinforced composite plates.

Vibrational analysis of carbon nanotube-reinforced composite quadrilateral plates subjected to thermal environments using a weak formulation of elasticity

Superlative properties of nanocomposites have motivated considerable research efforts in recent years. Nanocomposite plates of quadrilateral shapes are important structural components used in a variety of engineering structures. This article aims to develop a variational formulation to describe the vibrational behavior of functionally graded (FG) nanocomposite straight-sided quadrilateral plates reinforced by carbon nanotubes (CNTs) in thermal environments. Various profiles of single-walled carbon nanotubes (SWCNTs) distribution along the thickness are taken into consideration. The mathematical formulation is developed in the variational form based on the first order shear defamation plate theory (FSDPT) with consideration of thermal effects. Discretization process of the energy functional is done on a computational domain using a mapping-differential quadrature (DQ) methodology. Discrete form of the governing equations is directly derived from a weak formulation which does not involve any transformation and discretization of the high order derivatives appeared in the equations of the strong form. Numerical results are given and compared with the ones reported in the literature to evaluate the convergence behavior and accuracy of the proposed solution. Subsequently, the influences of temperature on natural frequencies of the nanocomposite quadrilateral plates with different geometric parameters, CNT distributions in thickness direction and boundary conditions are investigated.

Geometrically nonlinear large deformation analysis of functionally graded carbon nanotube reinforced composite straight-sided quadrilateral plates

Abstract An improved moving least-squares (IMLS) approximation for the field variables is proposed for geometrically nonlinear large deformation analysis of functionally graded carbon nanotube (FG-CNT) reinforced composite quadrilateral plates. The plate considered is of moderate thickness and, hence, the first-order shear deformation theory (FSDT) and Von Karman assumption are adopted to incorporate the transverse shear strains, rotary inertia and moderate rotations. The CNTs are assumed to be uniaxially aligned in the axial direction and functionally graded in the plate thickness direction. The discrete nonlinear governing equation is derived based on the IMLS-Ritz method. The modified Newton–Raphson method combined with the arc-length iterative algorithm is employed to solve the nonlinear deformation of the FG-CNT reinforced composite quadrilateral plates. Improvements in computational efficiency and elimination of shear and membrane locking are achieved using a stabilized conforming nodal integration scheme to evaluate the system’s bending stiffness. Through detailed parametric studies, CNT distribution, CNTs volume fraction, aspect ratio and thickness-to-width ratio and different boundary conditions are demonstrated to effect significantly on the large deflection behaviors of the quadrilateral FG-CNT reinforced composite plates.