Composite Plates In Thermal Environments Research Articles

Stochastic dynamic analysis of composite plates in thermal environments using nonlinear autoregressive model with exogenous input in polynomial chaos expansion surrogate

The application of composite materials has increased manifolds in aerospace and high-speed vehicle industries, where structures experience dynamic loads along with temperature variation. To ensure safety of these structures, the stochastic dynamic analysis in varying thermal environments is essential. The generalized polynomial chaos (gPC) expansion method is a well-known metamodel used to quantify uncertainties in engineering systems instead of using the direct Monte Carlo simulation. Though the gPC expansion method is used extensively for engineering systems, its classical version has some limitations while implementing in dynamical systems. The accuracy of the gPC expansion method reduces in delayed time domain and can be improved to some extent by increasing the order of polynomial, which though is computationally intensive. Furthermore, the classical gPC expansion method is suitable for low-dimensional problems having independent random parameters. To overcome these limitations in the classical gPC expansion method, a system identifier, i.e., nonlinear autoregressive model with exogenous input (NARX) is coupled with it to avoid response degeneration in delayed time domain. The temperature-dependent material properties of composite lamina can be random and correlated, however the classical gPC expansion method is unable to accommodate the correlated random parameters. To address these challenges, the NARX-gPC expansion method is modified to conduct stochastic dynamic analysis of composite plates using correlated random material properties of the composite lamina in varying thermal environments. The study indicates that the correlation has a significant effect on the stochastic dynamic response at low and high temperatures for cross-ply laminates in comparison with angle-ply laminates, which is not captured through uncorrelated random material properties. The prediction efficiency of the developed surrogate by using the adaptive NARX-gPC expansion method is established even though it is trained using data in a shorter time domain, thereby computational performance is enhanced. Additionally, this surrogate is implemented effectively for higher order randomness in the input parameters.

Damping analysis of stiffened laminated composite plates in thermal environment

High-strength and lightweight composites used in high-speed vehicles and aircraft experience increased temperature owing to aerodynamic friction. Because of the rise in temperature, the elastic moduli of the composites are degraded and inherent viscous damping is increased to the glass transition temperature. In this work, the damping performance of unstiffened and stiffened polyetheretherketone (PEEK) based intermediate modulus (IM7) carbon fiber laminated composite plates is evaluated at various temperatures using displacement- and energy-based approaches. In the displacement-based approach, the logarithmic decrement of the damped vibration is determined to investigate the effect of lamina sequences, stiffener orientation, and stiffener depth at different temperatures. A first-order shear deformation theory considering the viscoelastic property of the composite lamina is implemented to simulate the damped dynamic response of the laminated composite plates in a thermal environment. The best suitable damping model, among Rayleigh damping and modal expansion damping, has been identified to evaluate the damping matrix. Furthermore, the energy-based damping analysis appeared to be a robust approach to evaluate the damping performance as compared to the displacement-based analysis. It is concluded that stiffened plates effectively suppress the dynamic response at elevated temperature, whereas the unstiffened plates show relatively better damping performance at lower temperature.

Dynamic response of stiffened laminated composite plate in thermal environment

Composite materials are increasingly used in aerospace and automobile sectors. These materials are characterized by high stiffness and light-weight in comparison to conventional structural materials. During high-speed maneuvering of these vehicles, associated composite structures are subjected to dynamic loadings and are often exposed to varying thermal environments. To ensure high load carrying capacity and to avoid thermal buckling, stiffened laminated composite plates are preferred in some important structural components, e.g., aircraft’s fuselages, wings etc., than unstiffened laminated composite plates. For safe designing of these structures, it is thus necessary to investigate the dynamic behavior of stiffened laminated composite plates in thermal environment. In this paper, the dynamic response of stiffened laminated composite plates made of polyetheretherketone (PEEK) with intermediate modulus (IM7) carbon fibers in thermal environment has been investigated. Furthermore, development of a generalized finite element (FE) formulation using an 8-node isoparametric plate element employing first-order shear deformation theory (FSDT) has also been presented to analyze unstiffened and stiffened laminated composite plates in thermal environment. Detailed parametric study reveals that the dynamic deflection and the corresponding normal stress decrease with adding stiffener, and decreases further with increasing depth of the stiffener in thermal environment.

Isogeometric analysis for buckling and postbuckling of graphene platelet reinforced composite plates in thermal environments

This work aims at examining the buckling and postbuckling behaviour of laminated composite plate in which GPLs (graphene platelets) are functionally dispersed under various kinds of thermal loadings. For this purpose, IGA (isogeometric analysis) method of which merits encompass the precise geometric representation, smoothness of higher-order, cost-efficiency and high accuracy is taken advantage of. Shear deformable plate theory into which a hyperbolic shear shape function and the von Kármán type nonlinear kinematics are incorporated is used to derive the nonlinear equations of equilibrium for the GPL reinforced composite plate subjected to thermal gradients. On the basis of the total Lagrangian formulation, the governing equation for the thermal buckling is established and the nonlinear thermal postbuckling path is traced together with the modified Newton-Raphson iteration. Three schemes of the symmetric GPL distributions are considered. The IGA approach proposed here, by checking the performance capacity via the multiple numerical tests, is substantiated to successfully follow the nonlinear buckling and postbuckling path of the nanocomposite plate in thermal environments. The further parametric investigations highlight the impacts of the thermal load type, GPL weight fraction, GPL arrangement pattern, plate geometric parameter, plate constraint condition and surface temperature contour on the thermal buckling and postbuckling responses of the GPL strengthened composite plate.

Influence of CNTs grading and reinforcement on dynamic characteristics of composite Plates in thermal environment

This analytical work deals with the dynamic analysis of the functionally graded composite plate reinforced with single walled carbon nanotubes is discussed in this article. By using the extended rule of mixtures, the material properties were computed. The dimensionless frequency parameter was discovered by generating ABAQUS-solved eigenvalues and eigenvectors. The subspace process was used to produce buckling Eigenvalues for the plate. The purpose of the current research work was to analyse the influence of varying temperatures, CNTs and CNTs grading volume fractions on dimensionless frequencies and buckling factors or parameters. From the findings available in the literature, the results of this analysis have been established. CNTs volume percentage and its distribution were found to have a substantial impact on the dimensionless fundamental frequencies. Moreover, similar effect of these parameters on plate buckling were also been observed. Results reveal that the addition of CNT enhances the stiffness of the plate.

Fundamental frequency analysis of functionally graded plates with temperature-dependent properties based on improved exponential-trigonometric two-dimensional higher shear deformation theory

The objective of this paper is to provide a computational method to analyze free vibrations of advanced composite plates in thermal environments according to a recently developed higher-order shear deformation theory. This method is based upon the assumptions that displacements field include just four unknowns and considers a combination of trigonometric and exponential shear shape functions which satisfy shear stress free boundary conditions on the plate surfaces. The FG plates are simply supported and subjected to uniform, linear, nonlinear and sinusoidal temperature rise. The temperature field considered is assumed to vary in the thickness direction and constant in the axial directions of plates. It is supposed that the constituent materials possess temperature-dependent properties changing across the thickness with a simple power law function. The equations of motion are obtained by employing Hamilton’s principle and solved based on Navier’s method to determine natural frequencies of the FG plate. A parametric study for FGM plates with different values of power law index and under different sets of thermal environmental conditions has been carried out. The obtained results are compared for temperature-dependent and temperature-independent FG Plates and validated with available results in the literature.

Parametric instability of functionally graded carbon nanotube-reinforced hybrid composite plates in thermal environments

This paper studies the parametric instability of hybrid nanocomposite plates under an arbitrary periodic load in thermal environments. The hybrid nanocomposite plate is a three-layer board. It has metal layers on both surfaces and one core reinforced with functionally graded (FG) carbon nanotubes (CNTs). The Galerkin method with a reduced eigenfunction transformation is applied to establish the governing equations of motion. According to the Bolotin method, a set of Mathieu-type differential equations is formed to determine dynamic instability regions and dynamic instability index (DII). The in-plane periodic stress is taken to be a combination of pulsating axial and bending stresses in the example problems. The effects of the layer thickness ratio, CNTs volume fraction, CNTs distribution type, temperature, bending stress, static and dynamic load on the dynamic instability of hybrid nanocomposite plates are investigated and discussed.

A novel hyperbolic plate theory including stretching effect for free vibration analysis of advanced composite plates in thermal environments

This paper presents a new hyperbolic shear deformation plate theory including the stretching effect for free vibration of the simply supported functionally graded plates in thermal environments. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The present one has a new displacement field which introduces undetermined integral variables. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equation of motion of the vibrated plate obtained via the classical Hamilton’s principle and solved using Navier’s steps. The accuracy of the proposed solution is checked by comparing the present results with those available in existing literature. The effects of the temperature field, volume fraction index of functionally graded material, side-to-thickness ratio on free vibration responses of the functionally graded plates are investigated. It can be concluded that the present theory is not only accurate but also simple in predicting the natural frequencies of functionally graded plates with stretching effect in thermal environments.

Vibration Analysis of Orthotropic Functionally Graded Composite Plates in Thermal Environment Using High-Order Shear Deformation Theory: Frequency Suppression by Tuning the In-Plane Forces

The vibration absorption of rectangular functionally graded cross-ply thick laminates is achieved analytically. The high-order shear deformation theory containing von Karman strains is employed to study the plate. The laminate structure is assumed to function in a thermal environment subjected to in-plane loadings. Mechanical properties are assumed to vary continuously through the thickness, while each layer of the plate represent an orthotropic composite lamina. The governing equations are derived using Hamilton’s principle and the Levy solution is utilized for the direct implementation of various boundary conditions, including simply support, free, and clamped on the edges of the structure. A particular solution is derived that takes into account the in-plane thermal stresses. Effect of the temperature variation, in-plane loadings, and boundary conditions on the natural frequency of the plate was quantified. Finally, the magnitude of the in-plane forces has been designed in such a way that it can suppress the vibration of the plate under each thermal and boundary condition.

Vibration and stability of initially stressed functionally graded carbon nanotube-reinforced hybrid composite plates in thermal environments

The vibration and stability of hybrid functionally graded (FG) composite plates subject to an arbitrary initially stress in thermal environments is investigated. The plate is reinforced by single walled carbon nanotubes (CNTs). Various profiles of CNTs distributions and volume fractions of hybrid nanocomposite plates are considered. Based on the perturbation method, the governing equations for the hybrid nanocomposite plate considering the effects of non-uniform initial stresses are established. The effects of the CNTs volume fraction, CNTs distribution type, layer thickness ratio, temperature and initial stress on the buckling loads and natural frequencies of hybrid nanocomposite plates are studied in detail.

Modeling of the nonlinear dynamic degradation characteristics of fiber-reinforced composite thin plates in thermal environment

In this research, the nonlinear dynamic degradation characteristics of fiber-reinforced composite plates in thermal environment are investigated through a novel dynamic degradation model, which is established by introducing the thermal and time fitting coefficients simultaneously to express dynamic elastic moduli of such composite materials. Based on the classical laminated plate theory, the improved exponential function method, the complex modulus approach and the Ritz method, the dynamic equations are derived to solve the dynamic parameters. Besides, a particle swarm optimization algorithm is employed to iteratively calculate dynamic elastic moduli, and the nonlinear least squares technique in MATLAB software is utilized to draw the three-dimensional fitted surfaces of dynamic elastic moduli, degradation time and temperature data, so that the concerned fitting coefficients in the model developed can be identified. In order to validate the dynamic degradation model, experimental measurements of E120 carbon fiber/ FRD-YG-03 resin composite thin plates are undertaken. The first three natural frequencies, resonant responses and modal damping ratios obtained from the model are compared with experimental results at different degradation time and stabilized thermal environment, which are shown to be in good agreement. Also, the specific influences with and without consideration of the degradation behavior on the dynamic characteristics are investigated and evaluated.

Stability analysis of embedded graphene platelets reinforced composite plates in thermal environment

This study mainly focuses on buckling characteristics of polymer composites reinforced with graphene platelets (GPLs) in a thermal environment resting on viscoelastic foundation. The micromechanical Halpin-Tsai model is employed to determine GPL-reinforced polymer composite plate properties. Four patterns are considered for the GPLs distribution in a structure matrix. The governing equations of the polymer composite plate reinforced with GPL are developed applying Hamilton’s principle. Navier’s method is used to analyze and solve the problem. The results of this study have been verified by comparing them with those of a previous study. The effects of various parameters, such as geometry effect, GPL weight fraction, temperature changes and viscoelastic foundation on the buckling characteristics are discussed in detail.

Vibratory response and acoustic radiation behavior of laminated functionally graded composite plates in thermal environments

The present study is concerned with vibro-acoustic behavior analyses of laminated functionally graded carbon nanotube reinforced composite plates based on Reddy’s higher order shear deformation theory. Four types of carbon nanotubes distributions along the plate thickness are considered, which include uniformly distributed and three other functionally graded distributions. Governing differential equations are derived by means of Hamilton’s principle. The sound pressure and radiation efficiency are calculated with Rayleigh integral. A numerical comparison with available results in the literature is carried out to show the validity of the present model. Furthermore, effects of the carbon nanotubes volume fraction, different thermal environments, lamination angle and carbon nanotubes distribution types on the structural and acoustic response of laminated functionally graded carbon nanotube reinforced composite plates are also investigated.

Quasi-3D isogeometric buckling analysis method for advanced composite plates in thermal environments

A quasi-3D isogeometric thermal buckling analysis method for advanced composite plates such as functionally graded plates is presented. A new quasi-3D plate theory for the numerical analysis, which enables the normal deformations to be considered with only four unknowns, is introduced. A simple trigonometric normal shape function that is able to accurately express the through-thickness displacement while facilitating the numerical computation is developed. The refined quasi-3D theory is combined with the non-uniform rational B-spline (NURBS)-based isogeometric analysis (IGA) which satisfies the C1-continuity of the displacement field required by the proposed theory to resolve the thermal buckling issue. Several numerical examples which entail buckling analysis of diverse types of functionally graded plates including the one with a complex cutout under different temperature gradients through the thickness are simulated to validate the quasi-3D isogeometric approach, and to explore the thermal buckling response of functionally graded plates. The present quasi-3D IGA is concluded to be accurate and effective numerical method, and significance of including the thickness expansion effects in the thermal buckling assessment of functionally graded plates is confirmed.

Free vibration analysis of stiffened laminated composite plate in a thermal environment

In this paper, the free vibration responses of stiffened composite plates in thermal environment are investigated. The flat panel geometry is modelled by using ANSYS parametric design language (APDL) code based on first order shear deformation theory (FSDT)midplane kinematics. Firstly, the validity of the present model is established along with the convergence. Further, several numerical examples have been solved and discussed in detail to bring out the effect of change in temperature, modular ratio and the coefficient of thermal expansion on the free vibration responses of stiffened laminated composite flat panels. It is observed that the values of natural frequencies decrease with temperature.

A new plate model for vibration response of advanced composite plates in thermal environment

In this work, a novel hyperbolic shear deformation theory is developed for free vibration analysis of the simply supported functionally graded plates in thermal environment and the FGM having temperature dependent material properties. This theory has only four unknowns, which is even less than the other shear deformation theories. The theory presented is variationally consistent, without the shear correction factor. The present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton\'s principles and solved via Navier\'s procedure. The convergence and the validation of the proposed theoretical model are performed to demonstrate the efficacy of the model.

Isogeometric large amplitude free vibration of graphene reinforced laminated plates in thermal environment using NURBS formulation

Present study proposes a nonlinear formulation to study the large amplitude free vibration of composite laminated plates reinforced by graphene sheets. Volume fraction of graphene sheets as reinforcements may be different in the layers. Material properties of the constituents are assumed to be temperature dependent. Properties of the composite media are obtained using a refined Halpin–Tsai approach where the auxiliary parameters are included into the formulation to capture the size dependency of the nanocomposite media. With the aid of third order shear deformation plate theory and the von Kármán type of kinematic assumptions, the basic governing equations of the plate are established. Afterwards, a non-uniform rational B-spline (NURBS) based isogeometric finite element method is used to study the large amplitude free vibration response of the graphene reinforced composite plates in thermal environment. Large amplitude frequencies as a function of centre point deflection are provided for different functionally graded patterns, aspect ratios, side to thickness ratios and boundary conditions.

Nonlinear stability analysis of imperfect three-phase polymer composite plates in thermal environments

This paper presents an analytical investigation on the nonlinear response of the thin imperfect laminated three-phase polymer composite plate in thermal environments. The formulations are based on the classical plate theory taking into account the interaction between the matrix and the particles, geometrical nonlinearity, initial geometrical imperfection. By applying Galerkin method, explicit relations of load–deflection curves are determined. Obtained results show effects of the fibers and the particles, material, geometrical properties and temperature on the buckling and post-buckling loading capacity of the three phase composite plate, therefore we can proactively design materials and structural composite meet the technical requirements as desired when adjustment components.

Dynamic stability analysis of laminated composite plates in thermal environments

This paper studies the dynamic instability of laminated composite plates under thermal and arbitrary in-plane periodic loads using first-order shear deformation plate theory. The governing partial differential equations of motion are established by a perturbation technique. Then, the Galerkin method is applied to reduce the partial differential equations to ordinary differential equations. Based on Bolotin's method, the system equations of Mathieu-type are formulated and used to determine dynamic instability regions of laminated plates in the thermal environment. The effects of temperature, layer number, modulus ratio and load parameters on the dynamic instability of laminated plates are investigated. The results reveal that static and dynamic load, layer number, modulus ratio and uniform temperature rise have a significant influence on the thermal dynamic behavior of laminated plates.

Dynamic stability analysis of laminated composite plates in thermal environments

This paper studies the dynamic instability of laminated composite plates under thermal and arbitrary in-plane periodic loads using first-order shear deformation plate theory. The governing partial differential equations of motion are established by a perturbation technique. Then, the Galerkin method is applied to reduce the partial differential equations to ordinary differential equations. Based on Bolotin\'s method, the system equations of Mathieu-type are formulated and used to determine dynamic instability regions of laminated plates in the thermal environment. The effects of temperature, layer number, modulus ratio and load parameters on the dynamic instability of laminated plates are investigated. The results reveal that static and dynamic load, layer number, modulus ratio and uniform temperature rise have a significant influence on the thermal dynamic behavior of laminated plates.