Thermal Postbuckling Analysis Research Articles

Thermal and thermo-mechanical post-buckling analysis of GNP-reinforced composite laminated plates

This research utilizes isogeometric analysis (IGA) method to analyze buckling and post-buckling responses of composite laminated plates embedded with graphene nanoplatelets (GNPs) subjected to three-dimensional (3D) conduction of heat or combined 3D heat conduction and mechanical edge compression. A formulation to determine temperature profile produced by 3D conduction of heat in the GNP-reinforced laminate is established, and a new function with smooth transition form of GNP volume fraction across the thickness is presented for dictating the volume fraction of layer. Shear deformable quasi-3D theory with the von Kármán type nonlinearity which takes initial geometric deformation and thermal effect into consideration is employed to construct the nonlinear equilibrium states. Four types of GNP arrangements encompassing uniform, O, X and V shapes are considered. The IGA approach presented, through the benchmark test, is evidenced to estimate the thermal buckling temperature accurately and to successfully trace the thermal post-buckling path. Additional parametric study is carried out to scrutinize the thermal and the thermo-mechanical post-buckling features of the GNP-reinforced composite laminated plates, and the new findings are sure to be served as the benchmark solutions.

A new set of explicit solutions for postbuckling behaviour of anisotropic shear deformable laminated cylindrical shells with general imperfection distribution and thermal loading

Thermal postbuckling analysis is presented for shear-deformable anisotropic laminated cylindrical shell with general imperfection distribution under several typical temperature fields are analyzed, including uniform temperature, tent-like linear distribution, axial and circumferential quadratic parabolic temperature fields over the shell surface and through the shell thickness. On this basis, the general temperature distribution can be obtained based on the three-dimensional steady-state heat transfer equation. At the same time, based on the high order shear deformation theory including anisotropic coupling effect, geometrically nonlinear large deflection displacement-strain relationship, the general initial geometric imperfections obtained by measurement and analytical means are introduced, and the thermal buckling equilibrium differential equation of anisotropic shear deformable laminated cylindrical shell with initial imperfections is established. A two-step perturbation-Galerkin integral method is used to obtain explicit solutions for the path development direction of post-thermal buckling equilibrium. The results of parameter analysis show that the material properties and temperature dependence, temperature distribution, lay-up and geometric parameters such as radius-to-thickness ratio have important effects on the thermal buckling load and postbuckling equilibrium path. The present method provides an effective theoretical prediction and analysis method for the design of the carrying capacity of submarine pipelines.

Axisymmetric thermal postbuckling of functionally graded graphene nanocomposite annular plates with various geometric imperfections

This paper presents the axisymmetric thermal postbuckling analysis of functionally graded graphene platelets-reinforced composite (FG-GPLRC) annular plates with various geometric imperfections within the framework of first-order shear deformation theory and von Kármán geometric nonlinearity. An imperfection model composed of trigonometric and hyperbolic functions is used to simulate possible imperfections with different shapes, amplitudes and locations. The 3D Halpin–Tsai model is employed to estimate the effective modulus of graphene nanocomposites. Nonlinear governing equations are derived by the variational principle and are then solved by the generalized differential quadrature method combined with the modified Newton–Raphson iteration. Parametric studies are conducted to highlight the influences of imperfection amplitude, localization degree, location and half-wave number on the thermal postbuckling behaviour of FG-GPLRC annular plates. It is found that the thermal postbuckling resistance is reduced due to the existence of geometric imperfections, and this effect become more/less significant as the imperfection amplitude/half-wave number increases.

Static and dynamic thermal post-buckling analysis of imperfect sigmoid FG cylindrical shells resting on a non-uniform elastic foundation

In this study, an approach combining semi-analytical and analytical methods is utilized to investigate the dynamic and static thermal post-buckling behavior of imperfect sigmoid functionally graded (SFG) cylindrical shells in a thermal environment. Two types of SFG cylindrical shells consisting of ceramic-metal-ceramic (CMC) layers and metal-ceramic-metal (MCM) layers are considered. The structure is considered to rest on a non-uniform elastic foundation, and the parameters of elastic foundation used in the research are defined by using Selvadurai's methodology. Material distributions of the shells are graded through the thickness direction following a sigmoid distribution in terms of volume fraction. The nonlinear governing equation of the cylindrical shells is derived by applying the von-Kármán equation and the Donnell shell theory. Based on Galerkin's method, a discretized nonlinear governing equation is obtained for analyzing the behavior of the shells. To systematically study the dynamic thermal post-buckling response of the shells, the fourth-order P-T method is utilized. The research results obtained are verified. Moreover, to further validate the dynamic thermal post-buckling, comparisons are made with the fourth-order Runge-Kutta method. It is noted that the fourth-order P-T method has illustrated advantages over that of the fourth-order Runge-Kutta method in terms of accuracy and reliability. Furthermore, the fourth-order P-T method consumes less CPU time than that of the fourth-order Runge-Kutta method.

Nonlinear static simulation for thermal post-buckling analysis of composite annular system coupled with shape memory alloy fibers

The provided research deals with a mathematical formulation to achieve nonlinear statics for the sandwich annular structure’s thermal post-buckling behavior. The structure’s core is filled by graphene nanoplatelets (GPLs), while its face sheets have been made of SMA/graphite/epoxy. The first-order shear deformation (FOSD) model has been employed for modeling face sheets, and quasi-3D hybrid and quadratic kind of higher-order shear deformation (Q-3D-HSD) model is supposed for core’s in-plane transverse and displacements, respectively. The boundary conditions (BCs) and nonlinear governing equations have been modeled by employing the Hamiltonian, and they have been solved applying the generalized differential quadrature (GDQ) approach. The direct-iterative method has been provided for solving the set of equations, including highly nonlinear factors. Ultimately, the outcomes reveal that the radius ratio of outer to the inner, SMA fiber, GPLs’ configurational factors, and large amplitude would play a vital role in the annular sandwich structure’s thermal post-buckling response. Moreover, the system with GPL-O distribution pattern has maximum thermal post-buckling load while GPL-X type of distribution would result in the minimum thermal post-buckling to thermal buckling ratio for the annular structure.

Thermal postbuckling analysis of sandwich beams with functionally graded auxetic GRMMC core on elastic foundations

This article deals with thermal postbuckling of sandwich beams caused by uniform temperature rise and resting on elastic foundations. The sandwich beam is composed of auxetic graphene-reinforced metal matrix composite (GRMMC) core with negative Poisson's ratio (NPR) and two metal face sheets. The volume fraction of graphene through the thickness domain of the GRMMC core is arranged as a functionally graded (FG) pattern. The thermo-mechanical properties of both metal face sheets and the GRMMC core are assumed to be temperature dependent. The governing equations of the auxetic sandwich beam are formulated based on the higher order shear deformation beam theory coupled with von Kármán-type kinematic nonlinearity. The thermal effects and the beam-foundation interaction are also taken into account in the modeling. Thermal postbuckling solutions are obtained by employing a two-step perturbation approach. The effects of the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and foundation stiffness on thermal postbuckling behavior of sandwich beams with FG auxetic GRMMC core are studied in detail.

Thermal post-buckling analysis of graded sandwich curved structures under variable thermal loadings

Thermal post-buckling analysis of graded sandwich curved structures under variable thermal loadings

Reply to Discussion on “Isogeometric thermal postbuckling analysis of porous FGM quasi-3D nanoplates having cutouts with different shapes based upon surface stress elasticity” [Composite Structures 262 (2021) 113604

Reply to Discussion on “Isogeometric thermal postbuckling analysis of porous FGM quasi-3D nanoplates having cutouts with different shapes based upon surface stress elasticity” [Composite Structures 262 (2021) 113604

Perturbation Method for Thermal Post-Buckling Analysis of Shear Deformable FG-CNTRC Beams with Different Boundary Conditions

This research aims to analyze the thermal buckling and post-buckling of carbon nanotube (CNT) reinforced composite beams. It is assumed that the beam is rested on a nonlinear elastic foundation which contains the Winkler spring, shear layer, and nonlinear spring. Distribution of CNTs across the thickness may be non-uniform which results in a functionally graded media. The elastic properties of the beam are evaluated using the refined rule of mixtures which contains efficiency parameters. Temperature dependency of the constituents is also taken into account. Using three different beam models, namely, first-order, third-order, and sinusoidal theories, the governing equations for the composite beam are established. Three different types of edge supports are considered which are pinned–pinned, clamped–clamped, and clamped–roller. With the aid of the two-step perturbation technique, closed-form expressions are extracted to obtain the elevated temperature as a function of the post-buckling deflection in the beam. Results of this study are compared with the available data in the literature. After that, new results are given to discuss the effects of important factors such as foundation parameters, geometrical characteristics, boundary conditions, the CNT volume fraction, and CNT pattern. It is shown that the critical buckling temperature of pinned–pinned and clamped–roller beams is the same while their post-buckling responses are totally different.

A modified first shear deformation theory for three-dimensional thermal post-buckling analysis of FGM plates

A modified first shear deformation theory for three-dimensional thermal post-buckling analysis of FGM plates

“Isogeometric thermal postbuckling analysis of porous FGM quasi-3D nanoplates having cutouts with different shapes based upon surface stress elasticity” [Composite Structures 262 (2021) 113604

In this contribution, as comments to the paper in Composite Structures 262 (2021) 113604, will be shown that one of the shape function is not correctly described. This shape function is recorded during presenting the displacement field, and it was wrongly used as a part of the transverse shear strains. The correct form of the shape function is explained more deeply in the literature.

Thermal post buckling analysis of smart SMA hybrid sandwich composite plate

Thermal post-buckling analysis of smart sandwich plates has been presented with the incorporation of shape memory alloy (SMA) and shape memory polymer (SMP) in laminated composite structure under uniform temperature distribution. Buckling analysis is based on higher order shear deformation theory (HSDT) with von Karman nonlinearity by finite element method (FEM). Evaluation of critical buckling temperature has been performed under the action of inplane uniform temperature distribution for different boundary conditions, plate’s aspect and thickness ratio, modulus ratio, ply orientations of smart SMA hybrid sandwich composite plate. Shape memory alloys itself acting uniquely under temperature variation and with SMA reinforced SMP laminated composite plate this phenomenon extended further under dynamic temperature condition for thermal buckling behavior. Also SMA with different strain rate and variation in SMA volume fraction is also presented to understand the cumulative buckling behavior.

Isogeometric thermal postbuckling analysis of porous FGM quasi-3D nanoplates having cutouts with different shapes based upon surface stress elasticity

In the current investigation, a surface elastic-based three-dimensional (3D) nonlinear formulation is provided to explore the thermal postbuckling characteristics of porous composite nanoplates made of a functionally graded material (FGM) having a central cutout with different shapes. The surface stress factors are taken into the formulation by choosing the Gurtin-Murdoch theory of elasticity within the framework of a hybrid-type quasi-3D higher-order plate theory. With the aid of the isogeometric solving process using non-uniform rational B-splines as the basis functions, higher-order approximation with a precise geometric modelling of the structure is achieved. In the context of a refined power-law function together with the Touloukian scheme, the porosity-dependent as well as temperature-dependent material properties are achieved. It is portrayed that for a higher value of the material gradient index, the role of surface stress type of size dependency in the thermal postbuckling of porous FGM nanoplates becomes more important. Furthermore, it is deduced that by going to deeper part of the postbuckling regime which results in a higher value of the maximum deflection, the increment in the associated temperature rise caused by the surface stress size effect reduces. Also, it is found that by considering a higher value of the maximum deflection and moving to deeper region of the postbuckling domain, the existence of a central cutout leads to change the trend of the thermal postbuckling equilibrium path especially for a bigger central cutout.

Thermal Nonlinear Buckling of Shear Deformable Functionally Graded Cylindrical Shells with Porosities

In this paper, for the first time, two-term deflection is suggested for nonlinear analysis of shear deformable cylindrical shells and, to the authors’ knowledge, a first investigation on thermal nonlinear buckling behavior of functionally graded material (FGM) cylindrical shells including porosities is presented. Material properties are assumed to be temperature dependent, volume fractions of constituents are graded in the thickness direction according to a power law, and effective properties of porous FGM are estimated according to a modified rule of mixture. Porosities are evenly or unevenly distributed within the shell. Mathematical formulations are based on a first-order shear deformation theory taking into account geometrical nonlinearity and elasticity of in-plane restraints of edges. Two-term deflection and a multiterm stress function are assumed to satisfy simply supported boundary conditions. The Galerkin method and an iteration procedure are employed to evaluate critical buckling temperatures and trace temperature-deflection paths in the postbuckling region. The two-term solution of deflection is a significant suggestion for nonlinear buckling analysis of shear deformable cylindrical shells in general and thermal postbuckling analysis of porous FGM cylindrical shells in particular. This two-term solution includes inherent uniform deflection at the prebuckling state and overcomes mathematically tremendous difficulty in using three-term deflection for shear deformable cylindrical shells. Besides this innovative approach, the obtained results are of great interest for many engineering applications. Unlike the case of mechanical loads, porosities have beneficial influences on the stability of thermally loaded FGM cylindrical shells.

Correction to: Thermal post-buckling analysis of laminated composite plates embedded with shape memory alloy fibers using semi-analytical finite strip method

Correction to: Thermal post-buckling analysis of laminated composite plates embedded with shape memory alloy fibers using semi-analytical finite strip method

Post-buckling nonlinear analysis of sandwich laminated composite plate

Thermal post-buckling analysis of sandwich composite plates has been presented with the incorporation of shape memory alloy (SMA) under uniform temperature distribution by higher order shear deformation theory (HSDT) with von Karman nonlinear kinematics by finite element method (FEM) in MATLAB environment. The validity of the present utilized model is checked by performing validation study also convergence study has been done to select the mesh size to compute the results without affecting the results. Study clearly defines effect of layer variation, layup sequence, uniform temperature variation, and aspect ratio under different boundary conditions (BC) over nondimensional critical buckling temperature (NCBT). Study also clearly indicate the effect of the SMA volume fraction under different ply sequence over NCBT of sandwich composite plate.

Nonlinear Vibration Analyses of Stiffened Composite Panels under Combined Thermal and Random Acoustic Loads

This study using ABAQUS investigates the nonlinear vibration responses when thermal and random acoustic loads are applied simultaneously to the stiffened composite panels. The nonlinear vibration analyses are performed with changing the number of stiffeners, and layup condition of the skin panel. The panel and stiffeners both are modeled using shell elements. Thermal load (ΔT) is assumed to have the temperature gradient through the thickness direction of the stiffened composite panel. The random acoustic load is represented as stationary white-Gaussian random pressure with zero mean and uniform magnitude over the panels. The thermal postbuckling analysis is conducted using RIKS method, and the nonlinear dynamic analysis is performed using Hilber-Hughes- Taylor time integration method. When ΔT = 25.18 ℃ and SPL = 105 dB are applied to the stiffened composite panel, the effect of the number of stiffener is investigated, and the snap-through responses are observed for composite panels without stiffeners and with 1 and 3 stiffeners. For investigation of the effect of layup condition of the skin panel, when ΔT = 38.53 ℃ and SPL = 110 dB are applied to the stiffened composite panel, the snap-through responses are shown when the fiber angle of the skin panel is 0°, 30°, and 60°. Keywords: 보강된 복합재 패널, ìŠ¤ëƒ -스루, 랜덤 음향 하중, ë¹„ì„ í˜• 진동 응답 Keywords: Stiffened Composite Panel, Snap-through, Random Acoustic Load, Nonlinear Vibration Response

Investigation of thermal preloading and porosity effects on the nonlocal nonlinear instability of FG nanobeams with geometrical imperfection

The aim of the present research is twofold. The first is to present a study on nonlinear thermo-mechanical bending and thermal postbuckling analysis of functionally graded (FG) porous perfect/imperfect nanobeam according to the nonlocal elasticity theory. The second, concurrent aim is to address the snap-through phenomenon in the thermally preloaded graded porous nanobeams due to lateral mechanical load. Two types of thermal loading including, uniform temperature rise and heat conduction through the thickness as well as two cases of porosity distribution, including uniform and uneven, are considered. Geometrically imperfect FG porous nanobeam with four different types of immovable boundary conditions is also taken into account. Thermo-mechanical material properties of the porous nanobeam are assumed to be position-dependent according to the modified rule of mixture. The nonlinear equilibrium equations are constructed using the Euler–Bernoulli beam model and von-Kármán type of geometrical nonlinearity. Chebyshev polynomial based Ritz method is utilized into the principle of virtual displacement to obtain the matrix representation of the nonlocal governing equations. Two different strategies, including the Newton–Raphson technique and direct displacement control scheme, are first proposed to extract the nonlinear bending and postbuckling curves of the graded nanobeam. Afterwards, to capture the snapping behavior and trace the path beyond the limit loads of the thermally preloaded nanobeam, the cylindrical arch-length technique is adopted. Numerical results are provided to explore the effect of different parameters such as the power-law index, nonlocal parameter, boundary conditions, porosity distribution, thermal loading, and imperfection amplitude on the nonlinear thermo-mechanical bending and instability of the FG nanobeam.

Thermal Post-buckling Analysis of Laminated Composite Plates Embedded with Shape Memory Alloy Fibers Using Semi-analytical Finite Strip Method

The thermal buckling and post-buckling of geometrically perfect and imperfect hybrid laminated composite plates reinforced with shape memory alloys (SMA) subjected to a uniform thermal loading are investigated by a semi-analytical finite strip method. In this method, because of applying trigonometric functions, the energy integrations can be computed analytically. The first-order shear deformation theory in conjunction with von Karman nonlinear strain–displacement formulation is implemented. The solution procedure is based on minimization of the total potential energy and solving the eigenvalue problem or a set of nonlinear equations by using an iterative Newton–Raphson method for linear buckling and post-buckling analysis, respectively. By using 1-D simplified Brinson’s model, the effect of SMA fibers on thermal buckling and post-buckling of composite plates with various boundary conditions is studied.

Thermal postbuckling analysis of FG-CNTRC doubly curved panels with elastically restrained edges using Reddy's higher order shear deformation theory

For the first time, postbuckling behavior of thick doubly curved panels made of carbon nanotube reinforced composite (CNTRC), under preexisting external pressure and subjected to uniform temperature rise is analyzed in this paper. Carbon nanotubes (CNTs) are reinforced into matrix through functionally graded (FG) distribution patterns, and effective properties of CNTRC are determined according to extended rule of mixture. Formulations are based on a higher order shear deformation theory including Von Karman-Donnell nonlinearity, initial geometrical imperfection and elasticity of tangential constraints of boundary edges. Analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is used to obtain nonlinear load-deflection relation. Taking into account temperature dependence of material properties, postbuckling temperature-deflection paths are traced through an iteration process. The effects of preexisting external pressure, CNT volume fraction, tangential edge constraints, initial geometrical imperfection and curvature ratios on thermal postbuckling behavior of CNTRC doubly curved panels are analyzed through numerical examples. The study reveals that thermally loaded panels experiences a quasi-bifurcation response due to the presence of preexisting external pressure. For the most part, perfect panels are deflected toward convex side at the onset of undergoing thermal load. Particularly, imperfect panels may exhibit a bifurcation type buckling response when imperfection size satisfy a special condition.