Thermal Buckling Behavior Research Articles

Effect Of Volume Fraction On The Thermal Buckling Analysis Of Laminated Composite Plate With Square/Rectangular Cutout

A numerical study was conducted using the finite element method to determine the effects of square and rectangular cutouts on the thermal buckling behavior of a quasi-isotropic [0°/+45°/-45°/90°]2s symmetrically laminated rectangular composite plates. This study addresses the effects of the fiber type and resin type, fiber volume fraction, the size of the square/rectangular cutout, plate aspect ratio (a/b) and plate length/thickness ratio (a/t) on the thermal buckling behavior of the symmetrically laminated rectangular composite plate .Thermal Buckling temperatures were computed for six different fiber - resin combinations i.e Kevlar-epoxy, Kevlar-polyester, Graphite-epoxy, Graphite-polyester, Eglass-epoxy, Eglass-polyester. Results showed that the magnitudes of the critical buckling temperatures increase with increasing fiber volume fraction as well as d/b ratios or cutout size for plates with a square/rectangular cutout. The Graphite-polyester composite plate have highest critical buckling temperatures than all other analyzed various fiber-resin combinations composite plates. The magnitudes of the thermal buckling loads of a rectangular composite plate with square/rectangular cutout decrease with increasing plate aspect ratio (a/b) and plate length/thickness (a/t) ratio irrespective fiber volume fraction.

Thermal Buckling Analysis Of Laminated Composite Plate With Square/Rectangular, Elliptical/Circular Cutout

A numerical study was conducted using the finite element method to determine the effects of square and rectangular cutouts on the thermal buckling behavior of a 16-ply quasi-isotropic graphite/epoxy symmetrically laminated rectangular composite plates. This study addresses the effects of the size of the square/rectangular cutout, elliptical/circular cutout, orientation of the rectangular /elliptical cutout, plate aspect ratio (a/b), and plate length/thickness ratio (a/t) on the thermal buckling behavior of the symmetrically laminated rectangular composite plate .Thermal Buckling temperatures were computed for seven different quasi-isotropic laminate configurations [0°/+45°/-45°/90°]2s, [15°/+60°/-30°/-75°]2s, [30°/+75°/-15°/-60°]2s, [45°/+90°/0°/-45°]2s, [60°/-75°/+15°/-30°]2s, [75°/-60°/+30°/-15°]2s, [90°/-45°/+45/°0°]2s. Results showed that the magnitudes of the critical buckling temperatures increase with increasing cutout positioned angle as well as c/b and d/b ratios for plates with a square/rectangular cutout, elliptical/circular cutout. The symmetrically laminated quasi-isotropic [75°/-60°/+30°/-15°]2s composite plate have highest critical buckling temperatures than all other symmetrically analyzed laminated quasi-isotropic composite plates. The magnitudes of the thermal buckling loads of a rectangular composite plate with square/rectangular cutout, elliptical/circular cutout decrease with increasing plate aspect ratio (a/b) and plate length/thickness (a/t) ratio.

Nonlinear thermal buckling behaviour of laminated composite panel structure including the stretching effect and higher-order finite element

The nonlinear thermal buckling load parameter of the laminated composite panel structure is investigated numerically using the higher-order theory including the stretching effect through the thickness and presented in this research article. The large geometrical distortion of the curved panel structure due to the elevated thermal loading is modeled via Green-Lagrange strain field including all of the higher-order terms to achieve the required generality. The desired solutions are obtained numerically using the finite element steps in conjunction with the direct iterative method. The concurrence of the present nonlinear panel model has been established via adequate comparison study with available published data. Finally, the effect of different influential parameters which affect the nonlinear buckling strength of laminated composite structure are examined through numerous numerical examples and discussed in details.

Thermal Buckling of Nanocomposite Stiffened Cylindrical Shells Reinforced by Functionally Graded Wavy Carbon Nanotubes with Temperature-Dependent Properties

We study the thermal buckling behavior of cylindrical shells reinforced with Functionally Graded (FG) wavy Carbon NanoTubes (CNTs), stiffened by stringers and rings, and subjected to a thermal loading. The equilibrium equations of the problem are built according to the Third-order Shear Deformation Theory (TSDT), whereas the stiffeners are modeled as Euler Bernoulli beams. Different types of FG distributions of wavy CNTs along the radial direction of the cylinder are herein considered, and temperature-dependent material properties are estimated via a micromechanical model, under the assumption of uniform distribution within the shell and through the thickness. A parametric investigation based on the Generalized Differential Quadrature (GDQ) method aims at investigating the effects of the aspect ratio and waviness index of CNTs on the thermal buckling of FG nanocomposite stiffened cylinders, reinforced with wavy single-walled CNTs. Some numerical examples are here provided in order to verify the accuracy of the proposed formulation and to investigate the effects of several parameters—including the volume fraction, the distribution pattern of wavy CNTs, and the cylinder thickness—on the thermal buckling behavior of the stiffened cylinders made of CNT-reinforced composite (CNTRC) material.

Thermal Post-buckling Analysis of Moderately Thick Nanobeams

As a first attempt, the thermal buckling and post-buckling behaviors of moderately thick nanobeams subject to uniform temperature rise are investigated via employing the differential quadrature method (DQM). Considering the von-Karman’s assumptions, governing equations of the nanobeams are derived using the Eringen’s nonlocal elasticity theory in conjunction with the first-order shear deformation beam theory. The differential quadrature method is used to discretize the governing equations. The direct iterative displacement control method is coupled with the DQM to solve the nonlinear system of algebraic equations. Rapid rate of convergence and accuracy of the method for solving the problem are shown, and effects of the small-scale parameters on the thermal buckling and post-buckling behaviors of the nanobeams for different boundary conditions and length-to-thickness ratios are demonstrated.

On buckling and postbuckling behavior of nanotubes

For the first time, the size-dependent thermal buckling and post-buckling behavior of nanotubes made of functionally graded materials (FGMs) with porosities is investigated by using a refined beam theory. This non-classical nanotube model is based on Eringen nonlocal elasticity model which incorporates the small scale effect. Two types of porosity distribution, including even and uneven distribution, are taken into account. The material properties of the nanotubes are temperature-dependent and vary in the radial direction. The size-dependent governing differential equations are derived by employing the generalized variation principle and solved by using a two-step perturbation method. The effects of small scale parameter, porosity volume fraction, the volume fraction index and boundary conditions on thermal buckling and post-buckling of FGM nanotubes are studied by several numerical examples. It can be concluded that the porosity volume fraction and small scale parameter change the buckling and post-buckling behavior of the nanotubes.

Phase-field thermal buckling analysis for cracked functionally graded composite plates considering neutral surface

In this paper, the variational phase field model is adopted to analyze thermal buckling behavior of cracked functionally graded material (FGM) plates. Unlike existing works, the difference between neutral surface and mid-surface of FGM plates is taken into account in the present study. The kinematics of plate is based on first order shear deformation theory, while the crack is simulated by variational phase-field theory. The critical buckling temperature rises of cracked FGM plate is calculated, and the obtained results are then compared with those derived from extended isogeometric analysis by the authors and other numerical methods. We analyze the thermal buckling of cracked FGM plates for both cases: (a) the mid-surface coincides neutral surface, and (b) they are different between each other, and then showing their influence. We also investigate the effects of boundary condition and material properties on thermal buckling of cracked FGM plate. Through these results, it reveals the necessity to consider the difference between neutral surface and mid-surface in thermal buckling analysis.

Size dependent thermal buckling and postbuckling of functionally graded circular microplates based on modified couple stress theory

ABSTRACTIn this article, size-dependent thermal buckling and postbuckling behavior of a functionally graded circular microplate under uniform temperature rise field and clamped boundary conditions is investigated. Material properties are assumed to gradually vary through the thickness according to a simple power law. Equilibrium equations and associated boundary conditions are derived using variational method and based on modified couple stress theory, classical plate theory and von Kármán geometric nonlinearity. The differential quadrature method is used to discretize the governing equations. This technique is accompanied by an iterative method to determine the thermal postbuckling behavior of microplate. Finally, effects of length scale parameter, power law index and ratio of thickness to radius on the thermal buckling and postbuckling behavior of FG circular microplate are investigated.

On the thermal buckling behaviour of laminated composite plates with cut-outs

In this work, the thermal buckling behaviour of laminated plates with rectangular cut-outs is studied using the finite element method. Based upon the classical plate theory, the used finite element is a combination of a linear isoparametric membrane element and a high precision rectangular Hermitian element. After validating the results obtained by the finite element, a parametric study is made using three types of materials commonly used in the industry, namely: the T300/5208 Graphite/Epoxy, the AS4/3501-6 Graphite/Epoxy and the E-glass/Epoxy. The study was about the effect of the size of the cut-outs, the boundary conditions, the stacking sequence and the stress resultants distribution on the critical buckling temperature. The study showed that the critical buckling temperature is strongly affected by the discussed parameters.

A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates

This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.

Thermal buckling analysis of cylindrical shell with functionally graded material coating

As an excellent heat-resistant material with broad potential application, the mechanical behavior of functionally graded material (FGM) is of research focus in many fields. However, the thermal buckling behavior of FGM thin-walled shell has been widely investigated, but little work was done for the cylindrical shell with FGM coating due to more complex material distribution and mathematical expressions. Therefore, the present work mainly carried out the theoretical derivation and buckling behavior analysis for a cylindrical shell with FGM coating subjected to a thermal load. The results show that the theoretical solution of the critical buckling temperature rise is in good agreement with the developed numerical approach. In addition, an empirical engineering formula of the critical buckling temperature rise with a more concise mathematical expression is proposed for solving this practical complex engineering application based on the significant amount of numerical calculation and theoretical analysis.

Buckling and Free Vibration of Nonuniformly Heated Functionally Graded Carbon Nanotube Reinforced Polymer Composite Plate

Buckling and free vibration behavior of functionally graded carbon nanotube reinforced polymer composite plate subjected to nonuniform temperature fields have been investigated using finite element approach. The effective material constants of the plate are obtained using the extended rule of mixture along with efficiency parameters of the carbon nanotube (to include geometry-dependent material properties). Influence of boundary conditions, aspect ratio, functional grading of the carbon nanotube, nonuniform thermal loading on thermal buckling and free vibration behavior of the heated plate are analyzed. It is observed that temperature fields and functional grading are influenced on the critical buckling temperature of the plates. Further, nature of functional grading showed significant change in buckling mode shapes irrespective of the boundary conditions. The first few natural frequencies of the plate under thermal load decreases as the temperature increases and they are influenced significantly by the nature of temperature field. Variations in free vibration mode shapes of the square plates found with not significant change as temperature increases. However, free vibration modes of the rectangular plates are sensitive to the nature of temperature field whenever there is a free edge associated with the boundary condition. Influence of functional grading on the free vibration mode shapes is not significant in contrast with the free vibration natural frequencies. The magnitude of free vibration natural frequencies of functional grade-X type carbon nanotube reinforcement showed higher in comparison with other two types of reinforcements considered here.

Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates

This paper deals with the thermal buckling and postbuckling of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene platelets (GPLs). It is assumed that GPL reinforcements are randomly oriented and uniformly dispersed in each individual GPL-reinforced composite (GPLRC) layer but the concentration follows a layer-wise variation across the plate thickness. The modified Halpin-Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young's modulus of GPLRC layers. Within the framework of the first-order shear deformation theory, the nonlinear governing equations are derived by applying the principle of virtual displacements and then solved by using a differential quadrature-based iteration technique. Parametric studies are conducted to examine the influences of GPL distribution pattern, concentration and geometry, as well as in-plane force on the thermal buckling and postbuckling behaviours. Our results show that distributing more GPLs near the surface layers is capable of reinforcing the thermal buckling and postbuckling performances of GPLRC plates. Whether the thermal buckling and postbuckling resistance increases or decreases with the increases in GPL weight fraction, aspect ratio and width-to-thickness ratio is highly dependent on the GPL distribution pattern.

Thermal buckling behavior of two-dimensional imperfect functionally graded microscale-tapered porous beam

ABSTRACTThis article presents a study on the thermal buckling behavior of two-dimensional functionally graded microbeams made of porous materials. The material composition varies along thickness and length of the microbeam based on the power law distribution. The microbeam is modeled within the framework of Euler–Bernoulli beam theory. The microbeam is considered having variable material composition along thickness. The equations are derived using the modified couple stress theory and the solving process is based on the generalized differential quadrature method. The validity of the results is shown through comparison of the results with the results of other published research.

Thermal buckling analyses of FGM sandwich plates using the improved radial point interpolation mesh-free method

This study reports thermal buckling analyses of functionally graded material (FGM) sandwich plates using an improved mesh-free radial point interpolation method (RPIM). The buckling formulation of FGM sandwich plates is derived from the improved RPIM which employs a new radial basis function enabling the shape functions to be built without any supporting fixing parameters based on the higher-order shear deformation plate theory. Two types of FGM sandwich plates with different composition scheme, i.e. one with FGM skins and homogenous core and the other composed of homogenous skins and FGM core are considered in the analyses. The simulated results by the improved RPIM are compared with the analytical solutions found in the literature for the verification purpose. Detailed parametric studies are then carried out to scrutinize the effects of the volume fraction, plate length-to-thickness ratio, aspect ratio, boundary condition and FGM constituents on the critical buckling temperature changes of the FGM sandwich plates under various types of temperature variation through the thickness. Results demonstrate that the improved mesh-free RPIM can effectively predict the thermal buckling behavior of the FGM sandwich plates.

Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams

The hygro-thermal effects on vibration and buckling analysis of functionally graded beams are presented in this paper. The present work is based on a higher-order shear deformation theory which accounts for a hyperbolic distribution of transverse shear stress and higher-order variation of in-plane and out-of-plane displacements. Equations of motion are obtained from Lagrange’s equations. Ritz solution method is used to solve problems with different boundary conditions. Numerical results for natural frequencies and critical buckling temperatures of functionally graded beams are compared with those obtained from previous works. Effects of power-law index, span-to-depth ratio, transverse normal strain, temperature and moisture changes on the results are discussed.

A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates

A new higher shear deformation theory (HSDT) is presented for the thermal buckling behavior of functionally graded (FG) sandwich plates. It uses only four unknowns, which is even less than the first shear deformation theory (FSDT) and the conventional HSDTs. The theory considers a hyperbolic variation of transverse shear stress, respects the traction free boundary conditions and contrary to the conventional HSDTs, the present one presents a new displacement field which includes undetermined integral terms. Material characteristics and thermal expansion coefficient of the sandwich plate faces are considered to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are supposed as uniform, linear and non-linear temperature rises within the thickness direction. An energy based variational principle is used to derive the governing equations as an eigenvalue problem. The validation of the present work is carried out with the available results in the literature. Numerical results are presented to demonstrate the influences of variations of volume fraction index, length-thickness ratio, loading type and functionally graded layers thickness on nondimensional thermal buckling loads.

Exact solution of thermal buckling and post buckling of composite and SMA hybrid composite beam by layerwise theory

The thermal buckling and post-buckling behavior of laminated composite beam reinforced with Shape Memory Alloy (SMA) wires is explored. The thermo-mechanical behavior of embedded SMA wires is formulated based on one-dimensional Brinson SMA model. Using a variational approach, the Layer-Wise Theory (LWT) of beams is employed to develop the governing equations. The von Karman strain–displacement relations are used to account for the large deflection effects. A closed-form solution of the resulting systems of nonlinear equations is represented. Exemplary case studies are assessed by comparing with available literature. Considering symmetric and antisymmetric layups, the influence of thickness/span ratio, degree of anisotropy, SMA pre-strain and volume fraction upon the buckling and post-buckling of thick composite and hybrid composite beams are examined and discussed in detail.

Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT

This work presents a simplified higher order shear deformation theory (HSDT) for thermal buckling analysis of cross-ply laminated composite plates. Unlike the existing HSDT, the present one has a new displacement field which introduces undetermined integral terms and contains only four unknowns. Governing equations are derived from the principle of the minimum total potential energy. The validity of the proposed theory is evaluated by comparing the obtained results with their counterparts reported in literature. It can be concluded that the proposed HSDT is accurate and simple in solving the thermal buckling behavior of laminated composite plates.

Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory

• Thermal buckling analysis of FGM beams by various theories are presented. • A two-step perturbation method is employed to determine the critical buckling loads and post-buckling equilibrium paths. • The post-buckling equilibrium path for FGM beam with two clamped ends is also of the bifurcation type for any various displacement fields. In the present work, attention is focused on the prediction of thermal buckling and post-buckling behaviors of functionally graded materials (FGM) beams based on Euler–Bernoulli, Timoshenko and various higher-order shear deformation beam theories. Two ends of the beam are assumed to be clamped and in-plane boundary conditions are immovable. The beam is subjected to uniform temperature rise and temperature dependency of the constituents is also taken into account. The governing equations are developed relative to neutral plane and mid-plane of the beam. A two-step perturbation method is employed to determine the critical buckling loads and post-buckling equilibrium paths. New results of thermal buckling and post-buckling analysis of the beams are presented and discussed in details , the numerical analysis shows that, for the case of uniform temperature rise loading, the post-buckling equilibrium path for FGM beam with two clamped ends is also of the bifurcation type for any arbitrary value of the power law index and any various displacement fields.