Thermal Postbuckling Behavior Research Articles

Thermal Buckling and Postbuckling Analysis of Cracked FG-GPL RC Plates Using a Phase-Field Crack Model

A phase-field crack model is developed for numerical analysis of thermal buckling and postbuckling behavior of a functionally graded (FG) graphene platelet-reinforced composite (FG-GPLRC) plate with a central crack. The inclined central crack is represented according to a stable, effective phase-field formulation (PFF) by introducing a virtual crack rotation. The problem is formulated using first-order shear deformation theory (SDT) incorporated with von Kármán geometric nonlinearity. And it is approximated by combining regular Laplace interpolation functions and crack-tip singular functions in the framework of the 2D extended natural element method (XNEM). Troublesome shear locking is suppressed by applying the concept of the MITC (mixed-interpolated tensorial components)3+ shell element to the present numerical method. The results demonstrate the effectiveness of this method in accurately predicting the critical buckling temperature rise (CBTR) and the thermal postbuckling path. In addition, the parametric results reveal that the CBTR and postbuckling path of the FG-GPLRC plate are distinct from those of the FG carbon nanotube-reinforced composite (FG-CNTRC) plate and remarkably affected by the parameters associated with the crack and graphene platelet (GPL).

A meshfree formulation for size-dependent thermal buckling and post-buckling behaviour of porous microplates on elastic foundation subjected to localized heating

The semi-analytical framework is developed for in-plane thermal stresses within the microplates under localized heating. Localized heating is modelled using Fourier Series expansions over the complete domain of the plate. These stresses within the plate are estimated after solving the in-plane thermoelasticity problem using Airy's stress approach. Utilizing these stresses, present work also studies the buckling and post-buckling behaviour of a porous metal foam microplate resting on Winkler and Pasternak elastic foundations. The plate is modelled using Reddy's third-order shear deformation theory (TSDT) and von Kármán geometric nonlinearity, and the size-dependent effects are included using the modified strain gradient theory (MSGT). Galerkin's weighted residual method converts the partial differential equations (PDEs) into algebraic equations. The post-buckling equilibrium path is obtained using the modified Newton-Raphson method. The mode shapes of the microplate for the various configurations of the plate with different boundary conditions due to localized thermal loading are plotted. Also, these mode shapes are compared with the mode shapes of the microplate due to in-plane mechanical loading. The parametric effect of porosity, elastic foundation parameters, thickness of plate, size of plate, boundary conditions and loading concentrations on the buckling and post-buckling behaviour of the plate is studied.

Thermal postbuckling and thermally induced postbuckled flutter of tri-directional functionally graded plates in yawed supersonic flow

The current work examines the thermal postbuckling, aero-elastic flutter and thermally induced postbuckled flutter about a static equilibrium state of tri-directional functionally graded (TFGM) rectangular and tapered plates in yawed supersonic flow. Based on the von Kármán nonlinear strains, the general higher-order shear deformation theory (GHSDT) and the first-order piston theory, the governing equations of motion for TFGM plates in yawed supersonic flow are established via the Hamilton's principle. The isogemetric analysis (IGA), the load continue strategy associated with the Newton Raphson iterative technique are exploited synthetically to capture the postbuckling paths, and then the postbuckled flutter behaviors are acquired with the static equilibrium state being obtained. Comparative and convergence studies are provided to improve reliabilities of the present material model, formulae and code implementations. Subsequently, detailed parametric investigations are carried out to evaluate the influences of material volume fractions, boundary conditions and airflow angles on the thermal postbuckling, aero-elastic flutter and postbuckled flutter behaviors of TFGM plates. The results show that it is the in-plane volume fractions, rather than the thickness volume fraction, that exert a greater influence on the thermal postbuckling and flutter behaviors of TFGM plates. Furthermore, TFGM plates exhibit more diverse postbuckling paths and more complex deformations due to the inhomogeneity of the in-plane material properties compared with z-directional FGM plates.

Buckling failure analysis of storage tanks under the synergistic effects of fire and wind loads

Fire-induced domino effect is one of the main threats to hazardous material storage tanks, and many attempts have been conducted to assess the vulnerability of storage tanks exposed to fire to evaluate domino effect risk. However, past research ignored the influence of wind load on the thermal buckling behavior of storage tanks exposed to fire, which may underestimate the risk of exposed tanks. This paper thus conducts a numerical simulation of the thermal buckling behavior of steel vertical dome storage tanks under the synergistic effect of static wind loads and thermal effects. The effects of wind parameters and heat radiation parameters on the thermal post-buckling behavior and the time to failure (ttf) of storage tanks are investigated to analyze the synergistic effects of fire and wind loads. By comparing the circumferential and meridional stresses before and after the thermal post-buckling stage, it is found that under the disturbing effect of the positive wind pressure load, the thermal post-buckling of the tanks on downwind occurs earlier and more severe. Besides, the effects of wind angle, fire location height, and diameter on buckling damage were investigated. The comparative analysis of different scenarios shows that the tanks in the windy scenario are more prone to thermal post-buckling, and the deformation is intensified, with an increased likelihood of failure.

Thermal Postbuckling Analysis of Thin Uniform Square Plates On Winkler Foundation - Effect of Use of Green’s Strain-Displacement Relations

A new simple formulation is developed in this paper, to predict the realistic thermal postbuckling behavior of the square plates, on Winkler foundation. If the plate is subjected to a uniform temperature rise, and also undergoes large deflections, mechanical equivalent inplane compressive, and tensile loads are developed, with the condition of the inplane immovability of the normal edge displacements of the plate. The nature of the distribution of these inplane compressive and tensile loads are similar, but have different magnitudes, which act along the x- and y- directions of the plate. The use of the Green’s nonlinear strain-displacements relations, which do not impose any restriction on the magnitude of the large deflections, to predict the realistic thermal postbuckling loads. The thermal postbuckling results of the plates obtained from this formulation, are validated indirectly, as the corresponding results are not available in the literature, with those of the columns without the elastic foundation. For the non-zero values of the foundation parameter, the present numerical results of the plates, with respect to the central deflection, show the proper physical trends of the nonlinearity, and demonstrate the simplicity of the present formulation.

Prediction of Thermal Postbuckling Behavior Of Uniform Shear Flexible Column Undergoing Large Lateral Deflections Through An Intuitive Formulation

This paper presents a simple intuitive formulation to predict the thermal postbuckling behavior of uniform shear flexible columns, subjected a uniform temperature rise from its stress free condition, undergoing large lateral deflections. The two ends of the columns are restrained to move axially, so that a mechanical equivalent of the constant compressive load is developed, due to the increase in temperature. The proposed formulation is based on the use of nonlinearities existing in both the axial displacement and lateral deflection, which differs from the von-Karman type nonlinearity due to the moderately large lateral deflections only. In this paper, a simple analytical formula is developed to predict the thermal post buckling behavior of columns, considering both the nonlinearities. The numerical results obtained from the developed intuitive formulas match very well, for the slender columns. Since, there are no results available in the literature, to compare the current results with the case of the shear flexible columns, the authors are of the opinion that the trends of these results, given in this paper, show that there is a reasonable probability that the present results are reliable.

An Investigation of Thermal Postbuckling of Uniform Columns on Variable Winkler Foundation by Using Rayleigh-Ritz and Heuristic Formulations

An investigation of the two different formulations, to predict the thermal buckling and postbuckling behavior of uniform hinged-hinged and clamped-clamped columns on the elastic variable Winkler foundations, is presented in this paper. The first one is the Rayleigh-Ritz and the second one is relatively simple heuristic formulation. Though the effect of the uniform Winkler foundation is thoroughly studied for the columns and other structural members, the variable Winkler foundation is not received much attention by the researchers. In the present investigation, two types of variable Winkler foundations, wherein the first and second terms of the foundations contain a constant and the variable parts, which varies with two types of sine functions, are considered. It is shown that the expressions obtained from the two formulations, for the ratios of the thermal postbuckling to the buckling load parameters are, not only the same but also validate the results, for the specified values of the central deflection and foundation stiffness parameters. A comprehensive set of numerical results are presented in this investigation, to obtain the thermal postbuckling behavior of uniform hinged-hinged and clamped-clamped columns on the variable Winkler foundations.

Thermal Postbuckling of Heated Uniform Columns Considering Green Nonlinearity: A Novel Liner Finite Element Formulation

Thermal postbuckling behavior of uniform, heated columns is presented, by using a novel linear Finite Element (FE) formulation. In this investigation, the general Green axial nonlinear strain- displacement relation is used, instead of the popularly used simpler von-Karman nonlinearity, which is a subset of Green nonlinearity. In the earlier complex nonlinear FE formulations, time consuming iterative or step-by-step methods are used to obtain the solution for thermal postbuckling. In the novel FE formulation, normally used FES , for performing linear buckling analysis, is proposed to obtain thermal postbuckling loads. The nodal degrees of freedom are deflection and its first derivative with respect to the axial coordinate. The geometric nonlinearity is incorporated through the tensile loads induced, with axially restrained ends of the column, due to large deflections. The effectiveness of the novel FE formulation is demonstrated, from the numerical results obtained, in terms of the ratio of thermal postbuckling to buckling loads, for specified reference deflection and slenderness ratios, of the columns with different boundary conditions. The numerical results reveal some interesting phenomena of thermal postbuckling behavior of columns.

Re-examination of nonlinear vibration, nonlinear bending and thermal postbuckling of porous sandwich beams reinforced by graphene platelets

This paper re-examines the nonlinear free vibration, nonlinear bending and thermal postbuckling behaviors of porous sandwich beams with graphene platelets (GPL) reinforcements rested on elastic foundations. We remove the equivalent isotropic model (EIM) and introduce an inhomogeneous model. The shear modulus together with the Young’s moduli for porous GPLRC core is determined by a generic Halpin–Tsai model with porosity. Mechanical properties of both porous GPLRC core and metal face sheets are temperature dependent. Based on the framework of higher order shear deformation beam theory, the motion equations of porous sandwich beams with GPL reinforcements are established. In the modeling, the von Kármán kinematic nonlinearity, beam-foundation interaction and thermal effect are considered. By employing the two-step perturbation method, the analytical solutions are obtained for the nonlinear vibration and nonlinear bending as well as thermal postbuckling problems. Numerical investigations are performed for comparing the results obtained from the EIM and the present model. The outcomes reveal that the EIM is invalid for linear free vibration, thermal buckling and postbuckling analyses of porous sandwich beams with GPL reinforcements, but the EIM is valid in some cases for nonlinear bending and nonlinear vibration analyses of the same beam.

Arbitrary temperature gradient in thermal-postbuckling behavior of polymer nanocomposites reinforced by boron nitride nanotubes

Polymer nanocomposites reinforced by boron nitride nanotubes (BNNTs) have great potential for use in a wide variety of thermal environments. A closed-form solution for nonlinear bending and thermal-postbuckling behavior of BNNT-reinforced nanocomposite beams under arbitrary temperature gradient in the thickness and length directions is presented for the first time. The uniform and functionally graded (FG) distributions of BNNTs through the thickness of macro-or micro-sized beams are considered. For constant temperature or constant heat flux conditions at two ends of the beam, thermal analysis is carried out to obtain temperature field ΔTx,z using the two-dimensional heat conduction equation and the assumption of arbitrary variation in the z direction. The governing equations of modified couple stress Timoshenko beam theory with von Kármán geometric nonlinearity are derived for BNNT-RC beams subjected to thermomechanical loads. Applying change of variable technique, the governing equations are exactly solved to develop closed-form expression for nonlinear transverse deflection. Finally, parametric study is performed to investigate the effects of length scale parameter, aspect ratio (L/h), distribution of BNNTs, and temperature gradient on the nonlinear bending and postbuckling equilibrium paths. It is shown that the thermal-buckling behavior of clamped and cantilever beams is completely different. Under thermomechanical loading, an initial snap-through buckling behavior is observed in the cantilever beam, while there exist both stable and unstable configurations in the static equilibrium path of clamped beam. Moreover, it is found that the assumption of parabolic variation of temperature through thickness is not compatible with real situations, since the temperature field is obtained as harmonic functions with very short wavelengths in the length direction.

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.

Numerical investigation of thermal buckling and post-buckling behavior of an EN AW 6016-T4 car roof assembled in a steel body-in-white

The automotive industry is undergoing significant changes driven by factors such as reducing carbon dioxide emissions, advancing technology, evolving regulations, and the emergence of new energy sources. Lightweight materials, particularly aluminum alloys, are being extensively researched and integrated into vehicles to reduce weight and improve performance. However, the heating process during vehicle production can cause thermal buckling in thin aluminum alloy structures, affecting their appearance and quality. While thermal buckling has been studied in other industries, research in the automotive sector, particularly for non-structural parts like car roofs, is limited. This study uses numerical simulation to predict thermal buckling and post-buckling behavior of a EN AW 6016-T4 alloy car roof assembled in a predominantly steel body-in-white. The research findings indicate that roof buckling occurs at a relatively low temperature difference of approximately 60 °C, which is lower than the maximum temperatures experienced during the painting phases in the automotive industry. Consequently, undulations in the roof's shape become apparent, underscoring the importance of design modifications to ensure visual conformity. Validation through physical testing confirms the model's accuracy, providing valuable insights for designing lightweight structures with improved performance and aesthetics.

Nonlinear bending and thermal postbuckling of thermoplastic composite laminated plates under temperature variation

Carbon fiber reinforced thermoplastic composites (CFRTPCs) have received growing attentions in various engineering sectors. This paper proposes a physical model to report new features of CFRTPC laminated plates undergoing thermo-mechanical loads. The experiment-based approach is applied to determine the temperature-dependent and strain-dependent stress–strain relations of CFRTPC and further to predict the nonlinear bending responses and thermal postbuckling behaviors of CFRTPC laminated plates. Two cases, the nonlinear bending of CFRTPC laminated plates bearing a uniform pressure under temperature variation and the thermal postbuckling of CFRTPC laminated plates caused by an ambient temperature rise, are analyzed. The numerical investigations are carried out on [45/−45]s CFRTPC laminated plates. The influences of temperature variation, geometric parameters and boundary conditions of the CFRTPC laminated plates on nonlinear bending deflection and moment together with on the thermal postbuckling behaviors are compared in detail.

Thermal Buckling and Postbuckling Behaviors of Couple Stress and Surface Energy-Enriched FG-CNTR Nanobeams

Small-sized structural elements such as beams, plates, and shells are usually used as nanomechanical resonators, nanoscale mass sensors, nanoelectromechanical actuators, and nanoenergy harvesters. At the nanoscale, the structures usually possess a high surface area-to-bulk volume ratio, leading to the free energy related to surface atoms becoming considerable compared to that of the bulk part. Earlier reports indicated several physical reasons for size-dependent phenomena, e.g., nonlocal stress, surface energy, and couple stress. To provide an in-depth insight into the mechanical behavior of small-scale structures, size-dependent continuum models including two or more physical factors have attracted the attention of the academic community. This research analyzes the thermal buckling and postbuckling characteristics of functionally graded carbon nanotube-reinforced (FG-CNTR) nanobeams with a tri-parameter, nonlinear elastic foundation and subjected to a uniform temperature rise. Chen-Yao’s surface energy theory and Yang’s symmetrical couple stress theory are combined to capture two types of size effects in nanobeams. The postbuckling model is formulated based on the Euler–Bernoulli deformation hypothesis and Euler–Lagrange equation. Using a two-step perturbation technique, the related postbuckling equilibrium path is determined. In numerical analysis, the impacts of surface energy, couple stress, elastic foundation, boundary conditions, geometric factor, layout type, and volume fraction of CNTs on the thermal buckling and postbuckling behaviors of nanobeams are revealed. It is indicated that considering couple stress or surface energy can lead to a significant increase in the postbuckling stability of nanobeams compared to the case in which it is not considered. In addition, there is a reverse competition between couple stress or surface energy effects on the thermal buckling responses of nanobeams. As the temperature rise will cause the material elastic moduli softening, the thermal buckling load–deflection curves of nanobeams with the temperature-independent case are much higher than those with the temperature-dependent cases.

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.

Nonlocal nonlinear static/dynamic snap-through buckling and vibration of thermally post-buckled imperfect functionally graded circular nanoplates

The bi-stability characteristics of the post-buckled plates have demonstrated extensive potential applications for energy harvesting and vibration isolation. In this article, at first, thermal post-buckling, nonlinear bending, and vibration behavior of the functionally graded (FG) circular nanoplates in bifurcation buckling are investigated according to nonlocal elasticity theory. Then, the nonlinear static/dynamic snapping phenomena and free vibration responses of the thermally post-buckled nanoplate subjected to static and sudden types of mechanical load are presented. For this aim, the equations of motion in conjunction with the von-Kármán nonlinearity and geometrical imperfection are established in the framework of Hamilton's principle. In addition, two distinct cases of temperature distribution as well as two types of edge conditions are taken into consideration. The equations of motion are discretized using the Chebyshev-Ritz procedure along with three different numerical algorithms. To evaluate the nonlinear dynamic snap-through buckling, the Newmark time integration scheme is adopted. Next, by means of the Budiansky-Roth criterion and the phase-plane approach, the dynamic snap-through loads are identified. A set of parametric studies is presented to provide an insight into influences of the nonlocal parameter, geometrical imperfection, gradient index, and edge supports on the static and dynamic characteristics of the nanosystem.

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.

Influence of couple stress size dependency in thermal instability of porous functionally graded composite microplates having different central cutouts

In the present study, the isogeometric numerical solving process incorporating non-uniform rational B-splines is put to use to analyze the size-dependent thermal postbuckling behavior of porous functionally graded (FG) microplates having a central cutout with different shapes. Accordingly, the modified couple stress continuum elasticity is employed within the framework of a hybrid-type quasi-3D higher-order plate theory to take the through-thickness deformations into consideration by only four variables. On the basis of a refined power-law function together with the Touloukian scheme, the porosity-dependent as well as temperature-dependent material properties are achieved. The couple stress-based thermal postbuckling equilibrium paths are acquired corresponding to various geometrical and material parameters and different boundary conditions. It is found that the gap between thermal postbuckling equilibrium paths relevant to various patterns of the porosity dispersion is a bit higher for the couple stress-based case than the classical one. Furthermore, it is indicated that a central cutout causes to change the trend of the load-deflection response that leads to decrease the initial thermal postbuckling strength, while it enhances the microplate strength in deep thermal postbuckling region.

Thermal post-buckling analyses of magneto-electro-elastic laminated beams via generalized differential quadrature method

The present paper is concerned with the thermal post-buckling behaviors of magneto-electro-elastic laminated beams. Timoshenko beam theory accompanying the von Kármán geometric nonlinearity is considered to model the beams. Temperature and magneto-electric fields are obtained based on satisfying the interfacial continuity conditions and corresponding boundary conditions, and then introduced into the stress-strain constitutive relationships. Afterwards, three governing equations of motion are established with respect to the generalized kinematical variables according to Hamilton's principle, and solved by the generalized differential quadrature method and pseudo-arc length continuation technique. The numerical results aim at the studies on thermal post-buckling paths, post-buckling vibration characteristics and magneto-electric potential responses, the effects on which the lay-up modes, thermal load types and magneto-electric fields exert are discussed.

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.