Thermal Buckling Analysis Research Articles

Thermal Buckling Analysis of Porous Conical Shell on Elastic Foundation

In this research, the thermal buckling analysis of a truncated conical shell made of porous materials on elastic foundation is investigated. The equilibrium equations and the conical shell`s stability equations are obtained by using the Euler`s and the Trefftz equations .Properties of the materials used in the conical shell are considered as porous foam made of steel, which is characterized by its non-uniform distribution of porous materials along the thickness direction. Initially, the displacement field relation based on the classical model for double-curved shell is expressed in terms of the Donnell`s assumptions. Non-linear strain-displacement relations are obtained according to the von Karman assumptions by applying the Green-Lagrange strain relationship. Then, performing the Euler equations leads obtaining nonlinear equilibrium equations of cylindrical shell. The stability equations of conical shell are obtained based on neighboring equilibrium benchmark (adjacent state). In order to solve the stability equations, primarily, due to the existence of axial symmetry, we consider the cone crust displacement as a sinusoidal geometry, and then, using the generalized differential quadrature method, we solve them to obtain the critical temperature values of the buckling Future. In order to validate the results, they compare with the results of other published articles. At the end of the experiment, various parameters such as dimensions, boundary conditions, cone angle, porosity parameter and elastic bed coefficients are investigated on the critical temperature of the buckling.

Mechanical and thermal buckling analysis of laminated composite plates

The mechanical and thermal buckling analysis of laminated composite plates is presented in this document. Different theories of thick plates taking into account the parabolic distribution of transverse shear stresses and satisfying the condition of zero shear stresses on the top and bottom surfaces without using shear correction factor are presented and a comparison between the results obtained by these theories is also illustrated. The high order nonlinear stress-displacement relation of the plates was taken into consideration. The principle of potential energy is used to obtain the equations of equilibrium. The closed-form solutions of symmetric and antisymmetric cross-ply are obtained using Navier solution. Using math software Maple, the temperatures and the critical loads of buckling are determined. Finally, a parametric study of the influence of the various parameters such as: mode of buckling, the geometrical ratios a / b and a / h, Young's modulus, Coefficient of thermal expansion, loading type, the orientation of the fibers and the number of layers on the critical buckling temperature and the critical buckling charge is shown and discussed. Numerical results indicate that deformation due to transverse shear has a significant effect on both mechanical and thermal behavior of buckling of laminated simply supported plates.

Buckling and postbuckling behavior of shell type structures under thermo mechanical loads

The thermo mechanical buckling and post-buckling behavior of layered composite shell type structure are considered with the finite element method under the combination of temperature load and applied mechanical loads. To account for through-thickness shear deformation effects, the thermal elastic, and higher-order shear deformation theory is used in this study. The refined higher order theories, that takes into account the effect of transverse normal deformation, is used to develop discrete finite element models for the thermal buckling analysis of composite laminates. Attention in this study is focused on analyzing the temperature effects on buckling and post-buckling behavior of thin shell structural components. Special attention in this paper is focused on studying of values of the hole in curved panel on thermal buckling behavior and consequently to expend and upgrade previously conducted investigation. Using finite element method, a broader observation of the critical temperature of loss of stability depending on the size of the hole was conducted. The presented numerical results based on higher-order shear deformation theory can be used as versatile and accurate method for buckling and post-buckling analyzes of thin-walled laminated plates under thermo mechanical loads.

A novel general higher-order shear deformation theory for static, vibration and thermal buckling analysis of the functionally graded plates

This paper proposes a new general framework of higher-order shear deformation theory (HSDT) and solves the structural responses of the functionally graded (FG) plates using novel exponential shape functions for the Ritz method. Based on the fundamental equations of the elasticity theory, the displacement field is expanded in a unified form which can recover to many different shear deformation plate theories such as zeroth-order shear deformation plate theory, third-order shear deformation plate theory, various HSDTs and refined four-unknown HSDTs. The characteristic equations of motion are derived from Lagrange’s equations. Ritz-type solutions are developed for bending, free vibration and thermal buckling analysis of the FG plates with various boundary conditions. Three types of temperature variation through the thickness are considered. Numerical results are compared with those from previous studies to verify the accuracy and validity of the present theory. In addition, a parametric study is also performed to investigate the effects of the material parameters, side-to-thickness ratio, temperature rise and boundary conditions on the structural responses of the FG plates.

Thermal vibration and nonlinear buckling of micro-plates under partial excitation

In this study, a finite element formulation is proposed to study bending, thermal vibration, and buckling behavior of a modified couple stress-based micro-plate under partial piezoelectric excitation. To this end, the micro-plate is modeled using the classical plate theory (CPT) in conjunction with von Kármán nonlinear strains. The modified couple stress theory is employed to take into account the size-dependent behavior of the system. The nonlinear equations of motion are derived using Hamilton's principle. In order to obtain numerical solutions to the problem, the displacement finite element model is developed. A parameter study is conducted to study the effects of different parameters, such as temperature rise, material length parameter scale (MLSP), boundary conditions, aspect ratio, and piezoelectric layers configurations on nonlinear behavior of micro-plates. The results are divided into three separate sections: static bending analysis, thermal vibration analysis, and thermal buckling analysis; in each section, the accuracy of the model is checked by comparing the results with the ones reported in the literature. Obtained results show that the bending behavior of the micro-plate is influenced by the size effects and piezoelectric configurations; furthermore, it is observed that applied voltage to the piezoelectric layers and temperature rise affect the fundamental frequency of the system. Finally, the effect of piezoelectric layers on the buckling behavior of the model is studied; the results show that the fully covered model is less prone to buckling under the thermal loading cases. The proposed model provides good control over the mechanical performance of plate-like components, which makes the model widely applicable in the design and optimization of Micro-Electro-Mechanical-Systems (MEMS).

Analysis of orthotropic plates by the two-dimensional generalized FIT method

In this study, the two-dimensional generalized finite integral transform(FIT) approach was extended for new accurate thermal buckling analysis of fully clamped orthotropic thin plates. Clamped-clamped beam functions, which can automatically satisfy boundary conditions of the plate and orthogonality as an integral kernel to construct generalized integral transform pairs, are adopted. Through performing the transformation, the governing thermal buckling equation can be directly changed into solving linear algebraic equations, which reduces the complexity of the encountered mathematical problems and provides a more efficient solution. The obtained analytical thermal buckling solutions, including critical temperatures and mode shapes, match well with the finite element method (FEM) results, which verifies the precision and validity of the employed approach.

Vibration and thermal buckling analysis of rotating nonlocal functionally graded nanobeams in thermal environment

A new nonlocal model for free vibration and thermal buckling analysis of rotating temperature-dependent functionally graded (FG) nanobeams in thermal environment is developed by introducing an axial nonlinear second-order coupling deformation based upon the Eringen's nonlocal elasticity theory (ENET) and Euler-Bernoulli beam theory (EBT). Material properties of FG nanobeams are assumed to be through-thickness symmetric and the temperature distribution is uniform in the thickness direction. The Hamilton's principle is utilized to derive the governing equations and associated boundary conditions of the nonlocal rotating FG nanobeam model considering thermal, small-scale and centrifugal stiffening effects. The nonlocal governing differential equations are transformed into algebraic eigenvalue equations evaluating the vibration and buckling properties through the Galerkin method. The validity and accuracy of the present nonlocal model are verified by convergence and comparative studies. Numerical results are presented to investigate the influences of dimensionless angular velocity, hub radius ratio, temperature change, material gradient index, slenderness ratio and nonlocal parameter on the natural frequencies and critical buckling temperatures of rotating FG nanobeams. The obtained results clearly show that these effects significantly affect the thermal buckling and vibrational behaviors of rotating FG nanobeams.

Thermal buckling and dynamic characteristics of composite plates under pressure load

The effect of geometrical nonlinearities due to pressure load on the thermal buckling and dynamic characteristics of composite plates are investigated in this paper, which is the main contribution of this research work. The mechanical behavior of the plate is described with the first-order shear deformation theory. The geometrical nonlinearity due to both thermal effect and pressure load is introduced in the finite element model of the plate via additional stiffness matrices. Thermal buckling and modal analysis of a four-sided simply supported rectangular composite plate under different pressure fields are conducted. Numerical results show that both the mode frequencies and critical buckling temperature of the plate rise with the increase of the pressure. The vibrational mode shapes change with the gradient pressure load field. The maximum buckled deflection point moves from the center to the place where is easier to reach compressive stress state under uniform thermal load. The pressure distribution has a significant effect on the buckling mode shapes of the plate.

Buckling behavior of porous CNT-reinforced plates integrated between active piezoelectric layers

This work presents the buckling resistance of a novel active multidisciplinary sandwich plate (AMSP) under in-plane mechanical load or temperature change. The proposed sandwich plate includes an advanced porous core reinforced with carbon nanotubes (CNTs) integrated between two active piezoelectric faces. Functional graded (FG) profiles are considered for the dispersions of CNTs and porosity along the thickness of core layer. In addition, the effect of CNT agglomeration in core layer on the buckling resistance of the proposed AMSP has been studied by employing Eshelby-Mori-Tanaka (EMT)'s approach. A third order shear deformation theory (TSDT) of plates is adopted to obtain governing Eigen value equations for the thermal and mechanical buckling analyses of AMSP. The critical buckling resistance of each analysis has been extracted from the governing equations through a developed mesh-free solution based on moving least squares (MLSs) shape functions. The impacts of porosity, CNTs and geometrical dimensions on the buckling resistance of AMSPs have been investigated. The results show that embedding porosity in core results in a slight reduction in mechanical responses and a significant improvement in thermal buckling resistance. Moreover, reinforcing core layer with CNTs leads to remarkable drop and increase in thermal and mechanical buckling resistances, respectively. However, the formation of CNT agglomerations significantly reduces such CNTs impacts.

Thermal Buckling Analysis of Functionally Graded Euler-Bernoulli Beams with Temperature-dependent Properties

Thermal buckling behavior of functionally graded Euler-Bernoulli beams in thermal conditions is investigated analytically. The beam with material and thermal properties dependent on the temperature and position is considered. Based on the transformed-section method, the functionally graded beam is considered as an equivalent homogeneous Euler-Bernoulli beam with an effective bending rigidity under an eccentric thermal load. Then, the thermal elastic buckling equation associated with the bending deflection about the neutral axis is established. The easily usable closed-form solutions for the critical thermal buckling temperature of functionally graded beams under uniform and non-linear temperature rise are obtained and used to calculate the thermal buckling temperature. Some results are evaluated and compared with those by other investigators to validate the accuracy of the presented method. The effects of material compositions, temperature-dependent material properties, slenderness ratios and restraint conditions on thermal buckling behaviors are discussed. It is believed that the proposed model provides engineers and designers an easy and useful method to investigate the effects of various parameters affecting the thermal buckling characteristics of functionally graded beams.

A Parametric Study on the Elliptical hole Effects of Laminate Composite Plates under Thermal Buckling Load

AbstractIn this study, a thermal buckling analysis of laminate composite square plate was performed with elliptical hole cutout using the finite element method. Graphite/Epoxy laminate plate used in this study is symmetrical stacking sequence plate [(0/90)2]s. This laminate square plate was subjected to temperature loading with clamped support on all edges. Moreover, the parameters considered were fiber orientation (θ), a/b ratio (elliptical hole), elliptical hole inclination (φ), thermal expansion coefficient ratio (α1/α2), and thickness of plates (t). The results showed that as the thermal expansion coefficient ratio changes, the elliptical hole ratio and the elliptical hole inclination have inconsequential effects on the performance of the resistance of laminate composite plates. The maximum values of thermal buckling amplification factor were obtained when the ratio a/b = 1.0, which is a circle cutout,while the minimum values were obtained when the ratio a/b = 0.5, regardless of the thickness of plates. Moreover, the plate with elliptical or circle cutout hole provides about 4% to 9% higher buckling resistance than that of the plate without hole cutout, because when subjected to temperature loading the plate with hole can release stress better than the plate without hole.

Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

Nonlinear thermal buckling and postbuckling analysis of bidirectional functionally graded tapered microbeams based on Reddy beam theory

In the present study, the nonlinear thermal buckling, postbuckling, and snap-through phenomenon of higher-order shear deformable tapered bidirectional functionally graded (BDFG) microbeams are comprehensively investigated under different types of thermal loading, for the first time. The thermomechanical properties of the BDFG microbeam are assumed to be functions of temperature, axial, and thickness directions. Reddy’s parabolic shear deformation beam theory with the von Karman nonlinearity is employed to derive the variable coefficient governing nonlinear differential equations on the basis the physical neutral surface concept. Size-dependent effect is captured in the formulation employing the modified couple stress theory. The generalized differential quadrature method (GDQM) is used to discretize the motion equations considering different boundary conditions. The resulting system of nonlinear algebraic equations is solved iteratively using Newton’s method. Theoretical analysis and numerical results indicate that, depending on the shear deformation beam theory, boundary conditions, and the type of thermal load, the response of the BDFG microbeam may be of the bifurcation or snap-through buckling type of instability. Numerical parametric studies are conducted to explore the influences of thermal load type, material property gradient indexes, boundary conditions, material temperature dependency, taperness ratio, and microstructural length scale on critical thermal buckling load, thermal postbuckling, and equilibrium paths of the BDFG microbeam.

Vibration and thermal buckling analyses of three-layered centrosymmetric piezoelectric microplates based on the modified consistent couple stress theory

In this study, free and forced vibration investigations and thermal buckling analysis of three-layered centrosymmetric piezoelectric microplates are examined. To model the size effects, the size-dependent consistent couple stress theory is used. To be compatible with the modified coupled stress theory, a modification is proposed to apply to the consistent couple stress theory. Resorting to the Navier’s approach, the governing equations are treated in the case of simply supported boundary conditions to extract the free and forced vibration outcomes and the thermal buckling numerical results. The verifications demonstrate the effectiveness of the proposed modification. The effects of the material length scale parameter and the flexoelectricity coefficient on the findings are investigated. Moreover, the closed- and open-circuit condition impacts on the free and forced vibration and the thermal buckling analyses are studied.

Thermo-elastic buckling and post-buckling analysis of functionally graded thin plate and shell structures

In this paper, we extend the Kirchhoff–Love model to thermal buckling and post-buckling analysis of functionally graded structures. The kernel idea of the proposed model consists of the consideration of large displacements and finite rotation to accurately model the thermal effects on buckling and post-buckling behavior of such structures. Both uniform and nonuniform temperature distributions are considered. Material properties of the FG structures are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. The effectiveness and usefulness of the proposed model are highlighted through different numerical examples, and the effects of the volume fraction exponent, thermal loads, length-to-thickness ratio, boundary conditions and geometrical parameters on the buckling and post-buckling behavior of FGM structures are also examined.

Transient instability analysis of viscoelastic sandwich CNTs-reinforced microplates exposed to 2D magnetic field and hygrothermal conditions

Transient size-dependent mechanical and thermal buckling analyses of sandwich microplates with viscoelastic core and single-walled carbon nanotubes (CNTs)-reinforced face sheets are introduced in this paper. The CNTs are uniformly distributed or functionally graded (FG) through the thickness of the face layers. The viscoelastic sandwich microplate is resting on three-parameter viscoelastic foundations that modeled according to the viscoelastic Kelvin-Voigt model with a shear layer. Effects of a 2D magnetic field as well as hygrothermal conditions on the present analyses are studied. The modified couple stress model containing one material length scale parameter is employed to capture the small scale effect. A body force (Lorentz force) is deduced from Maxwell’s magnetic equations, that is applied to each particle of the structure. The higher-order shear deformation plate theory with four unknowns is utilized to describe the displacement field. The stability equations are obtained using the principle of virtual displacement. By applying Navier method, the stability equations are solved to obtain the mechanical and thermal buckling of viscoelastic sandwich microplates. Various numerical examples are presented including the effects of the length scale parameter, moisture concentration, magnetic field parameter and other parameters on the buckling of the viscoelastic FGCNTs-reinforced sandwich microplates.

Applying isogeometric approach for free vibration, mechanical, and thermal buckling analyses of functionally graded variable-thickness blades

This article presents free vibration and buckling analyses of functionally graded blades with variable thickness subjected to mechanical and thermal loading using isogeometric analysis as a powerful numerical method. The proposed method is based on deployment of Hamilton’s principle to the two-dimensional kinematics of blades. The governing equations are derived in the context of a modified form of higher order shear deformation plate theory that merely needs C0-continuity (C0-higher order shear deformation plate theory). Without the necessity of defining a shear correction factor, the theory can accurately predict the solution for different thickness-to-length ratios. The numerical predictions for the buckling loads and natural frequencies are successfully compared with the available solutions in the published articles and in the lack of relevant results, finite element analysis using ANSYS is used for verification of the model. The effects of variable thickness and aspect ratio on the natural frequencies and mode shapes known as the frequencies loci veering phenomena are assessed for the first time, which is an important design factor for the blades. The proposed method uses non-uniform rational B-spline element, which is able to approximate linear and nonlinear thickness distribution and the couple modes with an excellent numerical consistency. The influences of aspect ratio, thickness variation, taper ratio, volume fraction exponent, and boundary conditions on the free vibration and buckling of variable-thickness functionally graded blades are also examined.

Application of nonlocal strain–stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell

In this article, thermal buckling and frequency analysis of a size-dependent laminated composite cylindrical nanoshell in thermal environment using nonlocal strain–stress gradient theory are presented. The thermodynamic equations of the laminated cylindrical nanoshell are based on first-order shear deformation theory, and generalized differential quadrature element method is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The results show that by considering C–F boundary conditions and every even layers’ number, in lower value of length scale parameter, by increasing the length scale parameter, the frequency of the structure decreases but in higher value of length scale parameter this matter is inverse. Finally, influences of temperature difference, ply angle, length scale and nonlocal parameters on the critical temperature and frequency of the laminated composite nanostructure are investigated.

Thermal and thermomechanical buckling of shear deformable FG-CNTRC cylindrical shells and toroidal shell segments with tangentially restrained edges

This paper presents a simple and effective analytical approach to investigate buckling behavior of carbon nanotube-reinforced composite (CNTRC) cylindrical shells and toroidal shell segments surrounded by elastic media and subjected to elevated temperature, lateral pressure and thermomechanical load. The properties of constituents are assumed to be temperature-dependent, and effective properties of CNTRC are estimated according to extended rule of mixture. Carbon nanotubes (CNTs) are reinforced into matrix material such in a way that their volume fraction is varied in the thickness direction according to functional rules. Formulations are established within the framework of first-order shear deformation theory taking surrounding elastic media and tangential elasticity of edges into consideration. The solutions of deflection and stress function are assumed to satisfy simply supported boundary conditions, and Galerkin method is used to derive expressions of buckling loads. In thermal buckling analysis, an iteration algorithm is employed to evaluate critical temperatures. The effects of CNT volume fraction and distribution patterns, degree of in-plane edge constraints, geometrical parameters, preexisting loads and surrounding elastic foundations on the critical loads of nanocomposite shells are analyzed through a variety of numerical examples.

Nonlinear static and dynamic thermal buckling analysis of imperfect multilayer FG cylindrical shells with an FG porous core resting on nonlinear elastic foundation

In this article, a semi-analytical and analytical method for the nonlinear static and dynamic thermal buckling behavior of imperfect multilayer FG cylindrical shells with an FG porous core in the thermal environment is investigated. The structure is embedded within a generalized nonlinear elastic foundation which is composed of a two-parameter Winkler-Pasternak foundation augmented by a nonlinear cubic stiffness. Two types of multilayer FG cylindrical shells with an FG porosity core distribution consist of a uniform porosity distribution and a non-uniform porosity distribution core are considered. Using the Galerkin method with regard to the von Kármán equations, the discretized motion equation is obtained. The fourth-order Runge-Kutta method is utilized to obtain the nonlinear dynamic thermal buckling responses. The effects of various geometrical characteristics, material parameters, and elastic foundation coefficients are investigated on the nonlinear static thermal buckling and dynamic thermal buckling behavior of the multilayer FG system with an FG porous core. The results show that the various types of porosity core, imperfection and the elastic foundation parameters have strongly effect on the thermal buckling behaviors of the multilayer FG cylindrical shells with an FG porous core.