Thermal Buckling Analysis Research Articles

Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams

In the present study, thermo-electrical buckling characteristics of functionally graded piezoelectric (FGP) Timoshenko nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier type solution for the first time. Three kinds of thermal loading, namely, uniform, linear and nonlinear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model. Eringen’s nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton’s principle, the nonlocal governing equations together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the thermal buckling analysis of graded piezoelectric nanobeams including size effect and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate critical buckling temperature results of the FG nanobeams as compared some cases in the literature. In following a parametric study is accompanied to examine the effects of the several parameters such as various temperature distributions, external electric voltage, power-law index, nonlocal parameter and aspect ratio on the critical buckling temperature difference of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and electrical loading have a significant effect on buckling temperatures of FGP nanobeams.

DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory

TO INVESTIGATE THE THERMAL BUCKLING OF CURVED CARBON NANOTUBES (CCNTS) EMBEDDED IN AN ELASTIC MEDIUM, NONLOCAL ELASTICITY THEORY IS EMPLOYED IN COMBINATION WITH THE THEORY OF THIN CURVED BEAMS. DIFFERENTIAL QUADRATURE (DQ) METHOD IS IMPLEMENTED TO DISCRETIZE THE RESULTED GOVERNING EQUATIONS. SOLVING THESE EQUATIONS ENABLE US TO ESTIMATE THE CRITICAL TEMPERATURE AND THE CRITICAL AXIAL BUCKLING LOAD FOR CCNTS SURROUNDED BY AN ELASTIC MEDIUM AND UNDER THE EFFECT OF A UNIFORM TEMPERATURE CHANGE. THE ELASTIC INTERACTION BETWEEN THE NANOTUBE AND ITS SURROUNDING MEDIUM IS MODELED AS A WINKLER€“PASTERNAK ELASTIC FOUNDATION. THE FAST CONVERGENCE OF THE DQ METHOD IS DEMONSTRATED AND ALSO ITS ACCURACY IS VERIFIED BY COMPARING THE RESULTS WITH AVAILABLE SOLUTIONS IN THE LITERATURE. THE EFFECTS OF VARIOUS PARAMETERS SUCH AS DIFFERENT BOUNDARY CONDITIONS, NONLOCAL PARAMETER, WINKLER AND PASTERNAK ELASTIC MODULUS, TEMPERATURE AND NANOTUBE CURVATURE ON THE CRITICAL BUCKLING TEMPERATURE AND LOAD ARE SUCCESSFULLY STUDIED. THE RESULTS REVEAL THAT THE CRITICAL BUCKLING LOAD DEPENDS SIGNIFICANTLY ON THE CURVATURE OF THE CCNT.

Thermal Buckling Analysis of Perforated Functionally Graded Plates

In this research, the buckling behavior of functionally graded (FG) plates under thermal loading is investigated based on finite element analysis. It is assumed the plate is subjected to a uniform temperature rise across plate thickness. First-order shear deformation theory (FSDT) is utilized for developing the solution method. By using an appropriately designed mesh structure for a perforated plate, the critical thermal buckling temperature is obtained by numerical solution of the problem based on finite element method (FEM). The FG plate is perforated by multiple cutouts. The number of cutouts is assumed one, two, four, or six. Also different geometrical shapes of cutouts including triangle, square, rhombus, pentagon, hexagon, and circle are considered. The influence of the number of cutouts and their geometrical shapes on thermal buckling response is investigated. The effects of the number of sides of cutouts from three (triangle) to infinity (circle) are discussed. Two different boundary conditions are taken into account. Also the influences of the distance between the cutouts and the orientation of cutouts on critical buckling temperature are studied. In addition, the effects of the orientation of ellipse cutouts are studied. Some remarkable conclusions are gained that can be useful in practical applications.

Thermal Buckling of Piezolaminated Plates Subjected to Different Loading Conditions

A thermal buckling analysis is presented for simply supported rectangular laminated composite plates that are covered with top and bottom piezoelectric actuators, and subjected to the combined action of thermal load and constant applied actuator voltage. The thermomechanical properties of composite and piezoelectric materials are assumed to be linear functions of the temperature. The formulations of the equations are based on the higher-order laminated plate theory of Reddy and using the Sanders nonlinear kinematic relations. The closed-form solutions for the buckling temperature are obtained through the Galerkin procedure and solving the resultant eigenvalue problem, which are convenient to be used in engineering design applications. Numerical examples are presented to verify the proposed method. The effects of the plate geometry, fiber orientation in composite layers, lay-up configuration, different utilized piezoelectric materials, temperature dependency of material properties, thermal conductivity, and energy generation on the buckling load are investigated.

Thermal Buckling Analysis of Axially Loaded Columns of Thin-Walled Open Section with Nonuniform Sectional Properties

This paper presents an analytical study on the thermal buckling analysis of axially loaded columns of thin-walled open section with nonuniform sectional properties. Obtained herein are critical loads related to flexural, torsional and flexural-torsional buckling of an I-section column subjected to an axial compressive load applied at the geometric centroid, and under linearly varied non-uniform temperature distribution scenarios. The analysis is accomplished using traditional energy methods. The influences of thermal strain, nonuniform distribution of pre-buckling stresses, and variation of pre-buckling stresses along the longitudinal axis of the column on critical buckling loads are examined. The present results highlight the importance of nonuniform sectional properties in the buckling analysis of columns of doubly symmetric section.

Laboratory tests and thermal buckling analysis for pipes buried in Bohai soft clay

Upheaval buckling of submarine pipelines occurs due to relative movement of pipeline and surrounding soil and is often triggered by high operational temperature of the pipeline, initial imperfection of the pipeline, or a combination of both. Since buckling can jeopardize the structural integrity of a pipeline, it is a failure mode that should to be taken into account for the design and in-service assessment of trenched and buried offshore pipelines. In this study, a series of vertical (uplift) and axial pullout tests were carried out on model pipe segments buried in soft clay deposit similar to that present in Bohai Gulf, China. Pipe segments with three different diameters (= 30 mm, 50 mm and 80 mm) were buried in different depth-to-diameter ratios ranging from 1 to 8. Based on the results of laboratory tests, nonlinear force–displacement relations are proposed to model soil resistance mobilized during pipeline movement. The proposed nonlinear soil resistance models are employed in finite element analysis of buried pipelines with different amplitudes of initial geometric imperfections. Thermal upheaval buckling behavior of pipelines operating at different temperatures is studied. Results show that the capacity of pipeline against thermal buckling increases with the burial depth and decreases with the amplitude of initial imperfection.

Thermal Buckling Response of Functionally Graded Plates with Clamped Boundary Conditions

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The material properties of FGM plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are solved analytically for a plate with simply supported boundary conditions. Resulting equations are employed to obtain the closed-form solution for the thermal force resultant for each loading case. Numerical examples covering the effects of the plate aspect ratio, side-to-thickness ratio and gradient index on thermal force resultant are discussed.

Size-dependent thermal buckling analysis of micro composite laminated beams using modified couple stress theory

The thermal effect on size-dependent buckling analysis of micro composite laminated beams is studied based on the modified couple stress theory. The governing equations and boundary conditions are obtained by using the principle of minimum potential energy. The effect of shear deformation is investigated by considering the Euler–Bernoulli, Timoshenko and Reddy beam theories. In addition, the effect of boundary condition by using the hinged–hinged, clamped–hinged and clamped–clamped boundary conditions and the effect of lamination by applying four kinds of cross ply laminate i.e. [0, 0, 0], [0, 90, 0], [90, 0, 90] and [90, 90, 90] are investigated. Using the Fourier series expansions, the governing equations and boundary conditions are solved analytically just for hinged–hinged boundary condition. Also by using the generalized differential quadrature (GDQ) method, the governing equations and boundary conditions are solved numerically for all of the boundary conditions. Comparison between results obtained by numerical solution, analytical solution and those obtained by literature reveals the accuracy of GDQ method.

Thermal Buckling Analysis of Piezoelectric Functionally Graded Plates with Temperature-Dependent Properties

In this study, the thermal buckling analysis of hybrid laminated plates made of two-layered functionally graded materials (FGMs) that are integrated with surface-bonded piezoelectric actuators referred to as (P/FGM)s are investigated. Material properties for both substrate FGM layers and piezoelectric layers are temperature-dependent. Uniform temperature rise as a thermal load and constant applied actuator voltage are considered for this analysis. By definition of four new analytic functions, the five coupled governing stability equations, which are derived based on the first-order shear deformation plate theory, are converted into fourth-order and second-order decoupled partial differential equations (PDEs). Considering a Levy-type solution, these two PDEs are reduced to two ordinary differential equations. One of these equations is solved using an accurate analytical solution, which is named as power series Frobenius method. The effects of parameters, such as the plate aspect ratio, ratio of piezoelectric layer thickness to thickness of FGM layer, gradient index, actuator voltage, and the temperature dependency on the critical buckling temperature difference, are illustrated and explained. The critical buckling temperatures of (P/FGM)s with six various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.

Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments

In this paper, the thermal effect on buckling and free vibration characteristics of functionally graded (FG) size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution for the first time. Material properties of FG nanobeam are supposed to be temperature-dependent and vary continuously along the thickness according to the power-law form. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on Timoshenko beam theory through Hamilton’s principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as thermal effect, material distribution profile, small scale effects, beam thickness and mode number on the critical buckling temperature and normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the thermal buckling and vibration behavior of a FG nanobeams is significantly influenced by these effects.

Thermal buckling analysis of FG plates resting on elastic foundation based on an efficient and simple trigonometric shear deformation theory

In this paper, an efficient and simple trigonometric shear deformation theory is presented for thermal buckling analysis of functionally graded plates. It is assumed that the plate is in contact with elastic foundation during deformation. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns. It is assumed that the mechanical and thermal non-homogeneous properties of functionally graded plate vary smoothly by distribution of power law across the plate thickness. Using the non-linear strain-displacement relations, the equilibrium and stability equations of plates made of functionally graded materials are derived. The boundary conditions for the plate are assumed to be simply supported on all edges. The elastic foundation is modelled by two-parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The effects of thermal loading types and variations of power of functionally graded material, aspect ratio, and thickness ratio on the critical buckling temperature of functionally graded plates are investigated and discussed.

Thermal buckling analysis of functionally graded rectangular nanoplates based on nonlocal third-order shear deformation theory

In this work, thermal buckling analysis of functionally graded rectangular nanoplates is investigated. In order to consider the size effects, nonlocal elasticity theory and third-order shear deformation theory are used. It is assumed that the material properties of functionally graded nanoplates are varied through the thickness of nanoplates according to the power law distribution. Two types of uniform and nonlinear temperature distributions are considered in this paper. To show the accuracy of present methodology, our results are verified with the results available in the literature. Moreover, the influences of different parameters such as nonlocal parameter and piezoelectric layers are studied.

Thermal buckling analysis of porous circular plate with piezoelectric sensor-actuator layers under uniform thermal load

This study presents the thermal buckling analysis of solid circular plate made of porous material bounded with piezoelectric sensor-actuator patches. The porous material properties vary through the thickness with specific function. The general mechanical nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of piezoelectric porous plate. Thermal buckling load is derived for solid circular plates under uniform temperature load for the clamped edge condition. In recent paper the effects of porous plate’s thickness, porosity, porous thermal expansion coefficient, piezoelectric thickness, piezoelectric thermal expansion coefficient, and feedback gain on thermal stability of the plate are investigated.

Application of the VIM to thermal buckling of composite beams on an elastic foundation

AbstractIn this paper, thermal buckling analysis of composite laminated beams resting on a two-parameter elastic foundation is carried out by means of the variational iteration method (VIM). The solution procedure is based on the first-order shear deformation beam theory of Timoshenko combined with the von Karman type of geometrical non-linearity. Both edges of the beam are assumed to be axially restrained while may possess various out-of-plane boundary conditions. The elastic foundation is modelled via the two-parameter Pasternak medium which takes into account the vertical interaction of the elements. The governing equilibrium equations are obtained by means of the virtual displacement principle. Stability equations are then obtained by means of the adjacent equilibrium criterion. These equations are uncoupled to extract individual equations in terms of lateral displacement. The resulted differential equations are solved via the VIM. The study examines the VIM in obtaining the closed-form analytical solutions for thermal buckling of composite laminated beams. Furthermore, it is shown that for some special materials with negative thermal expansion coefficient, buckling may occur under cooling rather than heating or it may not occur at all.

Thermal Buckling Analysis of Circular Plates Made of Piezoelectric and Saturated Porous Functionally Graded Material Layers

AbstractThis study presents the thermal buckling of a radially solid sandwich circular plate made of a piezoelectric actuator and porous material. The porous material properties vary through the thickness of the plate for a specific function. The general thermoelastic nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of the piezoelectric porous plate. The geometrical nonlinearities are considered along with the higher-order shear deformation plate theory. The problem is simplified to an axisymmetric one, and then closed-form solutions for circular plates subjected to temperature load are obtained. The buckling temperatures that are derived for solid circular plates under uniform temperature rise through the thickness for an immovable clamped edge of the boundary conditions. The effects of the porous plate thickness, piezoelectric thickness, applied actuator voltage, and variation of porosity on the critical temperature loa...

Thermal Stress and Buckling Analysis of Functionally Graded Plates

— Finite element formulation for Functionally Graded Material (FGM) square plates subjected to Thermal loads are presented. The plate is assumed to be having linear temperature rise through the thickness. The power law distribution model is assumed for the composition of the FGM material along the thickness. A software program “COMSAP” has been developed using Semiloof shell element formulation and validation checks are carried out using the results available in the related literature. Results for thermal stress and thermal buckling analysis of functionally graded plates are reported.

Thermal Buckling Analysis of Cyclic Symmetry Mounting Structure

Buckling analysis is a technique used to determine buckling load and buckled mode shape. Buckling load is the critical load at which a structure becomes unstable while buckled mode shape is the characteristic shape associated with a structure's buckled response. In this paper, the elastic thermal buckling of a heated cyclic symmetry structure is carried out by means of finite element method. The buckling cyclic symmetry analysis is focused on a ring-strut-ring structure which is extensively used as a basic element in rotating machines. The linear eigenvalue buckling analysis is adopted to determine the buckling response with the temperature change of the structure.

Hermite Reproducing Kernel Meshfree Thermal Buckling Analysis of Euler-Bernoulli Beams with Elastic Foundation

The Hermite reproducing kernel meshfree method is employed for the stability analysis of Euler-Bernoulli beams with particular reference to the thermal buckling problem. This meshfree approximation employs both the nodal deflectional and rotational variables to construct the deflectional approximant according to the reproducing kernel conditions. In this paper, we apply this HRK meshfree method to the thermal buckling analysis of Euler-Bernoulli beam on elastic foundation. By comparison to the Gauss Integration method, HRK meshfree method shows much better solution accuracy.

Thermal Buckling Analysis of Functionally Graded Plates on an Elastic Foundation According to a Hyperbolic Shear Deformation Theory

A thermal buckling analysis of functionally graded thick rectangular plates on an elastic foundation is presented. The foundation is described by the Pasternak model. The formulation is based on a higher-order hyperbolic shear deformation theory. Two types of thermal loading, uniform temperature rise and graded temperature change across the thickness of the plates are considered, and their equilibrium and stability equations are obtained. The accuracy of the formulation presented is verified by comparing the results of numerical examples with data available in the literature.

Finite Element Analysis of Thermal Buckling of Rectangular Laminated Composite Plates with Circular Cut-Out

In this work, thermal buckling analysis of symmetric and anti-symmetric laminated composite plates with a cut-out is presented. The plate is assumed to be subjected to a uniform temperature rise for different boundary conditions. The thermal buckling analysis is performed using the code developed in MATLAB software. The stiffness matrices and thermal force vector are derived according to first-order shear deformation theory (FSDT). To have more control on the mesh pattern around the cut-out, convenient meshes are manually constructed using a mesh generation algorithm in which mesh density around the hole can be controlled. The results of FEM code is compared with ABAQUS's solutions and with those available in the literature. After that, the effects of cut-out size, boundary conditions, plate aspect ratio, and stacking sequence on critical thermal buckling temperature are investigated for symmetric and anti-symmetric plates. Also, plates with cut-out located at positions other than the center of plate are investigated and useful conclusions are derived from the numerical results.