Thermal Buckling Analysis Research Articles

Thermal Buckling of Functionally Graded Plates Resting On Elastic Foundations Using the Trigonometric Theory

In this article, thermal buckling analysis of functionally graded material (FGM) plates resting on two-parameter Pasternak's foundations is investigated. Equilibrium and stability equations of FGM plates are derived based on the trigonometric shear deformation plate theory and includes the plate foundation interaction and thermal effects. The material properties vary according to a power law form through the thickness coordinate. The governing equations are solved analytically for a plate with simply supported boundary conditions and subjected to uniform temperature rise and gradient through the thickness. Resulting equations are employed to obtain the closed-form solution for the critical buckling load for each loading case. The influences of the plate aspect ratio, side-to-thickness ratio, gradient index, and elastic foundation stiffnesses on the buckling temperature difference are discussed.

Thermal buckling analysis of rectangular microplates using higher continuity p-version finite element method

In this article, thermal buckling characteristics of rectangular flexural microplates (FMP) subjected to uniform temperature are investigated using higher continuity p-version finite element framework. Invariant form of the governing equation for a microplate with non-local effects based on “modified couple stress theory” is extended for thermal buckling analysis of FMP by considering the strain gradient effects. In this case, the constitutive equation for strain gradient model is based on one constant. Galerkin weak form of the governing equation is derived and subsequently solved for a variety of boundary conditions using higher continuity p-version finite elements to extract critical thermal buckling loads. The computational procedure is verified by comparing its predictions to those of the classical theory and analytic microplate studies that are based on the same strain gradient model. Investigations indicate that length scale parameter affects the computed flexural stiffness of a plate, and the effect is directly proportional to the value of gradient coefficient considered for that plate. Hence, there is a strong influence of length scale parameter on value of the thermal buckling load. Depending on boundary conditions and value of length scale parameter used in numerical experiments, the classical plate model severely underestimates (up to 90%) the thermal buckling load for microplates. Therefore, it is concluded and strongly suggested that the classical plate theory should not be used to predict structural response of microplates.

Model test based soil spring model and application in pipeline thermal buckling analysis

The buckling of submarine pipelines may occur due to the action of axial soil frictional force caused by relative movement of soil and pipeline, which is induced by the thermal and internal pressure. The likelihood of occurrence of this buckling phenomenon is largely determined by soil resistance. A series of large-scale model tests were carried out to facilitate the establishment of substantial data base for a variety of burial pipeline relationships. Based on the test data, nonlinear soil spring can be adopted to simulate the soil behavior during the pipeline movement. For uplift resistance, an ideal elasticity plasticity model is recommended in the case of H/D (depth-to-diameter ratio)>5 and an elasticity softened model is recommended in the case of H/D≤5. The soil resistance along the pipeline axial direction can be simulated by an ideal elasticity plasticity model. The numerical analyzing results show that the capacity of pipeline against thermal buckling decreases with its initial imperfection enlargement and increases with the burial depth enhancement.

Nonlinear Thermomechanical Post-Buckling Analysis of Thin Functionally Graded Annular Plates Based on Von-Karman's Plate Theory

In this article, a nonlinear bending and axisymmetric thermal buckling analysis of thin functionally graded (FG) annular plates is presented based on classical nonlinear Von-Karman's plate theory. Using a shooting method the nonlinear ordinary differential equations are solved numerically. The presented solution is validated by comparing the obtained results with those of an isotropic plate. The emphasis is placed on investigating the effect of varying the gradient index of the FG plate and thermal boundary conditions on the nonlinear bending and post buckling behavior of the FG plate in detail.

Thermal buckling of FGM shells resting on a two-parameter elastic foundation

This paper focuses on the thermal buckling analysis of FGM shells resting on the two-parameter elastic foundation. Material properties of the constituents are graded in the thickness direction according to the power-law distribution. The surrounding elastic medium is modeled as an elastic foundation of the Pasternak-type. After giving the fundamental relations, the stability and compatibility equations of an FGM truncated conical shell subjected to thermal load and resting on a two-parameter elastic foundation have been derived. Critical temperature differences of FGM truncated conical shells with or without elastic foundations subjected to non-linearly distributed temperature across the thickness of the shells are obtained by solving eigenvalue problems. The appropriate formulas for FGM cylindrical shells with or without elastic foundations are found as a special case. In order to assure the accuracy of the present study, convergence properties of the critical temperature are examined in detail.

A Closed-Form Solution for Thermal Buckling of Piezoelectric FGM Hybrid Cylindrical Shells with Temperature Dependent Properties

A thermal buckling analysis is presented for simply supported functionally graded cylindrical shells that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of thermal load and constant applied actuator voltage. The temperature dependent material properties of the functionally graded cylindrical shell are assumed to vary as a power form of the thickness coordinate. Derivation of the equations is based on the classical shell theory. The piezoelectric FGM cylindrical shell is assumed to be under two types of thermal loadings, namely; uniform temperature rise and non-linear temperature distribution through the thickness. The thermal and mechanical problems are assumed to be uncoupled and solved separately. Results for the critical buckling temperature differences are obtained in closed form solution, which are convenient to use in engineering design applications. The effects of the applied actuator voltage, shell geometry, and volume fraction exponent of functionally graded material on the buckling load are investigated.

Thermal buckling and postbuckling analysis of functionally graded annular plates with temperature-dependent material properties

As a first endeavor, the thermal buckling and postbuckling analysis of functionally graded (FG) annular plates with material properties graded in the radial direction is presented. The formulation is derived based on the first-order shear deformation theory (FSDT) and the geometrical nonlinearity is modeled using Green’s strain in conjunction with von Karman’s assumptions. The material properties are temperature-dependent and graded according to the power law distribution. It is assumed that the temperature varies along the radial direction. Using the virtual work principle, the pre-buckling and postbuckling equilibrium equations and the related boundary conditions are derived. Differential quadrature method (DQM) as an efficient numerical technique is adopted to solve the governing equations. The presented formulation and the method of solution are validated by performing convergence and comparison studies with available results in the literature. Finally, the effects of volume fraction index, geometrical parameters, mechanical/thermal properties of the constituent materials and boundary conditions on the thermal buckling and postbuckling behavior of the radially graded annular plate are evaluated and discussed.

Thermal Buckling Analysis of Moderately Thick Plates Using Functionally Graded Strips

In the current study, the critical buckling of functionally graded plates (FGPs) subjected to thermal loads is evaluated using the finite strip method based on the first order shear deformation theory (FSDT). The material properties of these plates are assumed to vary in the thickness direction of the plate according to the power law distribution in terms of volume fractions of the constituents. The plates’ boundary conditions are assumed to be simply supported in all the edges or clamped in side edges and simply supported on the ends. The fundamental eigen-buckling equations for the plates are obtained by discretizing the plate into some strips, called functionally graded strip (FGS). The solution is obtained by the minimization of the total potential energy as well as solving the eigenvalue problem. The effects of material gradient index, aspect ratio and different thermal loadings (i.e. uniform temperature rise and nonlinear temperature change across the thickness) on the critical buckling temperature difference will be presented in some graphical forms.

Thermally induced buckling of functionally graded hybrid composite plates

In this paper, thermal buckling analysis is performed on hybrid functionally graded plates (FGPs) with an arbitrary initial stress. The governing equations are derived using the average stress method, including the effect of transverse shear deformation. Then, an eigenvalue problem is formed to evaluate thermal buckling temperatures for simple supported initially stressed ceramic-FGM-metal plates. The effects of functionally graded material (FGM) layer thickness, volume fraction index, layer thickness ratio, thickness ratio, aspect ratio and initial stress on the thermal buckling temperature of hybrid FGPs are investigated. The results reveal that the volume fraction index, initial stresses and FGM layer thickness have significant influence on the thermal buckling of hybrid FGPs.

A closed-form solution for thermal buckling of piezoelectric FGM rectangular plates with temperature-dependent properties

A thermal buckling analysis is presented for functionally graded rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of thermal load and constant applied actuator voltage. The temperature-dependent material properties of the functionally graded plate are assumed to vary as a power form of the thickness coordinate. Derivation of the equations is based on the third-order shear deformation plate theory. Results for the critical buckling temperatures are obtained in closed-form solution, which are convenient to be used in engineering design applications. The effects of the applied actuator voltage, plate geometry, and volume fraction exponent of the functionally graded material on the buckling temperature are investigated.

Buckling and vibration analysis of layered and multiphase magneto‐electro‐elastic cylinders subjected to uniform thermal loading

PurposeThe purpose of the paper is to investigate the linear thermal buckling and vibration analysis of layered and multiphase magneto‐electro‐elastic (MEE) cylinders made of piezoelectric/piezomagnetic materials using finite element method.Design/methodology/approachThe constitutive equations of MEE materials are used to derive the finite element equations involving the coupling between mechanical, electrical, magnetic and thermal fields. The present study is limited to clamped‐clamped boundary conditions. The linear thermal buckling is carried out for an axisymmetric cylinder operating in a steady state axisymmetric uniform temperature rise. The influence of stacking sequences and volume fraction of multiphase MEE materials on critical buckling temperature and vibration behaviour is investigated. The influence of coupling effects on critical buckling temperature and vibration behaviour is also studied.FindingsThe critical buckling temperature is higher for MEE axisymmetric cylinder as compared to elastic cylinder.Originality/valueLinear thermal buckling and vibration analysis of MEE axisymmetric cylinders are studied using the finite element approach. The structure can be used for active vibration control, sensors and actuators. Studying the buckling and vibration behaviour of such structures and influence of coupling effect is extremely useful for the design of magnetoelectroelastic structures.

Three-dimensional thermal buckling analysis of functionally graded arbitrary straight-sided quadrilateral plates using differential quadrature method

The thermal buckling analysis of functionally graded (FG) arbitrary straight-sided quadrilateral plates is presented. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The thermal buckling equilibrium equations are based on the three-dimensional (3D) elasticity theory. The differential quadrature method as an efficient and accurate numerical tool is adopted to discretize the governing equations. The principle of virtual work in conjunction with the geometric mapping technique is used to derive the equilibrium equations and the related boundary conditions. After discretizing the governing equations, the resulting nonlinear eigenvalue system of equations is solved by an iterative procedure. The convergence of the method is shown through different examples and its accuracy is demonstrated by comparing the obtained solutions with the existing results in literature for FG plates. Finally, the effects of temperature dependence of material properties, temperature field, volume fraction index, geometrical parameters and the boundary conditions on the thermal buckling characteristic of the FG plates of various shapes are studied.

An element‐free analysis of mechanical and thermal buckling of functionally graded conical shell panels

AbstractThis paper presents a mechanical and thermal buckling analysis of metal and ceramic functionally graded conical shell panels using the element‐free kp‐Ritz method. The formulation is based on the first‐order shear deformation shell theory, which accounts for the transverse shear strains and rotary inertia, and mesh‐free kernel particle functions are employed to approximate the two‐dimensional displacement fields. The effective material properties of the functionally graded conical shell panels are assumed to be smooth and continuous through their thickness direction, and are determined according to a power‐law distribution of the volume fractions of their constituents. Convergence studies are performed in terms of the number of nodes, and comparisons between the current solutions and those reported in the literature are provided to verify the accuracy of the proposed method. Three types of functionally graded conical shell panels, Al/ZrO2, SUS304/Si3N4, and Al2O3/Ti−6Al−4V are selected for study, and the effects of the volume fraction, boundary condition, semi‐vertex angle, length‐to‐thickness ratio, and temperature‐dependent material properties on the buckling strength are discussed in detail. Copyright © 2010 John Wiley & Sons, Ltd.

Thermal buckling analysis of moderately thick functionally graded annular sector plates

In this article, thermal buckling analysis of moderately thick functionally graded annular sector plate is studied. The equilibrium and stability equations are derived using first order shear deformation plate theory. These equations are five highly coupled partial differential equations. By using an analytical method, the coupled stability equations are replaced by four decoupled equations. Solving the decoupled equations and satisfying the boundary conditions, the critical buckling temperature is found analytically. To this end, it is assumed that the annular sector plate is simply supported in radial edges and it has arbitrary boundary conditions along the circular edges. Thermal buckling of functionally graded annular sector plate for two types of thermal loading, uniform temperature rise and gradient through the thickness, are investigated. Finally, the effects of boundary conditions, power law index, plate thickness, annularity and sector angle on the critical buckling temperature of functionally graded annular sector plates are discussed in details.

Nonlinear Thermoelastic Buckling of Pin-Ended Shallow Arches under Temperature Gradient

This paper presents a nonlinear thermal buckling analysis of circular shallow pin-ended arches that are subjected to a linear temperature gradient field in the plane of curvature of the arch. The linear temperature gradient produces axial expansion and curvature changes in the arch. The bending action produced by the curvature change and the axial compressive action produced by the restrained axial expansion may lead the arch to buckle suddenly in the plane of its curvature. The end reactions resulting from the restrained axial expansion also produce bending actions that are opposite to that produced by the temperature differential and tend to produce deflections on the convex side of the arch. A geometrically nonlinear analysis for thermoelastic buckling has been carried out based on a virtual work technique, and analytical solutions for the critical temperature gradients for the in-plane limit instability and bifurcation buckling are obtained. It is found that antisymmetric bifurcation is the dominant b...

Compressive Response of Composites Under Combined Fire and Compression Loading

The thermal buckling of an axially restrained composite column that is exposed to a heat flux due to fire is studied by both analytical and experimental means. The column is exposed to fire from one-side and the resulting heat damage, the charred layer formation and non-uniform transient temperature distribution are calculated by the thermal model developed by Gibson et al. (Revue de l’Institute Francais du Petrole 50:69–74, 1995). For the thermal buckling analysis, the mechanical properties of the fire-damaged (charred) region are considered negligible; the degradation of the elastic properties with temperature (especially near the glass transition temperature of the matrix) in the undamaged layer, is accounted for by using experimental data for the elastic moduli. Due to the non-uniform stiffness and the effect of the ensuing thermal moment, the structure behaves like an imperfect column, and responds by bending rather than buckling in the classical Euler (bifurcation) sense. Another important effect of the non-uniform temperature is that the neutral axis moves away from the centroid of the cross section, resulting in another moment due to eccentric loading, which would tend to bend the structure away from the fire. In order to verify the mechanical response, the compressive buckling behavior of the same material subjected to simultaneous high intensity surface heating and axial compressive loading were investigated experimentally. Fire exposure was simulated by subjecting the surface of rectangular specimens to radiant heating in a cone calorimeter. Heat flux levels of 25 kW/m2, 50 kW/m2 and 75 kW/m2 were studied. All specimens exhibited buckling and subsequent catastrophic failure, even at compressive stresses as low as 3.5 MPa under a surface heat flux of 25 kW/m2. Details of the experimental procedure, including modifications made to a cone calorimeter to allow simultaneous mechanical loading are presented.

Thermal Buckling and Post-Buckling of Laminated Composite Plates with SMA Fibers using Layerwise Theory

Thermal buckling and post-buckling analysis of laminated composite plates with SMA fibers subjected to uniform temperature distribution is presented using non-linear FEM. A 3-D Layerwise theory is employed in developing the system equations using variational approach. The Lagrangian interpolation functions are used to approximate the displacement components along the thickness as well as in the in-plane direction. The pre-buckling stresses are considered in the derivation of the geometric stiffness matrix. An incremental load technique and an incremental displacement technique using Newton-Raphson method are adopted to obtain thermal buckling temperature. The results are compared with the existing results in the literature.

Three-dimensional thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates using finite layer method

Finite layer method is the most efficient numerical method for 3D analysis of simply supported rectangular plates. Using this method, the 3D analysis is transformed into one dimensional analysis by virtue of the orthogonal properties of trigonometric interpolation functions. In the present study, the finite layer method is extended to the thermal buckling analysis of piezoelectric antisymmetric angle-ply laminates, which may be combined with some symmetrical cross-plies. Full coupling between the thermal, electrical and mechanical fields is taken into consideration. Pre-buckling state is assumed to be steady, and initial thermal stresses are computed accordingly. The geometrical stiffness matrix is then formed, and the critical temperature and buckling mode are obtained. Numerical examples are presented to verify the proposed method. The critical temperature is determined for both the adiabatic and isothermal buckling processes. The thermal buckling behaviours of some piezoelectric laminates and the effects of the thermo-electro-mechanical coupling are investigated.

Effects of random system properties on the thermal buckling analysis of laminated composite plates

This paper examines the effect of random system properties on thermal buckling load of laminated composite plates under uniform temperature rise having temperature dependent properties using HSDT. The system properties such as material properties, thermal expansion coefficients and thickness of the laminate are modeled as independent random variables. A C 0 finite element is used for deriving the eigenvalue problem. A Taylor series based first-order perturbation technique is used to handle the randomness in the system properties. Second-order statistics of the thermal buckling load are obtained. The results are validated with those available in the literature and Monte Carlo simulation.

Mechanical and thermal buckling analysis of functionally graded plates

The mechanical and thermal buckling analysis of functionally graded ceramic–metal plates is presented in this study. The first-order shear deformation plate theory, in conjunction with the element-free kp-Ritz method, is employed in the current formulation. It is assumed that the material property of each plate varies exponentially through the thickness. The displacement field is approximated in terms of a set of mesh-free kernel particle functions. The bending stiffness is evaluated using a stabilized conforming nodal integration technique, and the shear and membrane terms are computed using a direct nodal integration method to eliminate the shear locking effects of very thin plates. The mechanical and thermal buckling behaviour of functionally graded plates with arbitrary geometry, including plates that contain square and circular holes at the centre, are investigated, as are the influence of the volume fraction exponent, boundary conditions, hole geometry, and hole size on the buckling strengths of these plates.