Thermal buckling behaviour of composite laminated plates with a circular hole

Thermal buckling of antisymmetric cross-ply laminates having central circular holes subjected to uniform or non-uniform temperature distribution are analysed by the finite element method. To account for the transverse shear deformation, the thermo-elastic Mindlin plate theory is used. Numerical results show that significant reduction of the critical buckling temperature occurs for laminates having a central hole.     

Thermal buckling of bimodular sandwich beams

This paper presents a model that explores the thermal buckling of three-layer sandwich beams possessing thick facings and moderately stiff cores. Bimodular facings and core material are used. In contrast to conventional theory, the effects of transverse shear deformation in the facings as well as the effect of the stretching and bending action in the core on thermal buckling are considered. The governing equations are derived using the principle of minimum total potential energy and the fact that its second derivative is zero. The finite-element results are presented in order to investigate the effects of important parameters such as thickness, thermal expansion coefficients and moduli ratio on critical buckling temperatures.     

Thermal buckling of laminated cylindrical plates

Thermal buckling of a laminated cylindrical plate subjected to a temperature change is studied. The governing differential equations for Donnell-type laminated cylindrical shells are used and Galerkin's method is employed to determine the critical buckling temperature. Clamped and simply supported boundary conditions are both considered. The effects of various parameters on thermal buckling are examined.     

功能梯度材料薄球壳热屈曲问题

研究了由金属和陶瓷组成的功能梯度材料薄球壳热屈曲问题。用张量方法推导得到轴对称球壳稳定性方程。将热本构方程应用到球壳稳定性方程中,得到以位移表示的球壳热屈曲方程组。分别考虑均布外压和温度作用,采用伽辽金法计算分析简支球壳的热屈曲问题,给出薄球壳厚度、物性参数变化、内外表面温差变化引起的临界温度变化趋势和临界压力变化趋势。     

Thermal buckling behavior of laminated composite plates with temperature-dependent properties

The thermal buckling behavior of composite laminated plates subjected to a uniform temperature field is investigated by the finite element method. Temperature-dependent elastic and thermal properties are considered. The stiffness and geometry matrices are derived based on the principle of minimum potential energy. The assumed displacement state over the middle surface of the plate element is expressed as the product of one-dimensional, first-order Hermitian polynomials. An iterative method is employed to determine the thermal buckling load. It is shown by numerical results that the influence of temperature-dependent mechanical properties on the thermal buckling behavior is significant.     

Thermal buckling and postbuckling analysis of a laminated composite beam with embedded SMA actuators

In this paper, the thermal buckling and postbuckling behaviours of a composite beam with embedded shape memory alloy (SMA) wires are investigated analytically. For the purpose of enhancing the critical buckling temperature and reducing the lateral deflection for the thermal buckling, the characteristics of thermal buckling are investigated through the use of the shape recovery force associated with SMA wire actuators. The results of both thermal buckling and postbuckling behaviours present quantitatively how the shape recovery force affects the thermal buckling behaviour. The analytical results show that the shape recovery force reduces the thermal expansion of the composite laminated beam, which results in both an increment of the critical buckling temperature and also a reduction of the lateral deflection of postbuckling behaviours. A new formula is also proposed to describe the critical buckling temperature of the laminated composite beam with embedded SMA wire actuators.     

Thermal buckling of cross-ply laminated composite beams

Summary Thermal buckling of thick, moderately thick and thin cross-ply laminated beams subjected to uniform temperature distribution are analyzed. Exact analytical solutions of refined beam theories are developed to obtain the critical buckling temperature of cross-ply beams with various boundary conditions. The state space concept in conjunction with Jordan canonical form will be used to solve exactly the governing equations of the thermal buckling problems. The effects of length to thickness ratio, modulus ratio, thermal expansion coefficients ratio, various boundary conditions and number of layers on the critical buckling temperature are investigated.     

Thermal buckling behavior of composite laminated plates

Thermal buckling behavior of composite laminated plates was studied by making the use of finite element method. The thermal buckling mode shapes of cross-ply and angle-ply laminates with various E₁/E₂ ratios, aspect ratios, fiber angle, stacking sequence and boundary condition were studied in detail. The results indicate that the high E₁/E₂ and α₂/α₁ ratios of AS4/3501-6 and T 300/5208 laminates produce higher bending rigidity along the fiber direction and higher in-plane compressive force in a direction perpendicular to the fiber direction. Therefore, the higher thermal buckling mode shapes are formed. The thermal buckling mode that composite laminated plate will buckle into is mainly dependent on the E₁/E₂ ratio, α₂/α₁ ratio, fiber orientation and aspect ratio of the plate.     

Thermal buckling analysis of functionally graded material beams

Buckling of beams made of functionally graded material under various types of thermal loading is considered. The derivation of equations is based on the Euler–Bernoulli beam theory. It is assumed that the mechanical and thermal nonhomogeneous properties of beam vary smoothly by distribution of power law across the thickness of beam. Using the nonlinear strain–displacement relations, equilibrium equations and stability equations of beam are derived. The beam is assumed under three types of thermal loading, namely; uniform temperature rise, nonlinear, and linear temperature distribution through the thickness. Various types of boundary conditions are assumed for the beam with combination of roller, clamped and simply-supported edges. In each case of boundary conditions and loading, a closed form solution for the critical buckling temperature for the beam is presented. The formulations are compared using reduction of results for the functionally graded beams to those of isotropic homogeneous beams given in the literature.     

Thermal buckling of various types of FGM sandwich plates

The sinusoidal shear deformation plate theory is used to study the thermal buckling of functionally graded material (FGM) sandwich plates. This theory includes the shear deformation and contains the higher- and first-order shear deformation theories and classical plate theory as special cases. Material properties and thermal expansion coefficient of the sandwich plate faces 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 core layer is still homogeneous and made of an isotropic material. Several kinds of symmetric sandwich plates are presented. Stability equations of FGM sandwich plates include the thermal effects. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio, loading type and sandwich plate type on the critical buckling for sandwich plates.     

Thermal buckling of shallow/nonshallow piezoelectric-composite cylindrical shells

A thermal buckling analysis is presented for laminated cylindrical shells with surface mounted piezoelectric actuators under combined action of thermal and electrical loads. Derivations of the equations are based on the classical laminated shell theory, using the Sanders nonlinear kinematic relations. The analysis uses the Galerkin method to obtain closed form solutions for the buckling loads of shallow and nonshallow piezolaminated cylindrical shells. Temperature dependency of material properties is taken into account. Illustrative examples are presented to verify the accuracy of the proposed formulation. The effects of the various design parameters on thermal buckling loads are investigated.     

Edge-localized effects in buckling and vibrations of a shell with free in circumferential direction ends

Summary. Edge vibrations of a cylindrical shell, as well as buckling localized in a neighboring edge for cylindrical and conical shells are analyzed. The method of asymptotic splitting has been applied and simple analytical solutions have been proposed.     

The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects

In this work, the influence of surface effects, including residual surface stress, surface elasticity and surface piezoelectricity, on the vibrational and buckling behaviors of piezoelectric nanobeams is investigated by using the Euler-Bernoulli beam theory. The surface effects are incorporated by applying the surface piezoelectricity model and the generalized Young-Laplace equations. The results demonstrate that surface effects play a significant role in predicting these behaviors. It is found that the influence of the residual surface stress and the surface piezoelectricity on the resonant frequencies and the critical electric potential for buckling is more prominent than the surface elasticity. The nanobeam boundary conditions are also found to influence the surface effects on these parameters. This study also shows that the resonant frequencies can be tuned by adjusting the applied electrical load. The present study is envisaged to provide useful insights for the design and applications of piezoelectric-beam-based nanodevices.     

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 post buckling behavior of rectangular antisymmetric cross-ply composite plates

Summary The thermal post buckling behavior of simply-supported, antisymmetric cross-ply plates with immovable edges is investigated in this paper. For this purpose, a one term approximation for the inplane and transverse displacements is assumed and Rayleigh-Ritz method is used to obtain the equations of equilibrium. The question, whether the true thermal buckling (bifurcation buckling under thermal loads) exists for such plates is also addressed to. The conditions under which the thermal buckling in the classical sense occurs are derived. It is shown that nonlinear bending stiffness for such plates is direction dependent, because of an extra quadratic nonlinear term in addition to the usual cubic nonlinear term in the governing equilibrium equation. Results are presented for various plate configurations.     

Lateral buckling of a cantilever beam with imperfections

Summary The stability problem of an elastic cantilever beam transversely and horizontally simultaneously end-loaded, with imperfections, as a two-parameter bifurcation problem is considered. Exact non-linear differential equations are used, which describe the buckling shape of a cantilever beam having a narrow rectangle as a cross-section. The exact solution to the linearized problem, in closed form via confluent hypergeometric functions is given. The first interaction curve, which corresponds to the critical values of the simultaneously transversely and horizontally load, is obtained. A stability analysis is based on singularity theory. The Liapunov-Schmidt method is used to generate the bifurcation equation.With 4 Figures     

Thermal analysis of a constructal T-shaped porous fin with radiation effects

This paper presents an analytical technique based on the decomposition method to determine the temperature distribution and thermal performance parameters of a constructal T-shape porous fin. The effect of radiation on natural convective heat transfer is considered in the analysis. The governing energy equations of the stem and flange part of this T-shaped porous fin for the aforementioned conditions are highly nonlinear. The adopted decomposition solution gives an explicit expression of temperature distribution in the fin as a function of a coordinate expressed by infinite power series from which fin performance parameters and heat transfer rates can easily be calculated without the need of linearization. The effects of different geometric and thermophysical parameters on the dimensionless temperature distribution and fin performances are studied. Finally, the increase in heat transfer is noticed by selecting porous medium condition in the fin.     

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.