Thermal Postbuckling Research Articles

Thermal post buckling behavior of rectangular antisymmetric cross-ply composite plates

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.

THERMAL BUCKLING AND POSTBUCKLING OF SYMMETRICALLY LAMINATED COMPOSITE PLATES

The thermal buckling and postbuckling response of symmetrically laminated composite plates are discussed. Using variational methods in conjunction with a Ray-leigh-Ritz formulation, thermal buckling and postbuckling are investigated for two laminates, a ( ±45/0/90) s and a ( ± 45/02 ) s, under two different simple support conditions, fixed and sliding. These laminates are subjected to the condition of a uniform temperature change. The effects of the principal material axes not being aligned with the edges of the plate, referred to here as material axis skewing, are also investigated. Although differences between buckling temperatures for the two support conditions were small, support conditions can have a large influence on thermal postbuckling response. In general, plates with fixed simple supports defied more than plates with sliding simple supports. In addition, support conditions can influence modal interaction. Skewing of the material axis decreases the buckling temperatures of both laminates and, like fixed support conditions, causes increased postbuckling deflections. Skewing also influences modal interaction.

Thermal postbuckling of thin-walled composite stiffeners

A study is made of the thermal postbuckling response of composite stiffeners subjected to prescribed edge displacement and a temperature rise. The flanges and web of the stiffeners are modeled by using two-dimensional plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. A reduction method is used in conjunction with mixed finite element models for determining the postbuckling response of the stiffeners. Sensitivity derivatives are evaluated and used to study the effects of variations in the different lamination and material parameters of the stiffeners on their postbuckling response characteristics. Numerical studies are presented for anisotropic stiffeners with Zee and channel sections.

Thermal post-buckling of thin simply supported orthotropic square plates

Thermal post-buckling behaviour of orthotropic square plates with simply supported edges has been studied in this note using the Rayleigh-Ritz method. The formulation and the solution for the linear buckling temperature and post-buckling temperature are presented in closed form together with a set of numerical results.

Thermal post-buckling of a square plate resting on an elastic foundation by finite element method

A simple finite element formulation is presented for evaluating the thermal post-buckling behaviour of rectangular plates. The results are presented in the form of linear thermal loads and ratios of nonlinear to linear thermal loads for various values of the central deflection and for three sets of boundary conditions. The effect of elastic foundation on the thermal post-buckling behaviour is also evaluated for various values of foundation stiffness parameter.

Thermal post-buckling of circular plates

The thermal post-buckling behaviour of isotropic circular plates has been studied in this paper through a simple finite element formulation. The accuracy of the solution by finite element method is established through a solution by Rayleigh-Ritz method for simply-supported circular plates. Effect of non-linearity on the load parameter is found to be much higher in the case of thermal loading than in the case of mechanical loading.

THERMAL BUCKLING AND POSTBUCKLING CHARACTERISTICS OF EXTENSIONAL SLENDER ELASTIC RODS

This paper presents an exact mathematical model for the postbuckling of a uniformly heated slender rod with axially immovable simply supported ends on the basis of geometrically nonlinear theory of extensible rods. The material is assumed linear elastic and its thermal strain-temperature relationship is considered nonlinear. Two approaches have been used in this study. The first approach is based on the extensible elastica theory. The governing equations are derived and solved analytically for the exact closed form solutions that include the equilibrium configurations of the rod, equilibrium paths, and temperature gradients. The exact solutions take the form of elliptic integrals of the first and second kinds. In the second approach, the multisegment integration technique is employed to solve a set of nonlinear differential equations with the associated boundary conditions. The equations are integrated by using the Runge-Kutta algorithm. A comparison study between the analytical elliptic integral solutions and the numerical multisegment integration technique solutions show excellent agreement of results. Special features of the solutions in the form of determination of buckling temperature, effects of slenderness ratio and nonlinear strain-temperature coefficients on the buckling and postbuckling behavior as a function of temperature are also discussed extensively. Keywords: Thermal postbuckling, elliptic integral, multisegment integration, critical buckling temperature. doi: 10.3329/jme.v40i1.3467 Journal of Mechanical Engineering, Vol. ME40, No.1, June 2009 1-8