Buckling analysis of composite laminates for critical temperatures under thermal loads is reported here. The formulation is based on linear theory and the finite element method using semiloof elements. The governing equation for critical temperature corresponding to the bifurcation budding is obtained by equating the second variation of total potential energy to zero. The validation checks on the program are carried out using results on homogeneous isotropic plates available in the literature. Results are presented for: 1. (1) cross-ply and angle-ply laminations with symmetry and antisymmetry stacking, 2. (2) simply supported, clamped and combination of boundary conditions, 3. (3) different aspect ratios, 4. (4) various moduli ratios, 5. (5) uniform and linearly varying temperature across thickness, 6. (6) varying ratios of coefficients of linear thermal expansion, and 7. (7) varying number of layers for given laminate thickness. Certain conclusions have been drawn based on these results. © 1989.

- Palaninathan

J. Ramachandran

COMPOSITE STRUCTURES--THERMAL EFFECTS

LAMINATED PRODUCTS--THERMAL EFFECTS

Mathematical Techniques--Finite Element Method

Composite laminated plates

Thermal buckling

Plates

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IIT Madras

Computers and Structures

This paper presents numerical studies on the vibration and acoustic response characteristics of a fiber-reinforced composite plate in a thermal environment by considering the inherent material damping property of the composite material. Initially the critical buckling temperature is obtained, followed by free and forced vibration analyses considering the pre-stress due to the imposed thermal environment. The vibration response predicted is then used to compute the sound radiation. The critical buckling temperature and vibration response are obtained using the finite element method based on the Classical Laminate Plate Theory (CLPT) while sound radiation characteristics are obtained using a coupled FEM/BEM technique. It is found that the vibration response of the structure reduces with an increase in uniform temperature rise for both Glass Epoxy and PEEK/IM7 materials, but the overall sound radiation of the plate reduces only marginally due to interaction between reduced stiffness and enhanced damping. © 2008 Elsevier Ltd. All rights reserved.

Journal of Sound and Vibration

Vibration and acoustic response of a composite plate with inherent material damping in a thermal environment

In the current paper, buckling and vibration behaviours of thin-walled box columns in a thermal environment made of functionally graded materials are investigated, using finiteelement method based on classical laminated plate theory. The four node thin-plate element with five degrees of freedom is employed in the study. The box column is considered as assemblages of plates, and a continuously graded variation in composition of the ceramic and metal phases across the plate wall thickness in terms of a simple power law distribution is implemented. The effects of temperature dependent material properties on the critical buckling and the free vibration response are studied. The analysis is carried out under thermal environment for clamped-damped boundary condition and results are presented. © IMechE 2008.

Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications

Finite-element buckling and vibration analysis of functionally graded box columns in thermal environments

A comparative study is presented on the vibratory characteristics of isotropic and orthotropic cylindrical shells with perfectly bonded piezoelectric material on the inner and outer surface of the shell lamina. The variation of free vibration natural frequencies and active damping ratios are simulated under varying magnitude of steady state axisymmetric temperatures. The objectives are explained by presenting the results of the numerical study on cylindrical shells made of mild steel and HS-graphite/epoxy bonded with PZT piezoelectric material. The vibratory characteristics under the above circumstances are interpreted from the point of view of initial stresses developed due to thermal loading. Apart from this, the changes in the vibratory characteristics due to different fiber orientations are examined. It is found from the studies that the frequency characteristic with respect to fiber orientation under thermal environment is highly dependent on the boundary condition considered for the shell laminate. © 2003 Elsevier Ltd. All rights reserved.

Studies on dynamic behavior of composite and isotropic cylindrical shells with PZT layers under axisymmetric temperature variation

The thermal buckling of laminated composite plates is analysed using the finite element method based on the Reissner-Mindlin first order shear deformation theory. The nine-node Lagrangian isoparametric element is employed for the thermal buckling analysis of symmetric cross-ply, symmetric angle-ply and quasi-isotropic laminates subjected to uniform temperature distribution. The effects of modulus ratio, fibre orientation, length to thickness ratio, aspect ratio and various boundary conditions on the critical temperature are analysed. The influence of the stress distribution on the variation of the critical temperature with fibre orientation is studied for different boundary conditions. Also, the variation of critical temperature with shear correction factor is considered. © 1994.

Thermal buckling of laminated composite plates

The characteristics of fundamental modes of vibration of initially stressed composite laminated plates are presented in this paper. The semiloof finite element is used in this formulation. Angle-ply and cross-ply rectangular laminates with simply supported and clamped edge conditions have been analyzed for which results have not been reported in the literature earlier. The effect of using "the same" and "different" boundary conditions for the calculation of initial stress and for the subsequent vibration analysis is studied. The number of layers in the laminate has been taken as a parameter for the study. The formulation of the geometric stiffness matrix includes moment resultants induced due to bending-stretching coupling. Its effect on the frequencies is also studied. Considerable differences are found in the frequencies of vibration between the cases of "the same" and "different" boundary conditions; the differences are greater for the simply supported (S2) and clamped (C2) boundary conditions. There is no difference in the case of S4 conditions. The variation of frequencies with initial stresses, whether fully linear or piecewise linear, depends not only on the aspect ratio of the plate but also on the orthotropy ratio and on the angle of fibre orientation. In the present paper, results for simple uniaxial loading alone are presented. However, the program developed has the capability to handle other complicated loading cases also. © 1990.

Free vibration of initially stressed composite laminates

In this paper, Semiloof shell finite element formulation has been extended to thermal stress analysis of laminated plates and shells. The accuracy of the formulation has been verified using sample problems available in the literature. Thermal stresses in cross-ply and angle-ply laminated plates and shells subjected to thermal gradients across the thickness are presented for different boundary conditions, taking into account the temperature dependence of the material properties. The behaviour of laminates under thermal load is found to be different from that under mechanical loads in certain respects. © 1988.

Journal	Computers and Structures
ISSN	00457949
Open Access	No