Thermal buckling of laminated composite shells

Abstract

The linear buckling analysis of laminated composite cylindrical and conical shells under thermal load using the finite element method is reported here. Critical temperatures are presented for various cases of cross-ply and angle-ply laminated shells. The effects of radius/thickness ratio, number of layers, ratio of coefficients of thermal expansion, and the angle of fiber orientation have been studied. The results indicate that the buckling behavior of laminated shell under thermal load is different from that of mechanically loaded shell with respect to the angle of fiber orientation. Content H IGH-speed aerospace vehicles consisting of thin-shell elements are subjected to aerodynamic heating. This induces a temperature distribution over the surface and thermal gradient through the thickness of the shell. The compressive stresses, which in these circumstances develop, may cause buckling. Recently fiber-reinforced, laminated composites have begun to be used extensively in aerospace vehicle construction due to the high specific properties of the composites. In view of the above, the thermal buckling analysis of laminated composite shell assumes importance. Thermal buckling of isotropic cylindrical and conical shells have been reviewed by Bushnell. 1 Chang and Card2 investigated thermal buckling of stiffened, orthotropic, multilayered cylindrical shells. The governing equations obtained through the minimization of the total potential energy were solved by the finite difference technique with a few cases of practical problems. Nevertheless, this technique cannot be extended to other complex geometries and loading conditions. In this paper the Semiloof shell element formulated by Irons,3 which was adapted by the authors for thermal stress analyses of laminated plates and shells,4 is being extended to thermal buckling problems. The derivation of governing equation is a standard procedure, which uses the principle of minimum total potential energy. The characteristic finite element equilibrium equation thus obtained is [Ks] [q] = [F] where [Ks] is the structural stiffness matrix, [q} is the nodal displacement vector and [F] is the consistent nodal load vector. In order to establish the critical buckling state corresponding to the neutral equilibrium condition, the second variation of the total potential must be equated to zero, which gives rise to the condition, | [Ks] + \[Kg] j = 0, where [Kg] is the geometric stiffness matrix and X is the eigenvalue. The computer program (COMSAP) developed based on this formulation can handle general temperature variations, lamination parameters, and various boundary conditions. The material properties considered in the analysis of laminated shells are En/En = 10, Glt/Ett = 0.5,