Buckling and Postbuckling Analysis of Laminated Shell Structures by Finite Elements Based on the Third Order Theory

Abstract

The present effort focuses on the development of finite element models to implement in the bifurcation and post buckling nonlinear analysis of laminated shells. This paper deals with the two aspects of the numerical simulation of the buckling and post buckling response of layered composite structures. The first aspect is the formulation and evaluation of an efficient shell finite element valid for geometrical nonlinear analysis of laminated shells. The formulation of the element is based on the third order shear deformation theory with the assumption of moderately large deflections but small rotations. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. Since the formulation is based on the third order theory, applicability is extended to moderately thick to thin situations using a discrete Kirchhoff technique. The second aspect pertains to the prediction of the onset of local delamination in the post buckling range and accurate determination of transverse shear stresses in the laminated structures. The accuracy and effectiveness of the finite element and the strategies developed are demonstrated by means of detailed numerical and experimental examples.