Stability analysis of composite laminated plate and cylindrical shell structures using semi-analytical finite strip method

Abstract

Abstract In the present paper, the linear eigen buckling analysis and the non-linear post-buckling equilibrium path of composite laminated plates and cylindrical shell structures are investigated. The method of analysis is the semi-analytical finite strip approach which has been developed originally on the basis of full energy methods. The strip established here is the one with the radius of curvature “R” in the transverse direction, whilst in the longitudinal direction the strip has no curvature. In the longitudinal direction, shape functions of trigonometric type are applied due to their continuous characteristics. The application of the latter shape functions has allowed the energy integrations to be performed analytically in the longitudinal direction. The method is generally known as “Semi-Analytical”. It is noted that the use of trigonometric functions has limited the boundary conditions at the loaded ends of the strip to the simple supported one. In the transverse direction, the first-order Lagrange shape functions are used for the in-plane displacements, and the third-order Hermitian functions are utilized to estimate the out-of-plane displacements. In the linear buckling analysis, the strain–displacement relationships are based on the Koiter–Sanders theory of shells, whilst in the non-linear post-buckling developments Donnell’s type of shell theory (Donnell’s strain–displacement relationships) is applied. It is noted that to the authors’ knowledge the incorporation of Donnell’s shell theory into the formulations of the semi-analytical finite strip method for the post-buckling non-linear analysis of the structures has not been attempted elsewhere. To check the validity and soundness of the results, some case studies are performed by implementing the finite strip method as well as the finite element method. For further validation, the obtained results are also compared with those available in the literature.