Three-dimensional stability analysis of laminated anisotropic circular cylinders

Abstract

Linear bifurcation stability of laminated anisotropic circular cylinders is investigated on the basis of three-dimensional elasticity using Biot's incremental deformation theory. A finite element code employing radial discretization is formulated for the calculations. By this approach, the laminate's thickness profile may be composed of an arbitrary number of bonded elastic anisotropic layers, each of which may have its own mechanical properties, thickness and initial stress state. Using a solution that is periodic axially and circumferentially in the variationally derived equilibrium equations yields an algebraic eigenvalue problem, where the critical (lowest) eigenvalue is sought. It represents the ratio of the buckling stress state to initial stress state and its associated eigenvector contains the radial distribution of the displacements. A parametric study on a series of regular symmetric and antisymmetric cross-ply and angle-ply laminated composite cylinders under axial compression and torsion was conducted, where the data can be used to assess the accuracy and range of validity of stability predictions based on shell theories. An example of the axial compression of a thick-walled laminated composite cylinder is presented to illustrate an instability phenomenon where internal and surface deformations are present.