Pseudo-Transient Analysis of Composite Shells Including Geometric and Material Non-Linearities

Abstract

An unified approach is presented for the pseudo-transient (static) linear, geometric, material and combined geometric and material non-linear analyses of lami nated composite shells. A nine-noded isoparametric quadrilateral finite element belonging to the Lagrangian family is used in space discretization. An explicit time marching scheme is employed for time integration of the resulting discrete ordinary differential equations with the special forms of diagonal fictitious mass and/or damping matrices. The elasto plastic material behaviour is incorporated using a flow theory of plasticity. In particular, the modified version of Hill's initial yield criterion is used in which anisotropy parameters of plasticity are introduced. The shear deformation is accounted for using an extension of Sander's shell theory, and the geometric non-linearity is considered in the sense of von Karman strains. The layered element approach is adopted for the treatment of elasto plastic behaviour through the thickness. A wide range of numerical examples are pre sented to demonstrate the validity and efficiency of the present approach. The results for combined non-linearity are also presented. The variety of results presented here is based on realistic material properties of more commonly used advanced composite materials. The results of the combined non-linear analysis should serve as reference for future in vestigations.