Elastic-Plastic Dynamic Response and Buckling of Laminated Thin Shells

Abstract

A 48 degree-of-freedom doubly-curved quadrilateral laminated thin shell element including the effect of anisotropic plasticity is formulated to study the static, dynamic response and buckling of thin shell structures. The effect of geometric nonlinearity is also included. The formulation is based on the Kirchhoff-Love thin shell theory and classical lamination theory. In the plastic range, the Huber-Mises yield criterion combined with the Prandtl-Reuss flow rule are used. The state of stresses and strains of each layer is calculated individually, and then integrated through the whole thickness of the shell to obtain the stress and moment resultants, and the stress-strain relation. The stress and strain components, the stress-strain relation, and the yield function which is used to identify the plastic surface are obtained in principal material directions of each layer and then transformed to those in local coordinate axes of the element. The formulation and solution procedure are evaluated by comparing results of two examples with existing alternative solutions. The practical applicability is demonstrated by performing a series of static and dynamic buckling analyses of laminated thin spherical and cylindrical shells.