Hysteretic Shell Finite Element

Abstract

A hysteretic shell finite element for the nonlinear, static, and dynamic analysis of structures is presented, formulated on the basis of classical theory of plasticity and finite deformation. The generalized smooth, rate-independent three-dimensional (3D) Bouc-Wen model is expressed in tensorial form incorporating the von Mises yield criterion and different types of nonlinear hardening laws. Based on this approach, a hysteretic shell finite element is derived in which the shell is considered as a number of fully bonded layers along the thickness. The elastic mixed interpolation of tensorial components with nine nodes (MITC9) element is extended by considering as additional hysteretic degrees of freedom the plastic strains, backstresses, and the variable yield stress. These are considered at the Gauss points of two faces and all interlaminar interfaces, the evolution of which is described by Bouc-Wen-type equations. Using this formulation, the effect of the nonlinear hardening on the response of a shell structure and in particular the phenomenon of ratcheting is investigated. The developed hysteretic shell element accounts for geometric nonlinear analysis and incorporates two constituent functionally graded materials. Numerical results are presented, demonstrating the efficacy, accuracy, and generality of the proposed approach.