Hysteretic Plate Finite Element

Abstract

A hysteretic plate finite element for inelastic, static and dynamic analysis is presented and its performance is compared with currently used methods. A smooth, 3D hysteretic rate-independent model is utilized generalizing the uniaxial Bouc–Wen model. This is expressed in tensorial form, which incorporates the yield criterion and hardening law. The elastic mixed interpolation of tensorial components with four nodes (MITC4) element is extended by considering as additional hysteretic degrees of freedom the plastic strains at the Gauss points of each layer interface, which evolve following Bouc–Wen equations. Incorporating hysteretic relations directly into the element’s formulation is proved computationally advantageous and enables a better identification of the involved parameters in cyclic loading. The solution advances by establishing the equilibrium of external and internal forces on the basis of the initially computed stiffness and hysteretic structural matrices, thereby avoiding Gauss integration at every iteration of Newmark’s method steps, over the volume of each element. The additional evolution equations decoupled at every Gauss point are integrated tracing the elastoplastic path. Numerical results are presented that validate the proposed method, demonstrating the efficacy, accuracy and generality of the proposed approach.