Hysteretic Finite Elements for the Nonlinear Static and Dynamic Analysis of Structures

A new numerical analysis procedure is presented for the nonlinear analysis of structures. The proposed methodology is developed within the framework of the direct stiffness method and the hysteretic formulation of finite elements. The derived numerical scheme relies on the natural evolution of localized inelastic quantities within the element, that is, the plastic deformation evaluated at properly defined collocation points rather than the evaluation of global and varying state matrices. This is accomplished by considering the additive decomposition of the total strain rate into elastic and plastic parts. Using the principle of virtual work, an equilibrium expression is derived in which the total applied load is equilibrated by an elastic internal force vector and an additional term acting as a nonlinear correction to the elastic component. The evolution of the plastic components is based on a smooth multiaxial hysteretic law that is derived within the framework of classical plasticity. Examples are presented that demonstrate the validity of the proposed method and its computational advantages with respect to existing methods of inelastic analysis.