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An inelastic Timoshenko beam element with axial–shear–flexural interaction

In this work, a novel numerical procedure for the nonlinear dynamic analysis of skeletal structures is presented. The elastic Timoshenko beam element formulation is extended by introducing a set of smoothly evolving hysteretic degrees of freedom. The theoretical framework provided sets a cross-connection between nonlinear dynamics and classical plasticity. The solution procedure is based on the derivation of two state matrices, the elastic stiffness and the hysteretic matrix. These are evaluated once at the beginning of the analysis and remain constant thereafter. Thus, the derived methodology bears significant computational advantages when compared to classical iterative Newton-Raphson procedures.