Pseudoesfuerzos y evaluación de tensiones en modelos hiperviga

This paper deals with the unified formulation of linear models in rod elastostatics and, specifically, with the class of models including generalized displacements that are additional to those defining rigid body motions of the cross-sections. The main feature of these models, named hyper beam models by the authors, is the coupling between static and kinematic variables in the equilibrium equations. New static variables called pseudo forces have been introduced to represent the action of the internal constraints which control the deformation of the cross-section. Using the pseudo forces, a systematic procedure to evaluate the model-consistent stress distributions on cross-sections -which is an approximation of the 3D elastic solution- has been developed. The application of the unified formulation to a problem requiring the introduction of non rigid-body-motional degrees of freedom -warped bending- shows its ability to systematically build the equations, and to assess the influence of the intervening parameters. The response-defining variables, parameters and equations, as well as the expressions of consistent stress distributions on the sections, are obtained by means of the proposed unified procedure, parting exclusively from the cross-sectional kinematics expressed in terms of the respective generalized displacements.