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- A new finite element formulation for the dynamic analysis of beams under moving loadsPublication . Freixial Argente Dos Santos, Hugo AlexandreEarly studies highlighted the fact that moving loads on beams may induce significantly higher dynamic deflections and stresses than those observed in the quasi-static case. Since then, the dynamics of beams under moving loads has been an active research area, in particular for the past decades, with the rapidly increasing computer power allowing the development of highly robust and sophisticated computational and numerical methods in applied mechanics and engineering. This work introduces a novel finite element formulation for the dynamic analysis of Euler-Bernoulli beams subjected to moving loads. The formulation is consistent with a complementary form of the well known Hamilton’s variational principle, and will be used to address some numerical tests in both modal and time domains. The effectiveness and accuracy of the formulation will be assessed and discussed by comparison between the obtained results and those rendered by the standard displacement-based finite element formulation. As it will be demonstrated, the proposed formulation not only renders continuous bending-moment and shear-force distributions, a desired feature in the structural design field, but also has a superior accuracy than that provided by the displacement formulation that uses the same number of nodal degrees-of-freedom.
- Buckling analysis of layered composite beams with interlayer slip: A force-based finite element formulationPublication . Freixial Argente Dos Santos, Hugo AlexandreA force-based finite element formulation for the buckling analysis of two-layer composite beam structures with partial interaction is presented. The geometrically nonlinear beam elements possess a single flexible shear interface and each layer is modelled by means of Timoshenko's theory. The formulation relies on a hybrid variational principle of complementary energy only involving force/moment-like variables as fundamental unknown fields. The approximate field variables are selected such that all equilibrium differential equations are satisfied in strong form. The inter-element equilibrium, as well as Neumann boundary conditions are enforced by means of the Lagrangian-multiplier method. The accuracy and effectiveness of the proposed formulation is demonstrated through the analysis of several numerical tests.