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Freixial Argente dos Santos, Hugo Alexandre
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- On the observability of the pseudo-Rayleigh waves on submerged cylindrical shellsPublication . Iakovlev, S.; Lefieux, A.; Huntemann, B.; Freixial Argente Dos Santos, Hugo Alexandre; Pyke, D.The field radiated by a transiently responding submerged cylindrical shell is addressed, with the focus on the pseudo-Rayleigh wave A0. The main objective of the study is to offer further insights into the experimentally observed issues with the observability of the A0 wave on certain types of thin shells. The presented analysis employs a semi-analytical methodology based on combining the use of classical methods of mathematical physics with a finite-difference approximation for the resulting structural modes. Two shell materials are considered, steel and duraluminum. The radiated hydrodynamic fields are explicitly imaged, and the A0 wave is analyzed. It is demonstrated that for the steel shell, the A0 wave is much more pronounced and has a much lower attenuation than for the same duraluminum shell, a result that is in agreement with the experimental studies. The shell material density is identified as the most likely primary cause of the observed differences in the radiation of the A0 wave.
- 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.
- Finite element analysis of non-uniform functionally graded multi-cracked Timoshenko beams using an equilibrium-based formulationPublication . Freixial Argente dos Santos, Hugo Alexandre; Silberschmidt, V. V.A novel finite element formulation is introduced for the static analysis of non-uniform functionally graded multi-cracked Timoshenko beams with small deformations. The cracks, assumed to remain open, are modelled using the so-called discrete spring approach, in which Dirac delta generalized functions are introduced into the bending flexibility of the beams. The formulation is derived on the basis of a complementary variational approach that involves only the elements' shear forces and bending moments as the fundamental unknown fields. The corresponding element flexibility matrix is obtained in closed-form, with the crack contributions explicitly separated from the standard bending and shear flexibility terms. The numerical solutions produced by the formulation are strictly equilibrated, i.e., they satisfy all equilibrium conditions of the associated boundary-value problem in strong form. The effectiveness and accuracy of the formulation are numerically assessed through its application to several benchmark problems. The obtained results are analysed and compared, where possible, to exact (or reference) solutions and solutions given by the standard displacement-based finite element formulation, clearly illustrating the capability of the formulation to deliver highly accurate results for both thin and thick beams, even on meshes with only a few degrees-of-freedom.
- A new, simple, and effective variationally consistent mixed finite element formulation for the geometrically exact planar analysis of beams and framesPublication . Freixial Argente dos Santos, Hugo AlexandreA robust and efficient mixed finite element formulation, applicable to both shear-rigid (Kirchhoff-type) and shear-flexible (Reissner-type) beam theories, is proposed for the geometrically exact planar analysis of beams and frames. The formulation is derived from a Hellinger-Reissner-type variational principle, in which the spatial components of the internal forces, bending moment, and cross-sectional rotation are adopted as primary unknowns. Equilibrium of the spatial internal forces is satisfied in strong form at the member level, while the assumed bending moment field is C0 -continuous and satisfies equilibrium boundary conditions. The formulation is intrinsically free from shear- and membrane-locking phenomena, admits explicit closed-form expressions for both the residual vector and the consistent symmetric tangent matrix, and yields a highly sparse and banded global system with a reduced number of unknowns compared with conventional displacement-based formulations and previously proposed hybrid-mixed formulations. Displacement fields are recovered a posteriori by integrating the kinematic compatibility relations, producing globally C0 -continuous fields that satisfy all prescribed kinematic boundary conditions. Nonlinear equilibrium paths are traced using an arc-length strategy with a linear extrapolation predictor, and critical points are identified through the determinant of a Schur-complement-based equivalent stiffness matrix that emerges naturally from the formulation. Numerical examples demonstrate the accuracy, convergence, and robustness of the proposed approach, including verification against analytical solutions under pure bending, assessment of shear-locking performance, and the simulation of complex nonlinear responses involving snap-through, snap-back, and symmetry-breaking bifurcation phenomena.