Résumé.HDR.2022_DOTTAVIO.Michele

HDR Michele D'OTTAVIO, Université Paris Nanterre
3 juin 2022

Abstract.
Composite structures are widely employed in engineering applications for increasing the structural weight efficiency. These deserve dedicated modeling strategies that consider their multi-scale heterogeneity and anisotropy. It is well known that structural models (beams, plates and shells) can accurately grasp the global and local response, provided their formulation is adapted to the intended analysis and to the considered problem (geometry, loading…). The present work discusses the variable kinematics approach as an axiomatic modeling tool for constructing arbitrary models, thus allowing to adapt the model assumptions in order to obtain the most accurate result without excess of model parameters. To this aim, in order to improve the accuracy of the transverse stresses, which play a prominent role in the strength of composite structures, Reissner’s mixed approach RMVT is considered in addition to the more classical displacement-based approaches.

After reviewing the variable kinematics models available in literature, that are conveniently expressed by referring to a so-called Unified Formulation, the Sublaminate Generalised Unified Formulation (SGUF) is presented as a particularly attractive framework for an efficient modeling of sandwich structures. The formulation is extended to multifield problems with reference to the weak thermo-mechanical coupling and the strong piezo-electric coupling. In this latter case, particular attention is dedicated to the representation of electrical boundary conditions.

The presentation is limited to plate geometries, but extensions to beam and shells are possible and referenced in the bibliography. Besides the classical quasi-analytical Navier-type solution, numerical solution methods (Ritz and Finite Element Method) are considered for solving the 2D governing equations: particular emphasis is then given to the formulation of numerical models that assure a good convergence rate, i.e., to the absence of numerical pathologies in order enhance the efficiency of the computational model. The problem of adopting suitable approximations for the transverse stress fields for RMVT-based models is given due attention.

The possibility is also discussed of constructing highly efficient computational models, in particular by coupling different axiomatic models so to adapt them locally depending on the gradients of the response; for this, an overlap-free coupling operator for incompatible kinematics has been proposed based on the eXtended Variational Formulation (XVF).

Results issued from the works already published by the author are exemplarily shown: laminated as well as sandwich plates are considered, for which global response problems (buckling, vibration) as well as local response (wrinkling and local stress response, including free-edge stress concentrations) are addressed. The promising results allow to devise future developments, in particular towards the inclusion of material and geometric nonlinearities.