Le 7 novembre 2023 à 11h00, Amphithéâtre François Canac, LMA
Abstract : The increasing complexity of numerical models for engineering systems, taking into account ever finer mesh, accurate material models and multiphysics phenomena, occurring at very different space and time scales, boosted the development of partitioning approaches. In the field of structural dynamics, the main advantage of partitioning approaches is to gain in computational efficiency by using different time integrators with their own time step, depending on the non-overlapping subdomains composing the global mesh. Subdomain coupling methods based on Lagrange multipliers at the interface between subdomains have been set up, following an energy-based argument. It leads to the proposition of Hybrid Asynchronous Time Integrator (HATI), stable and second order accurate. A large variety of HATI applications is then presented in the fields of structural dynamics and earthquake engineering, including smooth dynamics without contact as well as non-smooth dynamics with frictional contact phenomena.
First, HATI is employed for Reinforced Concrete structures under earthquake loading, without contact, using multi-fibre beam elements whose cross-section is divided into steel and concrete fibres associated with cyclic and nonlinear behaviors. Then, the frictional contact is explored by developing an explicit time integrator in Moreau’s framework, called CD-Lagrange scheme, based on the velocity-impulse formulation with the contact constraints enforced using Lagrange multipliers. The CD-Lagrange scheme is adopted for reproducing the frictional contact phenomena experiencing by crane bridge under earthquake loading following the HATI approach. It enables us to focus on high frequency phenomena with frictional contacts in small subdomains including the rails of the girder beams and the trolley wheels, using small time steps satisfying the CFL condition, whereas the main part of the complex problem is dealt with a classical implicit time integration scheme with large time steps. In this way, we benefit from advantages of the two time integrators, leading to computation time gains as well as versatility in applying appropriate damping formulations depending on explicit or implicit subdomains. CD-Lagrange scheme is also adopted for simulating the eccentric pounding phenomena between real scale two-storey steel-concrete structures, tested on the shaking table AZALEE (CEA Saclay, France), enabling us to obtain very satisfactory results with respect to experimental data, in terms of floor displacements and acceleration spectra in a large frequency range.
Soil Structure Interaction (SSI) problems are also considered by developing Multi Time Step Hybrid Perfectly Matched Layers (PML) in the context of the simulation of wave propagation in the time domain for 2D and 3D unbounded domains. Indeed, HATI approach is useful to integrate in time the complex space semi-discrete equations in the 2D/3D PMLs, independently from the time integration of the classical semi-discrete equations of motion in the domain of interest. Hybrid PMLs are also employed in research developed within LSMS laboratory, EPFL, concerning the simulation of an unbounded elastic block on a rigid flat plane: It involves rate and state friction laws at the interface, compared to classical Coulomb’s law with constant friction coefficient.
On the basis of the HATI approach, multi time step explicit/implicit co-simulation strategies are developed in order to couple a seismology software (EFISPEC3D, BRGM) based on 3D Hexahedral Spectral Elements with FE software (Akantu, EPFL) in the context of SSI applications: A seismic non-linear analysis of a concrete gravity dam is carried out using the HATI approach combined with mortar coupling to deal with non-matching meshes at the interface between the subdomains. The seismology software simulates the seismic source as well as the large medium concerned by the wave propagation, using an explicit time integrator, whereas the non-linear behavior of the dam is simulated by the FE software with an implicit time integrator.
To conclude, the presented works aim at developing numerical coupling approaches in order to tackle complex problems in structural dynamics. The conducted research has deep roots in Computational Mechanics while focusing on Earthquake Engineering problems in a constant effort to apply the developed innovative tools to engineering systems.