Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Soil-structure interaction during tunnelling in urban area: observations and 3D numerical modelling

This work illustrates a soil-tunnel-structure interaction study performed by an integrated,geotechnical and structural,approach based on 3D finite element analyses and validated against experimental observations.The study aims at analysing the response of reinforced concrete framed buildings on discrete foundations in interaction with metro lines.It refers to the case of the twin tunnels of the Milan (Italy) metro line 5,recently built in coarse grained materials using EPB machines,for which subsidence measurements collected along ground and building sections during tunnelling were available.Settlements measured under freefield conditions are firstly back interpreted using Gaussian empirical predictions. Then,the in situ measurements’ analysis is extended to include the evolving response of a 9 storey reinforced concrete building while being undercrossed by the metro line.In the finite element study,the soil mechanical behaviour is described using an advanced constitutive model. This latter,when combined with a proper simulation of the excavation process, proves to realistically reproduce the subsidence profiles under free field conditions and to capture the interaction phenomena occurring between the twin tunnels during the excavation. Furthermore, when the numerical model is extended to include the building, schematised in a detailed manner, the results are in good agreement with the monitoring data for different stages of the twin tunnelling. Thus, they indirectly confirm the satisfactory performance of the adopted numerical approach which also allows a direct evaluation of the structural response as an outcome of the analysis. Further analyses are also carried out modelling the building with different levels of detail. The results highlight that, in this case, the simplified approach based on the equivalent plate schematisation is inadequate to capture the real tunnelling induced displacement field. The overall behaviour of the system proves to be mainly influenced by the buried portion of the building which plays an essential role in the interaction mechanism, due to its high stiffness.

Design, development, and analysis of hybrid metal-composite tube for industrial application

In the aerospace, automotive, printing, and sports industries, the development of hybrid Carbon Fiber Reinforced Polymer (CFRP)-metal components is becoming increasingly important. The coupling of metal with CFRP in axial symmetric components results in reduced production costs and increased mechanical properties such as bending, torsional stiffness, mass reduction, damping, and critical speed compared to the single material-built ones. In this thesis, thanks to a novel methodology involving a rubbery/viscoelastic interface layer, several hybrid aluminum-CFRP prototype tubes were produced. Besides, an innovative system for the cure of the CFRP part has been studied, analyzed, tested, and developed in the company that financed these research activities (Reglass SRL, Minerbio BO, Italy). The residual thermal stresses and strains have been investigated with numerical models based on the Finite Element Method (FEM) and compared with experimental tests. Thanks to numerical models, it was also possible to reduce residual thermal stresses by optimizing the lamination sequence of CFRP and determining the influence of the system parameters. A novel software and methodology for evaluating mechanical and damping properties of specimens and tubes made in CFRP were also developed. Moreover, to increase the component's damping properties, rubber nanofibers have been produced and interposed throughout the lamination of specimens. The promising results indicated that the nanofibrous mat could improve the material damping factor over 77% and be adopted in CFRP components with a negligible increment of weight or losing mechanical properties.

Acoustic backscatter of small pelagic fish species in the Adriatic Sea

The aim of the present study is to apply a broad range of techniques to increase the knowledge of acoustic properties of Sprattus sprattus, Scomber colias and Trachurus mediterraneus in the Adriatic Sea. A novel study using tethered live fish but not involving hooks and anesthetic was tested on T. mediterraneus and S. colias through several ex situ experiments using a split-beam scientific echosounder operating at 38, 120, and 200 kHz. The mean TS was estimated for 29 live specimens, resulting in a conversion factor b20 value of -71.4 dB re 1 m2 and -71.6 dB re 1 m2 respectively which is ~3 dB lower than the current one in use in the Mediterranean Sea. Successively, two monospecific trawl hauls were analyzed through the application of in situ approach for the computation of TS values of S. sprattus which led to six b20 values for sprat (range, -68.8 dB re 1 m2 to -65.6 dB re 1 m2), all higher than the current known value of -71.7 dB re 1 m2. The high difference up to 4.2 dB compared to the current value translates in a significant decrease of absolute sprat biomass along the time series un to 20%. Finally, 149 specimens of the three species were collected for backscattering model application(i.e. Kirchhoff-ray mode model (KRM) and Finite Element Method (FEM)) from digital images of the fish body and swimbladder obtained from Computer Tomography (CT) and X-Ray scans. The values resulting from the application of KRM and FEM are in agreement with empirical results. In general terms the present work proposes the acoustic backscatter characterization of S. colias, S. sprattus and T. mediterraneus in the Mediterranean Sea.

Active control of sound radiated by vibrating surfaces on a McLaren supercar

Sound radiators based on forced vibrations of plates are becoming widely employed, mainly for active sound enhancement and noise cancelling systems, both in music and automotive environment. Active sound enhancement solutions based on electromagnetic shakers hence find increasing interest. Mostly diffused applications deal with active noise control (ANC) and active vibration control systems for improving the acoustic experience inside or outside the vehicle. This requires investigating vibrational and, consequently, vibro-acoustic characteristics of vehicles. Therefore, simulation and processing methods capable of reducing the calculation time and providing high-accuracy results, are strongly demanded. In this work, an ideal case study on rectangular plates in fully clamped conditions preceded a real case analysis on vehicle panels. The sound radiation generated by a vibrating flat or shallow surface can be calculated by means of Rayleigh’s integral. The analytical solution of the problem is here calculated implementing the equations in MATLAB. Then, the results are compared with a numerical model developed in COMSOL Multiphysics, employing Finite Element Method (FEM). A very good matching between analytical and numerical solutions is shown, thus the cross validation of the two methods is achieved. The shift to the real case study, on a McLaren super car, led to the development of a mixed analytical-numerical method. Optimum results were obtained with mini shakers excitement, showing good matching of the recorded SPL with the calculated one over all the selected frequency band. In addition, a set of directivity measurements of the hood were realized, to start studying the spatiality of sound, which is fundamental to active noise control systems.