159 research outputs found
Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers
We propose a solution strategy for a multimaterial minimum compliance
topology optimization problem, which consists in finding the optimal allocation
of a finite number of candidate (possibly anisotropic) materials inside a
reference domain, with the aim of maximizing the stiffness of the body. As a
relevant and novel application we consider the optimization of self-assembled
structures obtained by means of diblock copolymers. Such polymers are a class
of self-assembling materials which spontaneously synthesize periodic
microstructures at the nanoscale, whose anisotropic features can be exploited
to build structures with optimal elastic response, resembling biological
tissues exhibiting microstructures, such as bones and wood. For this purpose we
present a new generalization of the classical Optimality Criteria algorithm to
encompass a wider class of problems, where multiple candidate materials are
considered, the orientation of the anisotropic materials is optimized, and the
elastic properties of the materials are assumed to depend on a scalar
parameter, which is optimized simultaneously to the material allocation and
orientation. Well-posedness of the optimization problem and well-definition of
the presented algorithm are narrowly treated and proved. The capabilities of
the proposed method are assessed through several numerical tests
Optimal control in ink-jet printing via instantaneous control
This paper concerns the optimal control of a free surface flow with moving
contact line, inspired by an application in ink-jet printing. Surface tension,
contact angle and wall friction are taken into account by means of the
generalized Navier boundary condition. The time-dependent differential system
is discretized by an arbitrary Lagrangian-Eulerian finite element method, and a
control problem is addressed by an instantaneous control approach, based on the
time discretization of the flow equations. The resulting control procedure is
computationally highly efficient and its assessment by numerical tests show its
effectiveness in deadening the natural oscillations that occur inside the
nozzle and reducing significantly the duration of the transient preceding the
attainment of the equilibrium configuration
Multidisciplinary design optimization of a sailplan
In this paper, multi-disciplinary optimization techniques are applied to sail
design. Two different mathematical models, providing the solution of the fluid-dynamic and the
structural problems governing the behaviour of a complete sailplan, are coupled in a
fluid-structure interaction (FSI) scheme, in order to determine the real flying shape of the
sails and the forces acting on them. A numerical optimization algorithm is then
applied, optimizing the structural pattern of the sailplan in order to maximize the driving
force or other significant quantities
Computational fluid dynamics for naval engineering problems
The subject of this thesis is the numerical simulation of viscous free-surface flows in naval engineering applications. State-of-the-art numerical methods based on the solution of the Navier-Stokes equations are used to predict the flow around different classes of boats. We investigate the role of the Computational Fluid Dynamics in the design of racing boats, such as America's Cup yachts and Olympic class rowing hull. The mathematical models describing the different aspects of the physical problem, as well as the numerical methods adopted for their solution, are introduced and critically discussed. The different phases of the overall numerical simulation procedure, from grid generation through the solution of the flow equations to the post-processing of the results, are described. We present the numerical simulations that have been performed to investigate the role of different design parameters in the conception of America's Cup yachts and we describe how the results obtained from the simulations are integrated into the overall design process. The free-surface flow around an Olympic rowing boat is also considered. We propose a simplified approach to take into account the effect of the boat dynamics in the prediction of the hydrodynamic forces acting on the boat. Based on the results of the simulations, we propose a new design concept and we investigate its potential benefits on the boat performances. One of the aspects that is found to be not completely satisfactory, within the standard numerical methods adopted, is the modelling of complex free-surface flows. The second part of this thesis is devoted to a more theoretical and methodological investigation of this aspect. In particular, we present and analyse a new numerical method based on the level set approach for the solution of two-fluid flows. The numerical scheme based on a finite element discretization is introduced and different critical aspects of its implementation are discussed. In particular, we present and analyse a new technique for the stabilization of the advection equation associated to the level set problem. Moreover, we propose a new reinitialization procedure for the level set function which plays a crucial role in the accuracy of the algorithm. The convergence properties of this procedure are analysed and comparisons with more standard approaches are presented. Finally, the proposed method has been used to solve a variety of test cases concerning time dependent two-fluid viscous flows. The results of the simulation are presented and discussed
Structure-preserving neural networks in data-driven rheological models
In this paper we address the importance and the impact of employing structure
preserving neural networks as surrogate of the analytical physics-based models
typically employed to describe the rheology of non-Newtonian fluids in Stokes
flows. In particular, we propose and test on real-world scenarios a novel
strategy to build data-driven rheological models based on the use of
Input-Output Convex Neural Networks (ICNNs), a special class of feedforward
neural network scalar valued functions that are convex with respect to their
inputs. Moreover, we show, through a detailed campaign of numerical
experiments, that the use of ICNNs is of paramount importance to guarantee the
well-posedness of the associated non-Newtonian Stokes differential problem.
Finally, building upon a novel perturbation result for non-Newtonian Stokes
problems, we study the impact of our data-driven ICNN based rheological model
on the accuracy of the finite element approximation.Comment: Submitted for publication in the SIAM Journal on Scientific
Computing, 22 pages, 7 figures, 7 table
TEEN-IMMIGRANTS EXPLORE A MATH MOBILE APP
We present the pilot phase of the project "Teenagers Experience Empowerment by Numbers" (TEEN), which is funded by Politecnico di Milano through the Polisocial Award 2018 and concerns the development of a mobile app to teach essential mathematics to young immigrants. The project aims at preparing them for living in a conscious, autonomous way in a Western country, increasing their ability to deal with everyday tasks that require some mathematical understanding. We present the app, some materials and an activity with the learners who have interacted with that. The set of tasks, tested in small groups, is rooted in daily activities, such as shopping at the supermarket, choosing a mobile internet plan, planning a trip. Our theoretical background is related to existing research findings on teaching to immigrants, Rabardel’s instrumental orchestration and feedback
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