Analysis of Meshfree Methods for Lagrangian Fluid-Structure Interaction

In this dissertation a new numerical method for solving Fluid-Structure Interaction (FSI) problems in a Lagrangian framework is developed, where solids of different constitutive laws can suffer very large deformations and fluids are considered to be newtonian and incompressible. For that, we first introduce a meshless discretization based on local maximum-entropy interpolants. This allows to discretize a spatial domain with no need of tessellation, avoiding the mesh limitations. Later, the Stokes flow problem is studied. The Galerkin meshless method based on a max-ent scheme for this problem suffers from instabilities, and therefore stabilization techniques are discussed and analyzed. An unconditionally stable method is finally formulated based on a Douglas-Wang stabilization. Then, a Langrangian expression for fluid mechanics is derived. This allows us to establish a common framework for fluid and solid domains, such that interaction can be naturally accounted. The resulting equations are also in the need of stabilization, what is corrected with an analogous technique as for the Stokes problem. The fully Lagrangian framework for fluid/solid interaction is completed with simple point-to-point and point-to-surface contact algorithms. The method is finally validated, and some numerical examples show the potential scope of applications.

Airport Taxi Planning: Lagrangian Decomposition

The airport taxi planning (TP) module is a decision tool intended to guide airport surface management operations. TP is defined by a flow network optimization model that represents flight ground movements and improves aircraft taxiing routes and schedules during periods of aircraft congestion. TP is not intended to operate as a stand‐alone tool for airport operations management: on the contrary, it must be used in conjunction with existing departing and arriving traffic tools and overseen by the taxi planner of the airport, also known as the aircraft ground controller. TP must be flexible in order to accommodate changing inputs while maintaining consistent routes and schedules already delivered from past executions. Within this dynamic environment, the execution time of TP may not exceed a few minutes. Classic methods for solving binary multi‐commodity flow networks with side constraints are not efficient enough; therefore, a Lagrangian decomposition methodology has been adapted to solve it. We demonstrate TP Lagrangian decomposition using actual data from the Madrid‐Barajas Airport

A repairability index for reinforced concrete members based on fracture mechanics

This paper proposes a repairability index for damage assessment in reinforced concrete structural members. The procedure discussed in this paper differs from the standard methods in two aspects: the structural and damage analyses are coupled and it is based on the concepts of fracture and continuum damage mechanics. The relationship between the repairability index and the well-known Park and Ang index is shown in some particular cases.

Foundations and applications of non-equilibrium statistical mechanics

The full text of this article is available in the PDF provided.

Self Learning and self evaluation exercises database in basic mechanics: a theoretical-practical approach

In the School of Mines of the Technical University of Madrid (UPM) the first course of different degrees has been implemented and adapted to the European Higher Educational Area (EHEA). In all of the degrees there is a first semester course which gathers all the contents of basic mechanics: from the first kinematics concepts to the rigid solid plane motion Before the Bologna process took place, the authors had established the final assessment of the theoretical contents through open questions of theoretical-practical character In the present work, the elaboration of a wide database containing theoretical-practical questions that students can access on line is presented. The questions are divided in thirteen different questionnaires composed of a number of questions randomly chosen from a certain group in the database. Each group corresponds to a certain learning objective that the student knows. After answering the questionnaire and checking the grade assigned according to the performance of the student, the pupils can see the correct response displayed on the screen and widely explained by the professors. This represents a 10% of the final grade. As the student can access the questionnaires as many times as they want, the main goal is the self-assessment of each learning objective and therefore, getting the students involved in their own learning process so they can decide how much time they need to acquire the required level.

Lagrangian skeleton on the Gulf of Mexico oil spill

The understanding of the circulation of ocean currents, the exchange of CO2 between atmosphere and oceans, and the influence of the oceans on the distribution of heat on a global scale is key to our ability to predict and assess the future evolution of climate [1, 2]. Global climate change is affecting sea breathing through mechanisms not yet understood.

A Lagrangian descriptor applied to the Kuroshio current

The understanding of the circulation of ocean currents, the exchange of CO2 between atmosphere and oceans, and the in uence of the oceans on the distribution of heat on a global scale is key to our ability to predict and assess the future evolution of climate.

Involutivity of the Hamilton-Cartan equations of a second-order Lagrangian admitting a first-order Hamiltonian formalism

Involutivity of the Hamilton-Cartan equations of a second-order Lagrangian admitting a first-order Hamiltonian formalism

A global Lagrangian descriptor applied to the Kuroshio current

A global Lagrangian descriptor applied to the Kuroshio current

Lagrangian structure on the oil

The understanding of the circulation of ocean currents, the exchange of CO2 between atmosphere and oceans, and the influence of the oceans on the distribution of heat and momentum on a global scale is key to our ability to predict and assess the future evolution of climate.

The Lagrangian description of aperiodic flows: a case study of the Kuroshio Current

This article reviews several recently developed Lagrangian tools and shows how their com- bined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the climate impact of ocean transport processes, we illustrate a 2D application on altimeter data sets over the area of the Kuroshio Current, although the proposed techniques are general and applicable to arbitrary time depen- dent aperiodic flows. The first challenge for describing transport in aperiodical time dependent flows is obtaining a representation of the phase portrait where the most relevant dynamical features may be identified. This representation is accomplished by using global Lagrangian descriptors that when applied for instance to the altimeter data sets retrieve over the ocean surface a phase portrait where the geometry of interconnected dynamical systems is visible. The phase portrait picture is essential because it evinces which transport routes are acting on the whole flow. Once these routes are roughly recognised it is possible to complete a detailed description by the direct computation of the finite time stable and unstable manifolds of special hyperbolic trajectories that act as organising centres of the flow.

B.I.E.M. in solid mechanics

In solid mechanics the weak formulation produces an integral equation ready for a discretization and with less restrictive requiremets than the standard field equations. Fundamentally the weak formulation is a expresion of a green formula. An alternative is to choose another green formula materializing a reciprocity relationship between the basis unknowns and an auxiliary family of functions. The degree of smoothness requiered to practice the discretization is then translated to the auxiliar functions. The subsequent discretization (constant, linear etc.)produces a set of equations on the boundary of the domain. For linear 3-D problems the BIEM appears then as a powerful alternative to FEM, because of the reduction to 2-D thanks to the features previously described.

A characterization of conserved quantities in non-equilibrium thermodynamics

The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium thermodynamics formulated within the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) framework. The geometric meaning of symmetry is reviewed in this formal setting and then utilized to identify possible conserved quantities and the conditions that guarantee their strict conservation. Examples are provided that demonstrate the validity of the proposed definition in the context of finite and infinite dimensional thermoelastic problems.

A computational model coupling mechanics and electrophysiology in spinal cord injury

Traumatic brain injury and spinal cord injury have recently been put under the spotlight as major causes of death and disability in the developed world. Despite the important ongoing experimental and modeling campaigns aimed at understanding the mechanics of tissue and cell damage typically observed in such events, the differenti- ated roles of strain, stress and their corresponding loading rates on the damage level itself remain unclear. More specif- ically, the direct relations between brain and spinal cord tis- sue or cell damage, and electrophysiological functions are still to be unraveled. Whereas mechanical modeling efforts are focusing mainly on stress distribution and mechanistic- based damage criteria, simulated function-based damage cri- teria are still missing. Here, we propose a new multiscale model of myelinated axon associating electrophysiological impairment to structural damage as a function of strain and strain rate. This multiscale approach provides a new framework for damage evaluation directly relating neuron mechanics and electrophysiological properties, thus provid- ing a link between mechanical trauma and subsequent func- tional deficits.

Development and implementation of a virtual laboratory for training process improvement in the mechanics of continuous media

The project arises from the need to develop improved teaching methodologies in field of the mechanics of continuous media. The objective is to offer the student a learning process to acquire the necessary theoretical knowledge, cognitive skills and the responsibility and autonomy to professional development in this area. Traditionally the teaching of the concepts of these subjects was performed through lectures and laboratory practice. During these lessons the students attitude was usually passive, and therefore their effectiveness was poor. The proposed methodology has already been successfully employed in universities like University Bochum, Germany, University the South Australia and aims to improve the effectiveness of knowledge acquisition through use by the student of a virtual laboratory. This laboratory allows to adapt the curricula and learning techniques to the European Higher Education and improve current learning processes in the University School of Public Works Engineers -EUITOP- of the Technical University of Madrid -UPM-, due there are not laboratories in this specialization. The virtual space is created using a software platform built on OpenSim, manages 3D virtual worlds, and, language LSL -Linden Scripting Language-, which imprints specific powers to objects. The student or user can access this virtual world through their avatar -your character in the virtual world- and can perform practices within the space created for the purpose, at any time, just with computer with internet access and viewfinder. The virtual laboratory has three partitions. The virtual meeting rooms, where the avatar can interact with peers, solve problems and exchange existing documentation in the virtual library. The interactive game room, where the avatar is has to resolve a number of issues in time. And the video room where students can watch instructional videos and receive group lessons. Each audiovisual interactive element is accompanied by explanations framing it within the area of knowledge and enables students to begin to acquire a vocabulary and practice of the profession for which they are being formed. Plane elasticity concepts are introduced from the tension and compression testing of test pieces of steel and concrete. The behavior of reticulated and articulated structures is reinforced by some interactive games and concepts of tension, compression, local and global buckling will by tests to break articulated structures. Pure bending concepts, simple and composite torsion will be studied by observing a flexible specimen. Earthquake resistant design of buildings will be checked by a laboratory test video.