Geometric Surface Processing and Virtual Modeling

In this work we focus on two main topics "Geometric Surface Processing" and "Virtual Modeling". The inspiration and coordination for most of the research work contained in the thesis has been driven by the project New Interactive and Innovative Technologies for CAD (NIIT4CAD), funded by the European Eurostars Programme. NIIT4CAD has the ambitious aim of overcoming the limitations of the traditional approach to surface modeling of current 3D CAD systems by introducing new methodologies and technologies based on subdivision surfaces in a new virtual modeling framework. These innovations will allow designers and engineers to transform quickly and intuitively an idea of shape in a high-quality geometrical model suited for engineering and manufacturing purposes. One of the objective of the thesis is indeed the reconstruction and modeling of surfaces, representing arbitrary topology objects, starting from 3D irregular curve networks acquired through an ad-hoc smart-pen device. The thesis is organized in two main parts: "Geometric Surface Processing" and "Virtual Modeling". During the development of the geometric pipeline in our Virtual Modeling system, we faced many challenges that captured our interest and opened new areas of research and experimentation. In the first part, we present these theories and some applications to Geometric Surface Processing. This allowed us to better formalize and give a broader understanding on some of the techniques used in our latest advancements on virtual modeling and surface reconstruction. The research on both topics led to important results that have been published and presented in articles and conferences of international relevance

Modeling of ground excavation with the particle finite element method

The present work introduces a new application of the Particle Finite Element Method (PFEM) for the modeling of excavation problems. PFEM is presented as a very suitable tool for the treatment of excavation problem. The method gives solution for the analysis of all processes that derive from it. The method has a high versatility and a reasonable computational cost. The obtained results are really promising.Postprint (published version

A contribution to the finite element analysis of high-speed compressible flows and aerodynamics shape optimization

This work covers a contribution to two most interesting research elds in aerodynamics, the fi nite element analysis of high-speed compressible flows (Part I) and aerodynamic shape optimization (Part II). The fi rst part of this study aims at the development of a new stabilization formulation based on the Finite Increment Calculus (FIC) scheme for the Euler and Navier-Stokes equations in the context of the Galerkin nite element method (FEM). The FIC method is based on expressing the balance of fluxes in a spacetime domain of nite size. It is tried to prevent the creation of instabilities normally presented in the numerical solutions due to the high convective term and sharp gradients. In order to overcome the typical instabilities happening in the numerical solution of the high-speed compressible flows, two stabilization terms, called streamline term and transverse term, are added through the FIC formulation in space-time domain to the original conservative equations of mass, momentum and energy. Generally, the streamline term holding the direction of the velocity is responsible for stabilizing the spurious solutions produced from the convective term while the transverse term smooths the solution in the high gradient zones. An explicit fourth order Runge-Kutta scheme is implemented to advance the solution in time. In order to investigate the capability of the proposed formulation, some numerical test examples corresponding to subsonic, transonic and supersonic regimes for inviscid and viscous flows are presented. The behavior of the proposed stabilization technique in providing appropriate solutions has been studied especially near the zones where the solution has some complexities such as shock waves, boundary layer, stagnation point, etc. Although the derived methodology delivers precise results with a nearly coarse mesh, the mesh refinement technique is coupled in the solution to create a suitable mesh particularly in the high gradient zones. The comparison of the numerical results obtained from the FIC formulation with the reference ones demonstrates the robustness of the proposed method for stabilization of the Euler and Navier-Stokes equations. It is observed that the usual oscillations occur in the Galerkin FEM, especially near the high gradient zones, are cured by implementing the proposed stabilization terms. Furthermore, allowing the adaptation framework to modify the mesh, the quality of the results improves signi cantly. The second part of this thesis proposes a procedure for aerodynamic shape optimization combining Genetic Algorithm (GA) and mesh re nement technique. In particular, it is investigated the e ect of mesh re nement on the computational cost and solution accuracy during the process of aerodynamic shape optimization. Therefore, an adaptive remeshing technique is joined to the CFD solver for the analysis of each design candidate to guarantee the production of more realistic solutions during the optimum design process in the presence of shock waves. In this study, some practical transonic airfoil design problems using adap- tive mesh techniques coupled to Multi-Objective Genetic Algorithms (MOGAs) and Euler flow analyzer are addressed. The methodology is implemented to solve three practical design problems; the fi rst test case considers a reconstruction design optimization that minimizes the pressure error between a prede ned pressure curve and candidate pressure distribution. The second test considers the total drag minimization by designing airfoil shape operating at transonic speeds. For the final test case, a multi-objective design optimization is conducted to maximize both the lift to drag ratio (L/D) and lift coe cient (Cl). The solutions obtained with and without adaptive mesh re nement are compared in terms of solution accuracy and computational cost. These design problems under transonic speeds need to be solved with a ne mesh, particularly near the object, to capture the shock waves that will cost high computational time and require solution accuracy. By comparison of the the numerical results obtained with both optimization problems, the obtainment of direct bene ts in the reduction of the total computational cost through a better convergence to the final solution is evaluated. Indeed, the improvement of the solution quality when an adaptive remeshing technique is coupled with the optimum design strategy can be judged.El presente trabajo pretende contribuir a dos de los campos de investigaci on m as interesantes en la aerodin amica, el an alisis num erico de flujos compresibles a alta velocidad (Parte I) y la optimizaci on de la forma aerodin amica (Parte II). La primera parte de este estudio se centra en la soluci on num erica de las ecuaciones de Navier-Stokes, que modelan el comportamiento de flujos compresibles a alta velocidad. La discretizaci on espacial se lleva a cabo mediante el m etodo de elementos nitos (FEM) y se pone especial enfasis en el desarrollo de una nueva formulaci on estabilizada basada en la t ecnica de c alculo de Incremento fi nitos (FIC). En este ultima, los t erminos de estabilizaci on convectiva se obtienen de manera natural de las ecuaciones de gobierno a trav es de postulados de conservaci on y equilibrio de flujos en un dominio espacio-tiempo de tamaño nito. Ello lleva a la obtenci on de dos t erminos de estabilizaci on que funcionan de manera complementaria. Uno act ua en direcci on de las lineas de corriente proporcionando la estabilizaci on necesaria para contrarestrar las inestabilidades propias de la forma discreta de Galerkin y el otro t ermino, de tipo shock capturing, act ua de manera transversal a las l neas de corriente y permite mejorar la soluci on num erica alrededor de discontinuidades y otro tipos de fen omenos localizados en el campo de soluci on de problema. La forma discreta de las ecuaciones de gobierno se completa mediante un esquema de integraci on temporal expl icito de tipo de Runge-Kutta de 4to orden. El esquema de soluci on b asico propuesto se complementa con una t ecnica de re namiento adaptativo de malla que permite mejorar autom aticamente la soluci on num erica en zonas localizadas del dominio en que, dadas las caracter sticas del flujo, se necesita una mayor resoluci on espacial. Con el prop osito de investigar el comportamiento de la formulaci on num erica se estudian diferentes casos de an alisis que implican flujos viscosos y no viscosos en r egimen subs onico, trans onico y supers onico y se estudia con especial detalle el funcionamiento de la t ecnica de estabilizaci on propuesta. Los resultados obtenidos demuestran una exactitud satisfactoria y una buena correlaci on con resultados presentes en la literatura, incluso cuando se trabaja con discretizaciones espaciales relativamente gruesas. Adicionalmente, los estudios num ericos realizados demuestran que el empleo del esquema adaptativo de malla es e ficaz para incrementar la exactitud de la soluci on numerica manteniendo un bajo coste computacional. En la segunda parte de este estudio se propone un m etodo para la optimizaci on de formas aerodin amicas que combina algoritmos gen eticos multiobjetivo (MOGAs) y remallado adaptativo con el objetivo de asegurar, con un coste computacional m nimo, la calidad de la soluci on numerica empleada en el proceso de b usqueda de un determinado diseño objetivo, particularmente cuando el flujo presenta discontinuidades y gradientes muy localizados, ti picos de flujos a alta velocidad. La metodolog a se aplica a resolver tres problemas pr acticos de diseño de per les aerodin amicos en flujo trans onico que implican la optimizaci on de la distribuci on de presiones, minimizaci on de la resistencia de onda y maximizaci on conjunta de la sustentaci on y la relaci on sustentaci on/resistencia. Para cada uno de ellos se estudia el efecto del re namiento en la calidad de la soluci on num erica as como tambi en en el coste computacional y la convergencia del problema. Los estudios realizados demuestran la e cacia de la metodolog a propuesta

Modeling and Simulation Techniques Used in High Strain Rate Projectile Impact

A series of computational models and simulations were conducted for determining the dynamic responses of a solid metal projectile impacting a target under a prescribed high strain rate loading scenario in three-dimensional space. The focus of this study was placed on two different modeling techniques within finite element analysis available in the Abaqus software suite. The first analysis technique relied heavily on more traditional Lagrangian analysis methods utilizing a fixed mesh, while still taking advantage of the finite difference integration present under the explicit analysis approach. A symmetry reduced model using the Lagrangian coordinate system was also developed for comparison in physical and computational performance. The second analysis technique relied on a mixed model that still made use of some Lagrangian modeling, but included smoothed particle hydrodynamics techniques as well, which are mesh free. The inclusion of the smoothed particle hydrodynamics was intended to address some of the known issues in Lagrangian analysis under high displacement and deformation. A comparison of the models was first performed against experimental results as a validation of the models, then the models were compared against each other based on closeness to experimentation and computational performance

Smeared crack approach: Back to the original track

This paper reviews briefly the formulations used over the last 40 years for the solution of problems involving tensile cracking, both with the discrete and smeared crack approaches. The paper focuses in the smeared approach, identifying as its main drawbacks the observed mesh-size and mesh-bias spurious dependence when the method is applied “straightly”. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and strong discontinuity (discrete cracks) approaches are analyzed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure uniqueness of the solution, attaining the necessary stability and convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is well posed, stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious meshsize or mesh-bias dependence, comparing very favorably with those obtained with other fracture and continuum mechanics approaches

Challenges, tools and applications of tracking algorithms in the numerical modelling of cracks in concrete and masonry structures

The final publication is available at Springer via http://dx.doi.org/10.1007/s11831-018-9274-3The importance of crack propagation in the structural behaviour of concrete and masonry structures has led to the development of a wide range of finite element methods for crack simulation. A common standpoint in many of them is the use of tracking algorithms, which identify and designate the location of cracks within the analysed structure. In this way, the crack modelling techniques, smeared or discrete, are applied only to a restricted part of the discretized domain. This paper presents a review of finite element approaches to cracking focusing on the development and use of tracking algorithms. These are presented in four categories according to the information necessary for the definition and storage of the crack-path. In addition to that, the most utilised criteria for the selection of the crack propagation direction are summarized. The various algorithmic issues involved in the development of a tracking algorithm are discussed through the presentation of a local tracking algorithm based on the smeared crack approach. Challenges such as the modelling of arbitrary and multiple cracks propagating towards more than one direction, as well as multi-directional and intersecting cracking, are detailed. The presented numerical model is applied to the analysis of small- and large-scale masonry and concrete structures under monotonic and cyclic loading.Peer ReviewedPostprint (author's final draft

ICASE/LaRC Workshop on Adaptive Grid Methods

Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field

Galerkin projection of discrete fields via supermesh construction

Interpolation of discrete FIelds arises frequently in computational physics. This thesis focuses on the novel implementation and analysis of Galerkin projection, an interpolation technique with three principal advantages over its competitors: it is optimally accurate in the L2 norm, it is conservative, and it is well-defined in the case of spaces of discontinuous functions. While these desirable properties have been known for some time, the implementation of Galerkin projection is challenging; this thesis reports the first successful general implementation. A thorough review of the history, development and current frontiers of adaptive remeshing is given. Adaptive remeshing is the primary motivation for the development of Galerkin projection, as its use necessitates the interpolation of discrete fields. The Galerkin projection is discussed and the geometric concept necessary for its implementation, the supermesh, is introduced. The efficient local construction of the supermesh of two meshes by the intersection of the elements of the input meshes is then described. Next, the element-element association problem of identifying which elements from the input meshes intersect is analysed. With efficient algorithms for its construction in hand, applications of supermeshing other than Galerkin projections are discussed, focusing on the computation of diagnostics of simulations which employ adaptive remeshing. Examples demonstrating the effectiveness and efficiency of the presented algorithms are given throughout. The thesis closes with some conclusions and possibilities for future work