Smooth quasi-developable surfaces bounded by smooth curves

Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not adequate for generating smooth quasi-developable surfaces. We propose the first method which is capable of exploring the full solution space of continuous input curves to compute a smooth quasi-developable ruled surface with as large developability as possible. The resulting surface is exactly bounded by the input smooth curves and is guaranteed to have no self-intersections. The main contribution is a variational approach to compute a continuous mapping of parameters of input curves by minimizing a function evaluating surface developability. Moreover, we also present an algorithm to represent a resulting surface as a B-spline surface when input curves are B-spline curves.Comment: 18 page

Numerical Simulation of Frictional Contact Problems using Nagata Patches in Surface Smoothing

Tese de doutoramento em Engenharia Mecânica, na especialidade de Tecnologias de Produção, apresentada ao Departamento de Engenharia Mecânica da Faculdade de Ciências e Tecnologia da Universidade de CoimbraAll movements in the world involve contact and friction, from walking to car driving. The contact mechanics has application in many engineering problems, including the connection of structural members by bolts or screws, design of gears and bearings, sheet metal or bulk forming, rolling contact of car tyres, crash analysis of structures, as well as prosthetics in biomedical engineering. Due to the nonlinear and non-smooth nature of contact mechanics (contact area is not known a priori), such problems are currently solved using the finite element method within the field of computational contact mechanics. However, most of the commercial finite element software packages presently available are not entirely capable to solve frictional contact problems, demanding for efficient and robust methods. Therefore, the main objective of this study is the development of algorithms and numerical methods to apply in the numerical simulation of 3D frictional contact problems between bodies undergoing large deformations. The presented original developments are implemented in the in-house finite element code DD3IMP. The formulation of quasi-static frictional contact problems between bodies undergoing large deformations is firstly presented in the framework of the continuum mechanics, following the classical scheme used in solid mechanics. The kinematic description of the deformable bodies is presented adopting an updated Lagrangian formulation. The mechanical behaviour of the bodies is described by an elastoplastic constitutive law in conjunction with an associated flow rule, allowing to model a wide variety of contact problems arising in industrial applications. The frictional contact between the bodies is established by means of two conditions: the principle of impenetrability and the Coulomb’s friction law, both imposed to the contact interface. The augmented Lagrangian method is applied for solving the constrained minimization incremental problem resulting from the frictional contact inequalities, yielding a mixed functional involving both displacements and contact forces. The spatial discretization of the bodies is performed with isoparametric solid finite elements, while the discretization of the contact interface is carried out using the classical Node-to-Segment technique, preventing the slave nodes from penetrating on the master surface. The geometrical part of the contact elements, defined by a slave node and the closest master segment, is created by the contact search algorithm based on the selection of the closest point on the master surface, defined by the normal projection of the slave node. In the particular case of contact between a deformable body and a rigid obstacle, the master rigid surface can be described by smooth parameterizations typically used in CAD models. However, in the general case of contact between deformable bodies, the spatial discretization of both bodies with low order finite elements yields a piecewise bilinear representation of the master surface. This is the central source of problems in solving contact problems involving large sliding, since it leads to the discontinuity of the surface normal vector field. Thus, a surface smoothing procedure based on the Nagata patch interpolation is proposed to describe the master contact surfaces, which led to the development of the Node-to-Nagata contact element. The accuracy of the surface smoothing method using Nagata patches is evaluated by means of simple geometries. The nodal normal vectors required for the Nagata interpolation are evaluated from the CAD geometry in case of rigid master surfaces, while in case of deformable bodies they are approximated using the weighted average of the normal vectors of the neighbouring facets. The residual vectors and tangent matrices of the contact elements are derived coherently with the surface smoothing approach, allowing to obtain quadratic convergence rate in the generalized Newton method used for solving the nonlinear system of equations. The developed surface smoothing method and corresponding contact elements are validated through standard numerical examples with known analytical or semi-analytical solutions. More advanced frictional contact problems are studied, covering the contact of a deformable body with rigid obstacles and the contact between deformable bodies, including self-contact phenomena. The smoothing of the master surface improves the robustness of the computational methods and reduces strongly the non-physical oscillations in the contact force introduced by the traditional faceted description of the contact surface. The presented results are compared with numerical solutions obtained by other authors and experimental results, demonstrating the accuracy and performance of the implemented algorithms for highly nonlinear problems.Todos os movimentos no mundo envolvem contato e atrito, desde andar até conduzir um carro. A mecânica do contacto tem aplicação em muitos problemas de engenharia, incluindo a ligação de elementos estruturais com parafusos, projeto de engrenagens e rolamentos, estampagem ou forjamento, contato entre os pneus e a estrada, colisão de estruturas, bem como o desenvolvimento de próteses em engenharia biomédica. Devido à natureza não-linear e não-suave da mecânica do contato (área de contato desconhecida a priori), tais problemas são atualmente resolvidos usando o método dos elementos finitos no domínio da mecânica do contato computacional. No entanto, a maioria dos programas comerciais de elementos finitos atualmente disponíveis não é totalmente capaz de resolver problemas de contato com atrito, exigindo métodos numéricos mais eficientes e robustos. Portanto, o principal objetivo deste estudo é o desenvolvimento de algoritmos e métodos numéricos para aplicar na simulação numérica de problemas de contato com atrito entre corpos envolvendo grandes deformações. Os desenvolvimentos apresentados são implementados no programa de elementos finitos DD3IMP. A formulação quasi-estática de problemas de contato com atrito entre corpos deformáveis envolvendo grandes deformações é primeiramente apresentada no âmbito da mecânica dos meios contínuos, seguindo o método clássico usado em mecânica dos sólidos. A descrição cinemática dos corpos deformáveis é apresentada adotando uma formulação Lagrangeana reatualizada. O comportamento mecânico dos corpos é descrito por uma lei constitutiva elastoplástica em conjunto com uma lei de plasticidade associada, permitindo modelar uma grande variedade de problemas de contacto envolvidos em aplicações industriais. O contacto com atrito entre os corpos é definido por duas condições: o princípio da impenetrabilidade e a lei de atrito de Coulomb, ambas impostas na interface de contato. O método do Lagrangeano aumentado é aplicado na resolução do problema de minimização com restrições resultantes das condições de contato e atrito, produzindo uma formulação mista envolvendo deslocamentos e forças de contato. A discretização espacial dos corpos é realizada com elementos finitos sólidos isoparamétricos, enquanto a discretização da interface de contacto é realizado utilizando a técnica Node-to-Segment, impedindo os nós slave de penetrar na superfície master. A parte geométrica do elemento de contacto, definida por um nó slave e o segmento master mais próximo, é criada pelo algoritmo de deteção de contacto com base na seleção do ponto mais próximo na superfície master, obtido pela projeção normal do nó slave. No caso particular de contato entre um corpo deformável e um obstáculo rígido, a superfície rígida master pode ser descrita por parametrizações normalmente utilizadas em modelos CAD. No entanto, no caso geral de contato entre corpos deformáveis, a discretização espacial dos corpos com elementos finitos lineares origina uma representação da superfície master por facetas. Esta é a principal fonte de problemas na resolução de problemas de contato envolvendo grandes escorregamentos, uma vez que a distribuição dos vetor normais à superfície é descontínua. Assim, é proposto um método de suavização para descrever as superfícies de contacto master baseado na interpolação Nagata, que conduziu ao desenvolvimento do elemento de contacto Node-to-Nagata. A precisão do método de suavização das superfícies é avaliada através de geometrias simples. Os vetores normais nodais necessários para a interpolação Nagata são avaliados a partir da geometria CAD no caso de superfícies rígidas, enquanto no caso de corpos deformáveis são aproximados utilizando a média ponderada dos vetores normais das facetas vizinhas. Tanto os vetores de segundo membro como as matrizes residuais tangentes dos elementos de contacto são obtidas de forma coerente com o método de suavização da superfície, permitindo obter convergência quadrática no método de Newton generalizado, o qual é utilizado para resolver o sistema de equações não lineares. O método de suavização das superfícies e os elementos de contacto desenvolvidos são validados através de exemplos com soluções analíticas ou semi-analíticas conhecidas. Também são estudados outros problemas de contato mais complexos, incluindo o contato de um corpo deformável com obstáculos rígidos e o contato entre corpos deformáveis, contemplando fenómenos de auto-contato. A suavização da superfície master melhora a robustez dos métodos computacionais e reduz fortemente as oscilações na força de contato, associadas à descrição facetada da superfície de contato. Os resultados são comparados com soluções numéricas de outros autores e com resultados experimentais, demonstrando a precisão e o desempenho dos algoritmos implementados para problemas fortemente não-lineares.Fundação para a Ciência e Tecnologia - SFRH/BD/69140/201

In conversation with simulation: The application of numerical simulation to the design of structural nodal connections

The thesis explores methods for integration of structural analysis, design and production in a digital design environment. The somewhat ambiguous title implies the ambition to make such integration in relation to the explorative phase of the design process which is described by Donald Sch\uf6n as having a conversational character. A conversation between the designer and the representation by the means of the tool. The tool is in this context a simulation and instead of exploring the potential of automatic optimisation, the simulation is used for designer driven exploration. The aim of the thesis is to give an overview of how this type of integration is currently being approached and to contribute with new tools and methods in that pursuit. The motivation behind the work is to lower the threshold for the application of structural analysis in early-stage design, with an ambition of architectural qualities and resource efficiency in mind. An overview of the historical context is portrayed with broad brush strokes, followed by a more precise account of the mathematical and physical context, which is complemented by an attempt to describe how our tools and roles tend to interplay in the composition of the design process. Methods such as the finite element method, isogeometric analysis, smoothed particle hydrodynamics and peridynamics, including their related geometrical representations are introduced in relation to this context. A variety of production techniques are also discussed in relation to material mechanical properties for conventional building materials such as steel, concrete and wood.The method development is approached through the use of numerical and physical experiments which are applied for design of material-efficient structural components, with a particular design process perspective. The nodal connection is chosen as an application because it combines geometrical and structural complexity in an element that is of crucial importance for a holistic spatial setting, while often being produced in a material inefficient way, with poor attention to detail.The three articles that are included follow a trajectory from large to small, from the holistic to the particular. The first article is a description of the computational design work with the roof for the new international airport of Mexico City. The second article aims to address one of the challenges that were faced in that project with material inefficiency for nodal connections, with a critical perspective on optimisation. The final article presents an extension/modification for the peridynamics theory enabling variable particle sizes and an irregular particle distribution through the introduction of a concept called force flux density. The development is motivated by limitations found in the present theory through numerical experiments. The method enables simulation of phenomena such as brittle fracture, for which correlation with Griffith\u27s theory of fracture is shown. Further work includes an extension of the force flux method from 2D to 3D, including calibration of material a model for 3D printed steel. Other possibilities involve the exploration of how such a method can adapt to the various stages of the design process, where requirements of accuracy, speed and interactivity will vary

Feasible Form Parameter Design of Complex Ship Hull Form Geometry

This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design. In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry

Separation of concerns: strategies for complex parametric design modelling

Parametric design systems are indispensable in enabling flexibility during the delivery of solutions to geometrically complex and ill-formed design problems. However, this flexibility is provided at the expense of coercing designers into adopting a highly structured design process. While this inflexibility has been widely documented in the literature, there are no examples of strategies for overcoming it. I have investigated how to overcome the inflexibility inherent in parametric modeling systems through the development of two major strategies and eight sub strategies. The strategies were developed through a mixed-method research methodology combining the case-study method and the action research method, in order to analyse the eight real world case-studies presented in support of this thesis. The primary finding of this research is that we need better ways to integrate automation in design modelling while simultaneously we need more tacit interaction through “Direct Modelling” with our models in order to achieve a greater flexibility in design modelling. The approaches analysed in this thesis have demonstrated through the eight specific case-studies how designers can reasonably achieve disruptive variation within the flexible design environments which the parametric design paradigm fosters. The three intervention modes: Internal Code, External Code and Bespoke Approach, addressed challenges to flexibility within parametric design software and ways to overcome them depending on the nature of the problem and the suitability of the strategy to the design problem

Fabricate

Bringing together pioneers in design and making within architecture, construction, engineering, manufacturing, materials technology and computation, Fabricate is a triennial international conference, now in its third year (ICD, University of Stuttgart, April 2017). Each year it produces a supporting publication, to date the only one of its kind specialising in Digital Fabrication. The 2017 edition features 32 illustrated articles on built projects and works in progress from academia and practice, including contributions from leading practices such as Foster + Partners, Zaha Hadid Architects, Arup, and Ron Arad, and from world-renowned institutions including ICD Stuttgart, Harvard, Yale, MIT, Princeton University, The Bartlett School of Architecture (UCL) and the Architectural Association