08221 Abstracts Collection -- Geometric Modeling

From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

IST Austria Thesis

Fabrication of curved shells plays an important role in modern design, industry, and science. Among their remarkable properties are, for example, aesthetics of organic shapes, ability to evenly distribute loads, or efficient flow separation. They find applications across vast length scales ranging from sky-scraper architecture to microscopic devices. But, at the same time, the design of curved shells and their manufacturing process pose a variety of challenges. In this thesis, they are addressed from several perspectives. In particular, this thesis presents approaches based on the transformation of initially flat sheets into the target curved surfaces. This involves problems of interactive design of shells with nontrivial mechanical constraints, inverse design of complex structural materials, and data-driven modeling of delicate and time-dependent physical properties. At the same time, two newly-developed self-morphing mechanisms targeting flat-to-curved transformation are presented. In architecture, doubly curved surfaces can be realized as cold bent glass panelizations. Originally flat glass panels are bent into frames and remain stressed. This is a cost-efficient fabrication approach compared to hot bending, when glass panels are shaped plastically. However such constructions are prone to breaking during bending, and it is highly nontrivial to navigate the design space, keeping the panels fabricable and aesthetically pleasing at the same time. We introduce an interactive design system for cold bent glass façades, while previously even offline optimization for such scenarios has not been sufficiently developed. Our method is based on a deep learning approach providing quick and high precision estimation of glass panel shape and stress while handling the shape multimodality. Fabrication of smaller objects of scales below 1 m, can also greatly benefit from shaping originally flat sheets. In this respect, we designed new self-morphing shell mechanisms transforming from an initial flat state to a doubly curved state with high precision and detail. Our so-called CurveUps demonstrate the encodement of the geometric information into the shell. Furthermore, we explored the frontiers of programmable materials and showed how temporal information can additionally be encoded into a flat shell. This allows prescribing deformation sequences for doubly curved surfaces and, thus, facilitates self-collision avoidance enabling complex shapes and functionalities otherwise impossible. Both of these methods include inverse design tools keeping the user in the design loop

Advanced Techniques for Design and Manufacturing in Marine Engineering

Modern engineering design processes are driven by the extensive use of numerical simulations; naval architecture and ocean engineering are no exception. Computational power has been improved over the last few decades; therefore, the integration of different tools such as CAD, FEM, CFD, and CAM has enabled complex modeling and manufacturing problems to be solved in a more feasible way. Classical naval design methodology can take advantage of this integration, giving rise to more robust designs in terms of shape, structural and hydrodynamic performances, and the manufacturing process.This Special Issue invites researchers and engineers from both academia and the industry to publish the latest progress in design and manufacturing techniques in marine engineering and to debate the current issues and future perspectives in this research area. Suitable topics for this issue include, but are not limited to, the following:CAD-based approaches for designing the hull and appendages of sailing and engine-powered boats and comparisons with traditional techniques;Finite element method applications to predict the structural performance of the whole boat or of a portion of it, with particular attention to the modeling of the material used;Embedded measurement systems for structural health monitoring;Determination of hydrodynamic efficiency using experimental, numerical, or semi-empiric methods for displacement and planning hulls;Topology optimization techniques to overcome traditional scantling criteria based on international standards;Applications of additive manufacturing to derive innovative shapes for internal reinforcements or sandwich hull structures

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes

Collision Detection and Merging of Deformable B-Spline Surfaces in Virtual Reality Environment

This thesis presents a computational framework for representing, manipulating and merging rigid and deformable freeform objects in virtual reality (VR) environment. The core algorithms for collision detection, merging, and physics-based modeling used within this framework assume that all 3D deformable objects are B-spline surfaces. The interactive design tool can be represented as a B-spline surface, an implicit surface or a point, to allow the user a variety of rigid or deformable tools. The collision detection system utilizes the fact that the blending matrices used to discretize the B-spline surface are independent of the position of the control points and, therefore, can be pre-calculated. Complex B-spline surfaces can be generated by merging various B-spline surface patches using the B-spline surface patches merging algorithm presented in this thesis. Finally, the physics-based modeling system uses the mass-spring representation to determine the deformation and the reaction force values provided to the user. This helps to simulate realistic material behaviour of the model and assist the user in validating the design before performing extensive product detailing or finite element analysis using commercially available CAD software. The novelty of the proposed method stems from the pre-calculated blending matrices used to generate the points for graphical rendering, collision detection, merging of B-spline patches, and nodes for the mass spring system. This approach reduces computational time by avoiding the need to solve complex equations for blending functions of B-splines and perform the inversion of large matrices. This alternative approach to the mechanical concept design will also help to do away with the need to build prototypes for conceptualization and preliminary validation of the idea thereby reducing the time and cost of concept design phase and the wastage of resources

기하학적으로 정밀한 비선형 구조물의 아이소-지오메트릭 형상 설계 민감도 해석

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 조선해양공학과, 2019. 2. 조선호.In this thesis, a continuum-based analytical adjoint configuration design sensitivity analysis (DSA) method is developed for gradient-based optimal design of curved built-up structures undergoing finite deformations. First, we investigate basic invariance property of linearized strain measures of a planar Timoshenko beam model which is combined with the selective reduced integration and B-bar projection method to alleviate shear and membrane locking. For a nonlinear structural analysis, geometrically exact beam and shell structural models are basically employed. A planar Kirchhoff beam problem is solved using the rotation-free discretization capability of isogeometric analysis (IGA) due to higher order continuity of NURBS basis function whose superior per-DOF(degree-of-freedom) accuracy over the conventional finite element analysis using Hermite basis function is verified. Various inter-patch continuity conditions including rotation continuity are enforced using Lagrage multiplier and penalty methods. This formulation is combined with a phenomenological constitutive model of shape memory polymer (SMP), and shape programming and recovery processes of SMP structures are simulated. Furthermore, for shear-deformable structures, a multiplicative update of finite rotations by an exponential map of a skew-symmetric matrix is employed. A procedure of explicit parameterization of local orthonormal frames in a spatial curve is presented using the smallest rotation method within the IGA framework. In the configuration DSA, the material derivative is applied to a variational equation, and an orientation design variation of curved structure is identified as a change of embedded local orthonormal frames. In a shell model, we use a regularized variational equation with a drilling rotational DOF. The material derivative of the orthogonal transformation matrix can be evaluated at final equilibrium configuration, which enables to compute design sensitivity using the tangent stiffness at the equilibrium without further iterations. A design optimization method for a constrained structure in a curved domain is also developed, which focuses on a lattice structure design on a specified surface. We define a lattice structure and its design variables on a rectangular plane, and utilize a concept of free-form deformation and a global curve interpolation to obtain an analytical expression for the control net of the structure on curved surface. The material derivative of the analytical expression eventually leads to precise design velocity field. Using this method, the number of design variables is reduced and design parameterization becomes more straightforward. In demonstrative examples, we verify the developed analytical adjoint DSA method in beam and shell structural problems undergoing finite deformations with various kinematic and force boundary conditions. The method is also applied to practical optimal design problems of curved built-up structures. For example, we extremize auxeticity of lattice structures, and experimentally verify nearly constant negative Poisson's ratio during large tensile and compressive deformations by using the 3-D printing and optical deformation measurement technologies. Also, we architect phononic band gap structures having significantly large band gap for mitigating noise in low audible frequency ranges.본 연구에서는 대변형을 고려한 휘어진 조립 구조물의 연속체 기반 해석적 애조인 형상 설계 민감도 해석 기법을 개발하였다. 평면 Timoshenko 빔의 선형화된 변형률의 invariance 특성을 고찰하였고 invariant 정식화를 선택적 축소적분(selective reduced integration) 기법 및 B-bar projection 기법과 결합하여 shear 및 membrane 잠김 현상을 해소하였다. 비선형 구조 모델로서 기하학적으로 정밀한 빔 및 쉘 모델을 활용하였다. 평면 Kirchhoff 빔 모델을 NURBS 기저함수의 고차 연속성에 따른 아이소-지오메트릭 해석 기반 rotation-free 이산화를 활용하여 다루었으며, 기존의 Hermite 기저함수 기반의 유한요소법에 비해 자유도당 해의 정확도가 높음을 검증하였다. 라그랑지 승수법 및 벌칙 기법을 도입하여 회전의 연속성을 포함한 다양한 다중패치간 연속 조건을 고려하였다. 이러한 기법을 현상학적 (phenomenological) 형상기억폴리머 (SMP) 재료 구성방정식과 결합하여 형상의 프로그래밍과 회복 과정을 시뮬레이션하였다. 전단변형을 겪는 (shear-deformable) 구조 모델에 대하여 대회전의 갱신을 교대 행렬의 exponential map에 의한 곱의 형태로 수행하였다. 공간상의 곡선 모델에서 최소회전 (smallest rotation) 기법을 통해 국소 정규직교좌표계의 명시적 매개화를 수행하였다. 형상 설계 민감도 해석을 위하여 전미분을 변분 방정식에 적용하였으며 휘어진 구조물의 배향 설계 변화는 국소 정규직교좌표계의 회전에 의하여 기술된다. 최종 변형 형상에서 직교 변환 행렬의 전미분을 계산함으로써 대회전 문제에서 추가적인 반복 계산없이 변형 해석에서의 접선강성행렬에 의해 해석적 설계 민감도를 계산할 수 있다. 쉘 구조물의 경우 면내 회전 자유도 및 안정화된 변분 방정식을 활용하여 보강재(stiffener)의 모델링을 용이하게 하였다. 또한 본 연구에서는 휘어진 영역에 구속되어있는 구조물에 대한 설계 속도장 계산 및 최적 설계기법을 제안하며 특히 곡면에 구속된 빔 구조물의 설계를 집중적으로 다룬다. 자유형상변형(Free-form deformation)기법과 전역 곡선 보간기법을 활용하여 직사각 평면에서 형상 및 설계 변수를 정의하고 곡면상의 곡선 형상을 나타내는 조정점 위치를 해석적으로 표현할 수 있으며 이의 전미분을 통해 정확한 설계속도장을 계산한다. 이를 통해 설계 변수의 개수를 줄일 수 있고 설계의 매개화가 간편해진다. 개발된 방법론은 다양한 하중 및 운동학적 경계조건을 갖는 빔과 쉘의 대변형 문제를 통해 검증되며 여러가지 휘어진 조립 구조물의 최적 설계에 적용된다. 대표적으로, 전단 강성 및 충격 흡수 특성과 같은 기계적 물성치의 개선을 위해 활용되는 오그제틱 (auxetic) 특성이 극대화된 격자 구조를 설계하며 인장 및 압축 대변형 모두에서 일정한 음의 포아송비를 나타냄을 3차원 프린팅과 광학적 변형 측정 기술을 이용하여 실험적으로 검증한다. 또한 우리는 소음의 저감을 위해 활용되는 가청 저주파수 영역대에서의 밴드갭이 극대화된 격자 구조를 제시한다.Abstract 1. Introduction 2. Isogeometric analysis of geometrically exact nonlinear structures 3. Isogeometric confinguration DSA of geometrically exact nonlinear structures 4. Numerical examples 5. Conclusions and future works A. Supplements to the geometrically exact Kirchhoff beam model B. Supplements to the geometrically exact shear-deformable beam model C. Supplements to the geometrically exact shear-deformable shell model D. Supplements to the invariant formulations E. Supplements to the geometric constraints in design optimization F. Supplements to the design of auxetic structures 초록Docto

Diseño de nuevos algoritmos de guiado y navegación con evasión de colisiones para vehículos aéreos no tripulados.

Tesis por compendio[ES] Debido a la creciente popularidad sobre la variedad de los Vehículos No Tripulados tanto en el campo militar como en el comercial, y de sus capacidades para navegar por diversos entornos, ya sean terrestres, aéreos o marinos, se evidencia que la clásica planificación de trayectorias y movimientos bidimensionales 2D podría no ser suficiente en un futuro inmediato. De esta manera, se debe resaltar que el presente trabajo aborda el problema de los Vehículos Aéreos No Tripulados (UAVs) de ala fija. En este sentido, la necesidad de encontrar una trayectoria navegable en el espacio euclídeo 3D se hace cada vez más necesario. En el caso de los UAV, considerar su cinemática para generar trayectorias suaves en tres dimensiones puede tener un interés significativo para la navegación autónoma aérea. Finalmente, los beneficios adicionales que se pueden producir son importantes. La principal dificultad de este problema es que los vehículos aéreos de características no-holonómicas se ven obligados a avanzar sin la posibilidad de detenerse a través de trayectorias 3D con curvaturas limitadas. En este sentido, se ha investigado la manera de proporcionar una completa caracterización de trayectorias óptimas para UAVs con un radio de giro limitado que se mueve en el plano tridimensional a una velocidad constante. Para completar tales tareas, un planificador de trayectorias no sólo debe proporcionar rutas tridimensionales para alcanzar una posición de destino sin colisionar con obstáculos, sino también debe asegurar que tal trayectoria sea adecuada para los UAVs que poseen propiedades cinemáticas específicas. Por lo tanto, el desarrollo del trabajo ha completado la algoritmia que genera una trayectoria discreta tridimensional al definir un conjunto de puntos 3D, resultantes de una división del espacio euclídeo tridimensional de manera dinámica, determinando las mejores opciones de avance, evitando analizar cada espacio del entorno completo. De esta manera, partiendo de los puntos 3D resultantes de la planificación de trayectoria tridimensional, se ha generado una trayectoria en forma de curva suave construida en función de las limitaciones de giro del UAV (resaltando que es difícil asegurar que el camino resultante cumpla con las restricciones cinemáticas en las tres dimensiones simultáneamente). Finalmente, es importante destacar que a menudo las restricciones mencionadas se calculan secuencialmente y de forma bidimensional, sobre un par de dimensiones desacopladas, lo que limita la capacidad de optimización. Para todo ello, se ha desarrollado un algoritmo de suavizado para un planificador de trayectorias que considera las restricciones cinemáticas tridimensionales completas sin desacoplar las dimensiones.[CA] Debut a la creixent popularitat sobre la varietat dels Vehicles No Tripulats tant en el camp militar com en el comercial, i de les seves capacitats per navegar per diversos entorns, ja siguin terrestres, aeris o marins, s'evidencia que la clàssica planificació de trajectòries i moviments bidimensionals 2D podria no ser suficient en un futur immediat. D'aquesta manera, s'ha de ressaltar que el present treball aborda el problema dels Vehicles Aeris No Tripulats (UAV) d'ala fixa. En aquest sentit, la necessitat de trobar una trajectòria navegable en l'espai euclidià 3D es fa cada vegada més necessari. En el cas dels UAV, considerar la seva cinemàtica per generar trajectòries suaus en tres dimensions pot tenir un interès significatiu per a la navegació autònoma aèria. Finalment, els beneficis addicionals que es poden produir són importants. La principal dificultat d'aquest problema és que els vehicles aeris de característiques no-holonómicas es veuen obligats a avançar sense la possibilitat de detenir-se a través de trajectòries 3D amb curvatures limitades. En aquest sentit, s'ha investigat la manera de proporcionar una completa caracterització de trajectòries òptimes per UAVs amb un radi de gir limitat que es mou en el pla tridimensional a una velocitat constant. Per completar aquestes tasques, un planificador de trajectòries no només ha de proporcionar rutes tridimensionals per assolir una posició de destinació sense col·lisionar amb obstacles, sinó també ha d'assegurar que tal trajectòria sigui adequada per als UAVs que posseeixen propietats cinemàtiques específiques. Per tant, el desenvolupament de la feina ha completat la algorísmia que genera una trajectòria discreta tridimensional a l'definir un conjunt de punts 3D, resultants d'una divisió de l'espai euclidià tridimensional de manera dinàmica, determinant les millors opcions d'avanç, evitant analitzar cada espai de l' entorn complet. D'aquesta manera, partint dels punts 3D resultants de la planificació de trajectòria tridimensional, s'ha generat una trajectòria en forma de corba suau construïda en funció de les limitacions de gir de l'UAV (ressaltant que és difícil assegurar que el camí resultant compleixi amb les restriccions cinemàtiques en les tres dimensions simultàniament). Finalment, és important destacar que sovint les restriccions esmentades es calculen seqöencialment i de forma bidimensional, sobre un parell de dimensions desacoblades, el que limita la capacitat d'optimització. Per tot això, s'ha desenvolupat un algoritme de suavitzat per a un planificador de trajectòries que considera les restriccions cinemàtiques tridimensionals completes sense desacoblar les dimensions.[EN] Due to the growing popularity of the variety of Unmanned Vehicles in both the military and commercial fields, and their capabilities to navigate diverse environments, whether land, air or sea, it is evident that the classic two-dimensional 2D trajectory and motion planning may not be enough in the near future. Thus, it should be noted that this paper addresses the problem of fixed-wing Unmanned Aerial Vehicles (UAVs). In this sense, the need to find a navigable path in 3D Euclidean space becomes more and more necessary. In the case of UAVs, considering their kinematics to generate smooth trajectories in three dimensions may be of significant interest for autonomous air navigation. Finally, the additional benefits that can be produced are important. The main difficulty of this problem is that air vehicles with non-holonomic characteristics are forced to advance without the possibility of stopping through 3D trajectories with limited curvatures. In this regard, research has been conducted to provide a complete characterization of optimal trajectories for UAVs with a limited turning radius that move in the 3D plane at a constant speed. To complete such tasks, a path planner must not only provide three-dimensional paths to reach a target position without colliding with obstacles, but must also ensure that such a path is suitable for UAVs that possess specific kinematic properties. Therefore, the development of the work has completed the algorithm that generates a discrete three-dimensional path by defining a set of 3D points, resulting from a division of the three-dimensional Euclidean space in a dynamic way, determining the best forward options, avoiding to analyze each space of the whole environment. In this way, starting from the 3D points resulting from the three-dimensional path planning, a smooth curve path has been generated, built according to the UAV turning constraints (highlighting that it is difficult to ensure that the resulting path meets the kinematic constraints in the three dimensions simultaneously). Finally, it is important to note that often the constraints mentioned are calculated sequentially and in a two-dimensional shape, on a pair of decoupled dimensions, which limits the ability to optimize. For all this, a smoothing algorithm has been developed for a path planner that considers the complete three-dimensional kinematic constraints without decoupling the dimensions.Este trabajo ha sido parcialmente financiado por el Gobierno de España a través del Ministerio de Economía y Competitividad bajo el proyecto de Investigación DP I2015−71443−R, y por la administración local de la Generalitat Valenciana a través de los proyectos GV /2017/029 y AICO/2019/055. El autor ha sido beneficiario de una beca otorgada por el Instituto de Fomento al Talento Humano (IFTH) (2015−AR2Q9209) a través del Gobierno de Ecuador.Samaniego Riera, FE. (2021). Diseño de nuevos algoritmos de guiado y navegación con evasión de colisiones para vehículos aéreos no tripulados [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/161274TESISCompendi

Advances on Mechanics, Design Engineering and Manufacturing III

This open access book gathers contributions presented at the International Joint Conference on Mechanics, Design Engineering and Advanced Manufacturing (JCM 2020), held as a web conference on June 2–4, 2020. It reports on cutting-edge topics in product design and manufacturing, such as industrial methods for integrated product and process design; innovative design; and computer-aided design. Further topics covered include virtual simulation and reverse engineering; additive manufacturing; product manufacturing; engineering methods in medicine and education; representation techniques; and nautical, aeronautics and aerospace design and modeling. The book is organized into four main parts, reflecting the focus and primary themes of the conference. The contributions presented here not only provide researchers, engineers and experts in a range of industrial engineering subfields with extensive information to support their daily work; they are also intended to stimulate new research directions, advanced applications of the methods discussed and future interdisciplinary collaborations