Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture

International audienceIn this work, we apply a non-intrusive global/local coupling strategy for the modelling of local phenomena in a NURBS patch. The idea is to consider the NURBS patch to be enriched as the global model. This results in a simple, flexible strategy: first, the global NURBS patch remains unchanged, which completely eliminates the need for costly re-parametrization procedures (even if the local domain is expected to evolve); then, easy merging of a linear NURBS code with any other existing robust codes suitable for the modelling of complex local behaviour is possible. The price to pay is the number of iterations of the non-intrusive solver but we show that this can be strongly reduced by means of acceleration techniques. The main development for NURBS is to be able to handle non-conforming geometries. Only slight changes in the implementation process, including the setting up of suitable quadrature rules for the evaluation of the interface reaction forces, are made in response to this issue. A range of numerical examples in two-dimensional linear elasticity are given to demonstrate the performance of the proposed methodology and its significant potential to treat any case of local enrichment in a NURBS patch simply

Nichtlineare Optimierung geometrisch definierter Fugen von räumlich gekrümmten Betonfertigteilen mit isogeometrischen Verfahren

Die Vision dieses Projektes ist es, einen durchgängigen Prozess zu entwickeln, der es erlaubt, den Entwurf, die Berechnung und die Fugenoptimierung von flächigen Strukturen aus Betonfertigteilen sehr einfach und effizient durchzuführen. Damit soll die Herstellung von freien Formen, wie beispielsweise „Blobs“ und Hängeformen aus Beton, unterstützt und gefördert werden.The vision of this project is to develop a continuous process that allows very easy and efficient design, calculation and joint optimization of surface-like structures made of precast concrete elements. This should support and encourage the production of free forms, such as “blobs” and hanging forms made of concrete

CAD-integrierte Isogeometrische Analyse und Entwurf leichter Tragwerke

Isogeometric methods are extended for the parametric design process of complex lightweight structures. Three novel methods for the coupling of different structural elements are proposed: rotational coupling, implicit geometry description, and frictionless sliding contact. Moreover, the necessary steps for the integration of the numerical analysis, including pre- and post-processing, in CAD are investigated. It is possible to base several different analyses on each other in order to parametrically represent a construction process with multiple steps.Die isogeometrischen Methoden werden zur Anwendung im parametrischen Entwurfsprozess von komplexen Leichtbaustrukturen erweitert. Hierzu werden drei neue Methoden zur Kopplung unterschiedlicher Strukturelemente vorgeschlagen: Rotationskopplung, implizite Geometriebeschreibung und reibungsfreier Gleitkontakt. Ferner werden die nötigen Schritte zur Einbindung von Pre- und Postprocessing für numerische Simulationen in CAD untersucht. Mehrere unterschiedliche Analysen können auf einander folgen und werden verlinkt, um den Aufbauprozess in mehreren Schritten vollparametrisch abzubilden

Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models

This work presents numerical techniques to enforce continuity constraints on multi-patch surfaces for three distinct problem classes. The first involves structural analysis of thin shells that are described by general Kirchhoff-Love kinematics. Their governing equation is a vector-valued, fourth-order, nonlinear, partial differential equation (PDE) that requires at least $C^1$-continuity within a displacement-based finite element formulation. The second class are surface phase separations modeled by a phase field. Their governing equation is the Cahn-Hilliard equation - a scalar, fourth-order, nonlinear PDE - that can be coupled to the thin shell PDE. The third class are brittle fracture processes modeled by a phase field approach. In this work, these are described by a scalar, fourth-order, nonlinear PDE that is similar to the Cahn-Hilliard equation and is also coupled to the thin shell PDE. Using a direct finite element discretization, the two phase field equations also require at least a $C^1$-continuous formulation. Isogeometric surface discretizations - often composed of multiple patches - thus require constraints that enforce the $C^1$-continuity of displacement and phase field. For this, two numerical strategies are presented: For this, two numerical strategies are presented: A Lagrange multiplier formulation and a penalty method. The curvilinear shell model including the geometrical constraints is taken from Duong et al. (2017) and it is extended to model the coupled phase field problems on thin shells of Zimmermann et al. (2019) and Paul et al. (2020) on multi-patches. Their accuracy and convergence are illustrated by several numerical examples considering deforming shells, phase separations on evolving surfaces, and dynamic brittle fracture of thin shells.Comment: In this version, typos were fixed, Chapter 6.4 is added, Table 1 is updated, and clarifying explanations and remarks are added at several place

Ισογεωμετρική Στατική Ανάλυση με T-SPLines

Σκοπός αυτής της διπλωματικής είναι η διερεύνηση της ισογεωμετρικής στατικής ανάλυσης χρησιμοποιώντας ΄ενα νέο έιδος συναρτήσεων σχήματος , τις T-SPLines. Τόσο οι T-SPLines όσο και η ανάλυση πεπερασμένων στοιχείων εετάστηκαν ξεχωριστά αφού αποτελούν τις δύο συνιστώσες της ισογεωμετρικής μεθόδου. Τα θέματα που εξετάστηκαν είναι οι T-SPLines και οι ιδιότητές τους, οι τεχνικές πύκνωσης του δικτύου , η μόρφωση του μητρώου στιβαρότητας, η επεξεργασία των αποτελεσμάτων της ανάλυσης (πεδίο μετατοπίσεων, τάσεων και παραμορφώσεων) και εφαρμογές 2Δ για τη διερεύνηση διαφόρων φορέων.The scope of this thesis if the investigation of static isogeometric analysis unsing a new type of shape functions T-SPLines. T-SPLines and finite elements have been examined separately, as the two components of the isogeometric method. The topics considered are T-SPLine formulation and properties, refinement techniques, stiffness matrix formulation , result post-processing (displacement, stress and strain field) and linear 2D applications investigating models of various representations.Δημήτριος Γ. Τσαπέτη

Computer Aided Grid Interface: An Interactive CFD Pre-Processor

NASA maintains an applications oriented computational fluid dynamics (CFD) efforts complementary to and in support of the aerodynamic-propulsion design and test activities. This is especially true at NASA/MSFC where the goal is to advance and optimize present and future liquid-fueled rocket engines. Numerical grid generation plays a significant role in the fluid flow simulations utilizing CFD. An overall goal of the current project was to develop a geometry-grid generation tool that will help engineers, scientists and CFD practitioners to analyze design problems involving complex geometries in a timely fashion. This goal is accomplished by developing the Computer Aided Grid Interface system (CAGI). The CAGI system is developed by integrating CAD/CAM (Computer Aided Design/Computer Aided Manufacturing) geometric system output and / or Initial Graphics Exchange Specification (IGES) files (including all the NASA-IGES entities), geometry manipulations and generations associated with grid constructions, and robust grid generation methodologies. This report describes the development process of the CAGI system

Isogeometric analysis based on Geometry Independent Field approximaTion (GIFT) and Polynomial Splines over Hierarchical T-meshes

This thesis addresses an adaptive higher-order method based on a Geometry Independent Field approximatTion(GIFT) of polynomial/rationals plines over hierarchical T-meshes(PHT/RHT-splines). In isogeometric analysis, basis functions used for constructing geometric models in computer-aided design(CAD) are also employed to discretize the partial differential equations(PDEs) for numerical analysis. Non-uniform rational B-Splines(NURBS) are the most commonly used basis functions in CAD. However, they may not be ideal for numerical analysis where local refinement is required. The alternative method GIFT deploys different splines for geometry and numerical analysis. NURBS are utilized for the geometry representation, while for the field solution, PHT/RHT-splines are used. PHT-splines not only inherit the useful properties of B-splines and NURBS, but also possess the capabilities of local refinement and hierarchical structure. The smooth basis function properties of PHT-splines make them suitable for analysis purposes. While most problems considered in isogeometric analysis can be solved efficiently when the solution is smooth, many non-trivial problems have rough solutions. For example, this can be caused by the presence of re-entrant corners in the domain. For such problems, a tensor-product basis (as in the case of NURBS) is less suitable for resolving the singularities that appear since refinement propagates throughout the computational domain. Hierarchical bases and local refinement (as in the case of PHT-splines) allow for a more efficient way to resolve these singularities by adding more degrees of freedom where they are necessary. In order to drive the adaptive refinement, an efficient recovery-based error estimator is proposed in this thesis. The estimator produces a recovery solution which is a more accurate approximation than the computed numerical solution. Several two- and three-dimensional numerical investigations with PHT-splines of higher order and continuity prove that the proposed method is capable of obtaining results with higher accuracy, better convergence, fewer degrees of freedom and less computational cost than NURBS for smooth solution problems. The adaptive GIFT method utilizing PHT-splines with the recovery-based error estimator is used for solutions with discontinuities or singularities where adaptive local refinement in particular domains of interest achieves higher accuracy with fewer degrees of freedom. This method also proves that it can handle complicated multi-patch domains for two- and three-dimensional problems outperforming uniform refinement in terms of degrees of freedom and computational cost

A survey on personal computer applications in industrial design process

Thesis (Master)--Izmir Institute of Technology, Industrial Design, Izmir, 1999Includes bibliographical references (leaves: 157-162)Text in English, Abstract: Turkish and Englishxii, 194 leavesIn this thesis, computer aided design systems are studied from the industrial designer's point of view. The study includes industrial design processes, computer aided design systems and the integration aspects.The technical issues are priorly studied, including current hardware and software technologies. The pure technical concepts are tried to be supported with real-world examples and graphics. Several important design software are examined, whether by personal practice or by literature research, depending on the availability of the software.Finally, the thesis include a case study, a 17" LCD computer monitor designed with a set of graphic programs including two-dimensional and three-dimensional packages.Keywords: Computers, industrial design methods, design software, computer aided design

Intuitive freeform modeling using subdivision surfaces.

Lai Yuen-hoo.Thesis submitted in: November 2004.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 100-102).Abstracts in English and Chinese.Abstract --- p.i摘要 --- p.iiAcknowledgment --- p.iiiList of Figures --- p.ivTable of Content --- p.viiChapter 1. --- Introduction --- p.1Chapter 1.1. --- Problem Definition --- p.1Chapter 1.2. --- Proposed Solution --- p.2Chapter 1.3. --- Thesis Contributions --- p.2Chapter 2. --- Modeling Approaches --- p.4Chapter 2.1. --- Polygon Modeling --- p.4Chapter 2.2. --- Patch Modeling --- p.6Chapter 2.3. --- Freehand Sketch-based Modeling --- p.7Chapter 2.4. --- Template Based Modeling --- p.8Chapter 2.5. --- Curve Interpolation Method --- p.9Chapter 3. --- Surface Operations --- p.11Chapter 3.1. --- Surface Blending --- p.11Chapter 3.2. --- Surface Trimming --- p.13Chapter 3.3. --- Boolean Operations --- p.14Chapter 4. --- Subdivision Surface --- p.16Chapter 4.1. --- Basic Principle --- p.16Chapter 4.2. --- Catmull-Clark Surface --- p.17Chapter 5. --- Modeling Algorithm Overview --- p.21Chapter 6. --- Subdivision Surface Generation --- p.23Chapter 6.1. --- Input Curves --- p.23Chapter 6.2. --- Surface Sweeping --- p.24Chapter 6.3. --- Subdivision Surface Fitting --- p.29Chapter 7. --- Surface Blending --- p.32Chapter 7.1. --- Introduction --- p.32Chapter 7.2. --- Problem Definition --- p.32Chapter 7.3. --- Algorithm Overview --- p.36Chapter 7.4. --- Blend Region Detection --- p.39Chapter 7.4.1. --- Collision Detection --- p.40Chapter 7.4.2. --- Result and Analysis --- p.42Chapter 7.5. --- "Mesh Refinement, Surface Fitting and Region Removal" --- p.46Chapter 7.5.1. --- Mesh Refinement --- p.46Chapter 7.5.1.1. --- Adaptive Subdivision --- p.46Chapter 7.5.1.2. --- Additional Subdivision Constraint --- p.47Chapter 7.5.2. --- Surface Fitting --- p.49Chapter 7.5.2.1. --- General Approach --- p.49Chapter 7.5.2.2. --- Surface Point Correspondence --- p.50Chapter 7.5.2.3. --- Numerical Fitting Method --- p.51Chapter 7.5.3. --- Unwanted Region Removal --- p.55Chapter 7.5.4. --- Result and Analysis --- p.56Chapter 7.6. --- Boundary Smoothing --- p.58Chapter 7.6.1. --- General Approach --- p.59Chapter 7.6.2. --- Constraint on Deformation Direction of Vertex --- p.61Chapter 7.6.3. --- Result and Analysis --- p.63Chapter 7.7. --- Blend Curves --- p.65Chapter 7.7.1. --- Problem Definition --- p.65Chapter 7.7.2. --- Proposed Solution Overview --- p.66Chapter 7.7.3. --- Maintenance of Regular Vertex Valence along Blend Curve --- p.67Chapter 7.7.3.1. --- Pairing Up Blend Boundary Vertices --- p.70Chapter 7.7.4. --- Minimization of Distortion Caused by Extraordinary Vertices --- p.72Chapter 7.7.5. --- Blend Vertex Position Optimization Function --- p.74Chapter 7.7.5.1. --- Face Normal Expression --- p.74Chapter 7.7.5.2. --- Face Normal Difference Energy Function --- p.77Chapter 7.7.5.3. --- Midpoint Distance Energy Function --- p.78Chapter 7.7.5.4. --- Weighted Least Square Energy Minimization --- p.78Chapter 8. --- Implementation --- p.81Chapter 8.1. --- Data Structure --- p.81Chapter 8.2. --- User Interface --- p.82Chapter 9. --- Results --- p.83Chapter 9.1. --- Surface Generation --- p.83Chapter 9.2. --- Surface Blending --- p.86Chapter 9.2.1. --- Ideal Case --- p.86Chapter 9.2.2. --- Angle of Insertion --- p.87Chapter 9.2.3. --- Surface Feature Near Intersection --- p.88Chapter 9.2.4. --- Comparison --- p.89Chapter 9.2.5. --- Other Examples --- p.92Chapter 9.3. --- Overall Performance --- p.94Chapter 9.4. --- Limitations --- p.97Chapter 9.4.1. --- Limitation on Generated Shape --- p.97Chapter 9.4.2. --- Limitation on Input Surfaces --- p.98Chapter 10. --- Conclusion and Future Work --- p.99References --- p.10

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