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

Developable B-spline surface generation from control rulings

An intuitive design method is proposed for generating developable ruled B-spline surfaces from a sequence of straight line segments indicating the surface shape. The first and last line segments are enforced to be the head and tail ruling lines of the resulting surface while the interior lines are required to approximate rulings on the resulting surface as much as possible. This manner of developable surface design is conceptually similar to the popular way of the freeform curve and surface design in the CAD community, observing that a developable ruled surface is a single parameter family of straight lines. This new design mode of the developable surface also provides more flexibility than the widely employed way of developable surface design from two boundary curves of the surface. The problem is treated by numerical optimization methods with which a particular level of distance error is allowed. We thus provide an effective tool for creating surfaces with a high degree of developability when the input control rulings do not lie in exact developable surfaces. We consider this ability as the superiority over analytical methods in that it can deal with arbitrary design inputs and find practically useful results.Comment: 13 pages, 12 figrue

Designing aesthetically pleasing freeform surfaces in a computer environment

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, February 2001.Includes bibliographical references (p. 151-160).Statement: If computational tools are to be employed in the aesthetic design of freeform surfaces, these tools must better reflect the ways in which creative designers conceive of and develop such shapes. In this thesis, I studied the design of aesthetically constrained freeform surfaces in architecture and industrial design, formulated a requirements list for a computational system that would aid in the creative design of such surfaces, and implemented a subset of the tools that would comprise such a system. This work documents the clay modeling process at BMW AG., Munich. The study of that process has led to a list of tools that would make freeform surface modeling possible in a computer environment. And finally, three tools from this system specification have been developed into a proof-of-concept system. Two of these tools are sweep modification tools and the third allows a user to modify a surface by sketching a shading pattern desired for the surface. The proof-of-concept tools were necessary in order to test the validity of the tools being presented and they have been used to create a number of example objects. The underlying surface representation is a variational expression which is minimized using the finite element method over an irregular triangulated mesh.by Evan P. Smyth.Ph.D

Kinematics, Structural Mechanics, and Design of Origami Structures with Smooth Folds

Origami provides novel approaches to the fabrication, assembly, and functionality of engineering structures in various fields such as aerospace, robotics, etc. With the increase in complexity of the geometry and materials for origami structures that provide engineering utility, computational models and design methods for such structures have become essential. Currently available models and design methods for origami structures are generally limited to the idealization of the folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures having non-negligible thickness or maximum curvature at the folds restricted by material limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate representations of structural response and a new approach is needed. The first contribution of this dissertation is a model for the kinematics of origami structures having realistic folds of non-zero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of the smooth folds and the constraints on their associated kinematic variables are presented. A numerical implementation of the model allowing for kinematic simulation of structures having arbitrary fold patterns is also described. Examples illustrating the capability of the model to capture realistic structural folding response are provided. Subsequently, a method for solving the origami design problem of determining the geometry of a single planar sheet and its pattern of smooth folds that morphs into a given three-dimensional goal shape, discretized as a polygonal mesh, is presented. The design parameterization of the planar sheet and the constraints that allow for a valid pattern of smooth folds and approximation of the goal shape in a known folded configuration are presented. Various testing examples considering goal shapes of diverse geometries are provided. Afterwards, a model for the structural mechanics of origami continuum bodies with smooth folds is presented. Such a model entails the integration of the presented kinematic model and existing plate theories in order to obtain a structural representation for folds having non-zero thickness and comprised of arbitrary materials. The model is validated against finite element analysis. The last contribution addresses the design and analysis of active material-based self-folding structures that morph via simultaneous folding towards a given three-dimensional goal shape starting from a planar configuration. Implementation examples including shape memory alloy (SMA)-based self-folding structures are provided

The development of virtual leaf surface models for interactive agrichemical spray applications

This project constructed virtual plant leaf surfaces from digitised data sets for use in droplet spray models. Digitisation techniques for obtaining data sets for cotton, chenopodium and wheat leaves are discussed and novel algorithms for the reconstruction of the leaves from these three plant species are developed. The reconstructed leaf surfaces are included into agricultural droplet spray models to investigate the effect of the nozzle and spray formulation combination on the proportion of spray retained by the plant. A numerical study of the post-impaction motion of large droplets that have formed on the leaf surface is also considered

Multistable morphing structures using variable stiffness laminates

Mit zunehmender Thematisierung des Klimawandels vertiefen auch immer mehr Branchen und Forschungseinrichtungen die Suche nach ökologischen Energiequellen. Windenergie ist eine der billigsten sauberen Energieformen und somit eine attraktive Alternative zu nicht erneuerbaren Energien. Das Hochskalieren von Windkraftanlagen gilt klassischerweise als Mittel zur Kostensenkung je Kilowattstunde und ist nach wie vor im Trend. Mit zunehmender Größe der Rotorblätter von Windkraftanlagen besteht jedoch die Notwendigkeit, Konstruktionen zu entwickeln, die in der Lage sind, Extrem- und Ermüdungslasten zu reduzieren. Die aktive Hinterkantenklappe ist ein vielversprechendes Konzept zur Entlastung großer Rotorblätter von Windkraftanlagen. Die meisten existierenden Klappenmechanismen haben zwar das Potenzial zu einer schnellen Reaktionszeit, und damit verbundener Lastreduktion, sind aber oft mit komplizierten Aktuator-Systemen verbunden, was zu zusätzlichem Gewicht und zunehmender Komplexität führt. Darüber hinaus erfordern sie eine kontinuierliche Energiezufuhr, um eine bestimmte Position der Klappe beizubehalten. Multistabile Laminate mit variabler Steifigkeit (VS) haben ein großes Potenzial bei Morphing-Anwendungen, in erster Linie aufgrund der Existenz mehrerer stabiler Gleichgewichtslagen. Der Einsatz von VS-Laminaten mit kurvenförmigen Faserbahnen ermöglicht es, die Leistungsfähigkeit von multistabilen Laminaten als Morphing-Strukturen weiter zu verbessern. Das Hauptziel dieser Arbeit ist es, die Eigenschaften von multistabilen VS-Laminaten nutzbar zu machen, und sie bei einem neuartigen Entwurf von Morphing-Hinterkantenklappen anzuwenden. Um dies zu erreichen, bedarf es nicht nur der Entwicklung numerischer und analytischer Werkzeuge, sondern auch eines geeigneten Entwurfes, um die VS-Eigenschaften in eine Morphing-Klappe zu integrieren. Daher wird in dieser Arbeit ein schnelles semi-analytisches Berechnungsverfahren entwickelt, um stabile Gleichgewichtslagen von VS-Laminaten vorherzusagen. Darüber hinaus wird in einer systematischen Studie untersucht, wie sich die stabilen Zustände bei Variation der kurvenförmigen Faserbahnen ändern. Als Ergebnis dieser Untersuchungen wurden Kriterien abgeleitet durch die VS-Laminate in Familien mit gleichartigen multistabilen Gleichgewichtslagen eingeteilt werden können. Dies ist wiederum für den vorgesehenen Entwurf der Morphing-Klappe erforderlich. Durchschlagen, d. h. der Übergang von einer Gleichgewichtslage zur nächsten, ist ein wesentlicher Prozess bei der Charakterisierung multistabiler Laminate in Morphing-Anwendungen. Zwei unterschiedliche Durchschlagsmechanismen werden hier untersucht, einer mit Hilfe konzentrierter Krafteinleitung, und der andere mit piezoelektrischen Aktuatoren. Das oben genannte semi-analytische Berechnungsverfahren verschafft Einblicke in die zugrundeliegende Mechanik sowie die Eigenschaften des Durchschlagsprozesses. Die Erkenntnisse aus den semi-analytischen Berechnungen ermöglichen Entwurf und Analyse komplexerer multistabiler Rechteckplatten. Es wird der optimale Entwurf von rechteckigen Platten mit Aktuatoren bestimmt, der zu einer maximalen Verschiebung außerhalb der Ebene führt, jedoch eine minimale Durchschlagspannung erfordert. Ein neuartiges Konzept einer Morphing-Hinterkantenklappe mit integrierten rechteckigen bistabilen Platten wird vorgestellt. In diesem neuen Konzept ist die Auslenkung der Hinterkante durch multistabile Platten realisiert. Die Verifikation des vorgeschlagenen Morphing-Mechanismus wird mittels Finite Elemente-Software erbracht.As the concern about climate change grows, more industries and research organizations are stepping up in search of viable solutions. Wind energy is one of the cheapest clean forms of energy, making it an attractive alternative against non-renewable sources. Upscaling of wind turbine has traditionally been considered a means to decrease the cost per kWh, and it remains a trend. However, with an increase in the size of wind turbine rotor blades, there is a need to conceptualize designs capable of reducing ultimate and fatigue loads. Active trailing edge flap is one such promising concept to alleviate loads in large wind turbine blades. Most existing flap mechanisms have the potential for quick reaction time, but it often involves intricate actuation systems, adding additional weight and complexity. Moreover, it requires a continuous supply of energy input to maintain a particular position of the flap. Multistable variable stiffness (VS) laminates have a great potential in morphing applications primarily due to the existence of multiple stable shapes. The use of VS laminates with curvilinear fiber paths allows one to improve further the performance of multistable laminates as morphing structures. The principal aim of this thesis is to exploit the properties of multistable VS laminates and apply them to a novel design of morphing trailing edge flap. This requires not only developing numerical and analytical tools, but also a suitable design to integrate VS laminates into a morphing flap. Therefore in this work, a fast semi-analytical tool is developed to predict the stable shapes of VS laminates. In addition, a systematic study is carried out to investigate the variation the curvilinear fiber paths on the stable equilibrium shapes. As a result of these investigations, VS laminates could be classified into families with similar multistable equilibrium positions. This, in turn, is applied to the envisaged design of the morphing flap. Snap-through, which is a transition from one equilibrium state to another, is a crucial process to characterize multistable laminates in morphing applications. Two different snapping mechanisms are studied, one using concentrated force and the other using piezoelectric actuators. The extension of the aforementioned semi-analytical tool provides insights that reflect the underlying mechanics and characteristics of the snap-through process. The knowledge gained from the semi-analytical calculations facilitates the design and analysis of more complex multistable rectangular plates. Optimal design of rectangular plates with actuators that leads to maximum out-of-plane displacement but with minimum snap-through voltage is determined. A novel concept of a morphing trailing edge flap with integrated rectangular bistable plates is proposed. In this new concept, the trailing edge deflection is realized by the snap-through of the multistable rectangular plates. The viability of the proposed morphing mechanism is examined using finite element tools

The benefits of an additional practice in descriptive geomerty course: non obligatory workshop at the Faculty of Civil Engineering in Belgrade

At the Faculty of Civil Engineering in Belgrade, in the Descriptive geometry (DG) course, non-obligatory workshops named “facultative task” are held for the three generations of freshman students with the aim to give students the opportunity to get higher final grade on the exam. The content of this workshop was a creative task, performed by a group of three students, offering free choice of a topic, i.e. the geometric structure associated with some real or imagery architectural/art-work object. After the workshops a questionnaire (composed by the professors at the course) is given to the students, in order to get their response on teaching/learning materials for the DG course and the workshop. During the workshop students performed one of the common tests for testing spatial abilities, named “paper folding". Based on the results of the questionnairethe investigation of the linkages between:students’ final achievements and spatial abilities, as well as students’ expectations of their performance on the exam, and how the students’ capacity to correctly estimate their grades were associated with expected and final grades, is provided. The goal was to give an evidence that a creative work, performed by a small group of students and self-assessment of their performances are a good way of helping students to maintain motivation and to accomplish their achievement. The final conclusion is addressed to the benefits of additional workshops employment in the course, which confirmhigherfinal scores-grades, achievement of creative results (facultative tasks) and confirmation of DG knowledge adaption

The contemporary visualization and modelling technologies and the techniques for the design of the green roofs

The contemporary design solutions are merging the boundaries between real and virtual world. The Landscape architecture like the other interdisciplinary field stepped in a contemporary technologies area focused on that, beside the good execution of works, designer solutions has to be more realistic and “touchable”. The opportunities provided by Virtual Reality are certainly not negligible, it is common knowledge that the designs in the world are already presented in this way so the Virtual Reality increasingly used. Following the example of the application of virtual reality in landscape architecture, this paper deals with proposals for the use of virtual reality in landscape architecture so that designers, clients and users would have a virtual sense of scope e.g. rooftop garden, urban areas, parks, roads, etc. It is a programming language that creates a series of images creating a whole, so certain parts can be controlled or even modified in VR. Virtual reality today requires a specific gadget, such as Occulus, HTC Vive, Samsung Gear VR and similar. The aim of this paper is to acquire new theoretical and practical knowledge in the interdisciplinary field of virtual reality, the ability to display using virtual reality methods, and to present through a brief overview the plant species used in the design and construction of an intensive roof garden in a Mediterranean climate, the basic characteristics of roofing gardens as well as the benefits they carry. Virtual and augmented reality as technology is a very powerful tool for landscape architects, when modeling roof gardens, parks, and urban areas. One of the most popular technologies used by landscape architects is Google Tilt Brush, which enables fast modeling. The Google Tilt Brush VR app allows modeling in three-dimensional virtual space using a palette to work with the use of a three dimensional brush. The terms of two "programmed" realities - virtual reality and augmented reality - are often confused. One thing they have in common, though, is VRML - Virtual Reality Modeling Language. In this paper are shown the ways on which this issue can be solved and by the way, get closer the term of Virtual Reality (VR), also all the opportunities which the Virtual reality offered us. As well, in this paper are shown the conditions of Mediterranean climate, the conceptual solution and the plant species which will be used by execution of intensive green roof on the motel “Marković”