947 research outputs found
Trivariate Spline Representations for Computer Aided Design and Additive Manufacturing
Digital representations targeting design and simulation for Additive
Manufacturing (AM) are addressed from the perspective of Computer Aided
Geometric Design. We discuss the feasibility for multi-material AM for B-rep
based CAD, STL, sculptured triangles as well as trimmed and block-structured
trivariate locally refined spline representations. The trivariate spline
representations support Isogeometric Analysis (IGA), and topology structures
supporting these for CAD, IGA and AM are outlined. The ideas of (Truncated)
Hierarchical B-splines, T-splines and LR B-splines are outlined and the
approaches are compared. An example from the EC H2020 Factories of the Future
Research and Innovation Actions CAxMan illustrates both trimmed and
block-structured spline representations for IGA and AM.Comment: 30 pages, 14 figures. This project has received funding from the
European Union's Horizon 2020 research and innovation programme under grant
agreement No 68044
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
TiGL - An Open Source Computational Geometry Library for Parametric Aircraft Design
This paper introduces the software TiGL: TiGL is an open source high-fidelity
geometry modeler that is used in the conceptual and preliminary aircraft and
helicopter design phase. It creates full three-dimensional models of aircraft
from their parametric CPACS description. Due to its parametric nature, it is
typically used for aircraft design analysis and optimization. First, we present
the use-case and architecture of TiGL. Then, we discuss it's geometry module,
which is used to generate the B-spline based surfaces of the aircraft. The
backbone of TiGL is its surface generator for curve network interpolation,
based on Gordon surfaces. One major part of this paper explains the
mathematical foundation of Gordon surfaces on B-splines and how we achieve the
required curve network compatibility. Finally, TiGL's aircraft component module
is introduced, which is used to create the external and internal parts of
aircraft, such as wings, flaps, fuselages, engines or structural elements
Kirchhoff-Love shell representation and analysis using triangle configuration B-splines
This paper presents the application of triangle configuration B-splines
(TCB-splines) for representing and analyzing the Kirchhoff-Love shell in the
context of isogeometric analysis (IGA). The Kirchhoff-Love shell formulation
requires global -continuous basis functions. The nonuniform rational
B-spline (NURBS)-based IGA has been extensively used for developing
Kirchhoff-Love shell elements. However, shells with complex geometries
inevitably need multiple patches and trimming techniques, where stitching
patches with high continuity is a challenge. On the other hand, due to their
unstructured nature, TCB-splines can accommodate general polygonal domains,
have local refinement, and are flexible to model complex geometries with
continuity, which naturally fit into the Kirchhoff-Love shell formulation with
complex geometries. Therefore, we propose to use TCB-splines as basis functions
for geometric representation and solution approximation. We apply our method to
both linear and nonlinear benchmark shell problems, where the accuracy and
robustness are validated. The applicability of the proposed approach to shell
analysis is further exemplified by performing geometrically nonlinear
Kirchhoff-Love shell simulations of a pipe junction and a front bumper
represented by a single patch of TCB-splines
Dynamic Multivariate Simplex Splines For Volume Representation And Modeling
Volume representation and modeling of heterogeneous objects acquired from real world are very challenging research tasks and playing fundamental roles in many potential applications, e.g., volume reconstruction, volume simulation and volume registration. In order to accurately and efficiently represent and model the real-world objects, this dissertation proposes an integrated computational framework based on dynamic multivariate simplex splines (DMSS) that can greatly improve the accuracy and efficacy of modeling and simulation of heterogenous objects. The framework can not only reconstruct with high accuracy geometric, material, and other quantities associated with heterogeneous real-world models, but also simulate the complicated dynamics precisely by tightly coupling these physical properties into simulation. The integration of geometric modeling and material modeling is the key to the success of representation and modeling of real-world objects.
The proposed framework has been successfully applied to multiple research areas, such as volume reconstruction and visualization, nonrigid volume registration, and physically based modeling and simulation
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