TY - JOUR
A1 - Stein, Peter
A1 - Lahmer, Tom
A1 - Bock, Sebastian
T1 - Synthese und Analyse von gekoppelten Modellen im konstruktiven Ingenieurbau
BT - Sonderdruck‐DFG Graduiertenkolleg
JF - Bautechnik
N2 - Synthese und Analyse von gekoppelten Modellen im konstruktiven Ingenieurbau
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2011
SP - 8
EP - 11
ER -
TY - CHAP
A1 - Stein, Peter
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - NURBS-BASED ELEMENTS AS A BASIS FOR INTEGRATING ENGINEERING APPLICATIONS
N2 - Building information modeling offers a huge potential for increasing the productivity and quality of construction planning processes. Despite its promising concept, this approach has not found widespread use. One of the reasons is the insufficient coupling of the structural models with the general building model. Instead, structural engineers usually set up a structural model that is independent from the building model and consists of mechanical models of reduced dimension. An automatic model generation, which would be valuable in case of model revisions is therefore not possible. This can be overcome by a volumetric formulation of the problem. A recent approach employed the p-version of the finite element method to this problem. This method, in conjunction with a volumetric formulation is suited to simulate the structural behaviour of both „thick“ solid bodies and thin-walled structures. However, there remains a notable discretization error in the numerical models. This paper therefore proposes a new approach for overcoming this situation. It sugggests the combination of the Isogeometric analysis together with the volumetric models in order to integrate the structural design into the digital, building model-centered planning process and reduce the discretization error. The concept of the isogeometric analysis consists, roughly, in the application of NURBS functions to represent the geometry and the shape functions of the elements. These functions possess some beneficial properties regarding numerical simulation. Their use, however, leads to some intricacies related to the setup of the stiffness matrix. This paper describes some of these properties.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Architektur
KW - Computerunterstütztes Verfahren
KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28944
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN - 1611-4086
ER -
TY - THES
A1 - Stein, Peter
T1 - Procedurally generated models for Isogeometric Analysis
N2 - Increasingly powerful hard- and software allows for the numerical simulation of complex physical phenomena with high levels of detail. In light of this development the definition of numerical models for the Finite Element Method (FEM) has become the bottleneck in the simulation process. Characteristic features of the model generation are large manual efforts and a de-coupling of geometric and numerical model. In the highly probable case of design revisions all steps of model preprocessing and mesh generation have to be repeated. This includes the idealization and approximation of a geometric model as well as the definition of boundary conditions and model parameters. Design variants leading to more resource-efficient structures might hence be disregarded due to limited budgets and constrained time frames.
A potential solution to above problem is given with the concept of Isogeometric Analysis (IGA). Core idea of this method is to directly employ a geometric model for numerical simulations, which allows to circumvent model transformations and the accompanying data losses. Basis for this method are geometric models described in terms of Non-uniform rational B-Splines (NURBS). This class of piecewise continuous rational polynomial functions is ubiquitous in computer graphics and Computer-Aided Design (CAD). It allows the description of a wide range of geometries using a compact mathematical representation. The shape of an object thereby results from the interpolation of a set of control points by means of the NURBS functions, allowing efficient representations for curves, surfaces and solid bodies alike. Existing software applications, however, only support the modeling and manipulation of the former two. The description of three-dimensional solid bodies consequently requires significant manual effort, thus essentially forbidding the setup of complex models.
This thesis proposes a procedural approach for the generation of volumetric NURBS models. That is, a model is not described in terms of its data structures but as a sequence of modeling operations applied to a simple initial shape. In a sense this describes the "evolution" of the geometric model under the sequence of operations. In order to adapt this concept to NURBS geometries, only a compact set of commands is necessary which, in turn, can be adapted from existing algorithms. A model then can be treated in terms of interpretable model parameters. This leads to an abstraction from its data structures and model variants can be set up by variation of the governing parameters.
The proposed concept complements existing template modeling approaches: templates can not only be defined in terms of modeling commands but can also serve as input geometry for said operations. Such templates, arranged in a nested hierarchy, provide an elegant model representation. They offer adaptivity on each tier of the model hierarchy and allow to create complex models from only few model parameters. This is demonstrated for volumetric fluid domains used in the simulation of vertical-axis wind turbines. Starting from a template representation of airfoil cross-sections, the complete "negative space" around the rotor blades can be described by a small set of model parameters, and model variants can be set up in a fraction of a second.
NURBS models offer a high geometric flexibility, allowing to represent a given shape in different ways. Different model instances can exhibit varying suitability for numerical analyses. For their assessment, Finite Element mesh quality metrics are regarded. The considered metrics are based on purely geometric criteria and allow to identify model degenerations commonly used to achieve certain geometric features. They can be used to decide upon model adaptions and provide a measure for their efficacy. Unfortunately, they do not reveal a relation between mesh distortion and ill-conditioning of the equation systems resulting from the numerical model.
T3 - Schriftenreihe des DFG Graduiertenkollegs 1462 Modellqualitäten // Graduiertenkolleg Modellqualitäten - 7
KW - NURBS
KW - Isogeometric Analysis
KW - Procedural modeling
KW - Templates
KW - Mesh quality
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20130212-18483
SN - 978-3-86068-488-7
PB - Universitätsverlag
CY - Weimar
ER -