Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes

As a remarkable difference to the existing CAD technology, where shapes are represented by their boundaries, FEM-based isogeometric analysis typically needs a parameterization of the interior of the domain. Due to the strong influence on the accuracy of the analysis, methods for constructing a good parameterization are fundamentally important. The flexibility of single patch representations is often insufficient, especially when more complex geometric shapes have to be represented. Using a multi-patch structure may help to overcome this challenge. In this paper we present a systematic method for exploring the different possible parameterizations of a planar domain by collections of quadrilateral patches. Given a domain, which is represented by a certain number of boundary curves, our aim is to find the optimal multi-patch parameterization with respect to an objective function that captures the parameterization quality. The optimization considers both the location of the control points and the layout of the multi-patch structure. The latter information is captured by pre-computed catalogs of all available multi-patch topologies. Several numerical examples demonstrate the performance of the method.

Planar multi-patch domain parameterization via patch adjacency graphs

Regularity Criteria for the Topology of Algebraic Curves and Surfaces.- Quadrangle Surface Tiling Through Contouring.- Surfaces with Piecewise Linear Support Functions over Spherical Triangulations.- A Developable Surface of Uniformly Negative Internal Angle Deficit.- Rational Maximal Parametrisations of Dupin Cyclides.- Discrete Harmonic Functions from Local Coordinates.- Computing the Topology of an Arrangement of Quartics.- Non-uniform B-Spline Subdivision Using Refine and Smooth.- Scattered Data Fitting on Surfaces Using Projected Powell-Sabin Splines.- Implicit Boundary Control of Vector Field Based Shape Deformations.- Tuning Subdivision Algorithms Using Constrained Energy Optimization.- Description of Surfaces in Parallel Coordinates by Linked Planar Regions.- Discrete Surface Ricci Flow: Theory and Applications.- Guided C 2 Spline Surfaces with V-Shaped Tessellation.- MOS Surfaces: Medial Surface Transforms with Rational Domain Boundaries.- Mean Value Bezier Surfaces.- Curvature Estimation over Smooth Polygonal Meshes Using the Half Tube Formula.- Segmenting Periodic Reliefs on Triangle Meshes.- Estimation of End Curvatures from Planar Point Data.- Inversion, Degree and Reparametrization for Rational Surfaces.- Discrete Surfaces in Isotropic Geometry.- An Appropriate Geometric Invariant for the C 2-Analysis of Subdivision Surfaces.- Curvature-Based Surface Regeneration.- Bounded Curvature Subdivision Without Eigenanalysis.- Facial Shape-from-Shading Using Principal Geodesic Analysis and Robust Statistics.- Statistical Methods for Surface Integration.- Skeleton Surface Generation from Volumetric Models of Thin Plate Structures for Industrial Applications.- Parallel Tangency in .- Condition Numbers and Least Squares Regression.- Propagation of Geometric Tolerance Zones in 3D.

Mathematics of surfaces XII : 12th IMA International Conference, Sheffield, UK, September 4-6, 2007 : proceedings

Measurement-based geometric reconstruction for milling turbine blade using free-form deformation

This paper presents an improved mathematical model for calculation of distortion vectors of two aligned surface meshes. The model shows better accuracy when benchmarked to an existing model with ex...

An improved distortion compensation approach for additive manufacturing using optically scanned data

Adaptive fitting with THB-splines: Error analysis and industrial applications

We present a framework for generating a trivariate B-spline parametrization of turbine blades from measurement data generated by optical scanners. This new representation replaces the standard patch-based representation of industrial blade designs. In a first step, the blade surface is represented by a smoothly varying family of B-spline curves. In a second step, the blade is parametrized by a trivariate B-spline volume. The resulting model is suitable for numerical simulation via isogeometric analysis, as well as for a fully automatic structured mesh generation with standard finite elements. We focus on the industrial applicability of the framework, by using standard turbine blade features throughout the process.

/pdf/volumetric-geometry-reconstruction-of-turbine-blades-for-jt00f2kbct.pdf

Volumetric geometry reconstruction of turbine blades for aircraft engines

Spline surface fitting using normal data and norm-like functions

Die Erfindung betrifft ein Verfahren zur automatisierten Bewertung von Schaufeln, insbesondere Verdichterschaufeln. Das Verfahren umfasst folgende Schritte: a.) dreidimensionale Erfassung des Schaufelblattes (26, 28, 30; 32, 34) einer hergestellten Schaufel; b.) Uberfuhrung der erfassten Werte in mindestens einem Flachenmodell (S5); c.) Transformation der Schaufelblattdaten vom Messzustand in den Betriebszustand; d.) Bewertung der aerodynamischen und/oder strukturmechanischen Eigenschaften des Schaufelblattes (26, 28, 30; 32, 34); und e.) Bewertung der Performanz eines Bauteils (S9).

Ein Verfahren zur Herstellung von Schaufeln

Ein Verfahren zum automatisierten Erzeugen eines Flachenmodells eines Objekts, insbesondere einer Schaufel einer Turbomaschine, umfasst wenigstens folgende Schritte: - Vermessen der Oberflache des Objekts; - Bereitstellen der aus der Vermessung erhaltenen Daten in Form einer fehlerfreien Punktwolke, wobei die Daten in Form einer triangulierten Punktwolke bereitgestellt werden; - Diskretisierung und Untersuchung von Krummungen der triangulierten Punktwolke; - Segmentierung der triangulierten Punktwolke auf Basis der Ergebnisse der Krummungsuntersuchungen; - Aufbau einer eindeutig zuordenbaren Objekttopologie und - Erzeugung eines parametrisierten Flachenmodells.

Verfahren zum automatisierten Erzeugen eines Flächenmodells eines Objekts

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