2,153 research outputs found
A discrete methodology for controlling the sign of curvature and torsion for NURBS
This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign along the NURBS parametric domain of definition. The methodology provides a monotonic sequence of convex polyhedra, converging from the interior to the convex domain. If the latter is non-empty, a simple algorithm is proposed, that yields a sequence of polytopes converging uniformly to the restriction of the convex domain to any user-specified bounding box. The algorithm is illustrated for a pair of planar and a spatial Bézier configuration
A simple approach to the numerical simulation with trimmed CAD surfaces
In this work a novel method for the analysis with trimmed CAD surfaces is
presented. The method involves an additional mapping step and the attraction
stems from its sim- plicity and ease of implementation into existing Finite
Element (FEM) or Boundary Element (BEM) software. The method is first verified
with classical test examples in structural mechanics. Then two practical
applications are presented one using the FEM, the other the BEM, that show the
applicability of the method.Comment: 20 pages and 16 figure
Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization
In this paper, we propose a general framework for constructing IGA-suitable
planar B-spline parameterizations from given complex CAD boundaries consisting
of a set of B-spline curves. Instead of forming the computational domain by a
simple boundary, planar domains with high genus and more complex boundary
curves are considered. Firstly, some pre-processing operations including
B\'ezier extraction and subdivision are performed on each boundary curve in
order to generate a high-quality planar parameterization; then a robust planar
domain partition framework is proposed to construct high-quality patch-meshing
results with few singularities from the discrete boundary formed by connecting
the end points of the resulting boundary segments. After the topology
information generation of quadrilateral decomposition, the optimal placement of
interior B\'ezier curves corresponding to the interior edges of the
quadrangulation is constructed by a global optimization method to achieve a
patch-partition with high quality. Finally, after the imposition of
C1=G1-continuity constraints on the interface of neighboring B\'ezier patches
with respect to each quad in the quadrangulation, the high-quality B\'ezier
patch parameterization is obtained by a C1-constrained local optimization
method to achieve uniform and orthogonal iso-parametric structures while
keeping the continuity conditions between patches. The efficiency and
robustness of the proposed method are demonstrated by several examples which
are compared to results obtained by the skeleton-based parameterization
approach
Fast Isogeometric Boundary Element Method based on Independent Field Approximation
An isogeometric boundary element method for problems in elasticity is
presented, which is based on an independent approximation for the geometry,
traction and displacement field. This enables a flexible choice of refinement
strategies, permits an efficient evaluation of geometry related information, a
mixed collocation scheme which deals with discontinuous tractions along
non-smooth boundaries and a significant reduction of the right hand side of the
system of equations for common boundary conditions. All these benefits are
achieved without any loss of accuracy compared to conventional isogeometric
formulations. The system matrices are approximated by means of hierarchical
matrices to reduce the computational complexity for large scale analysis. For
the required geometrical bisection of the domain, a strategy for the evaluation
of bounding boxes containing the supports of NURBS basis functions is
presented. The versatility and accuracy of the proposed methodology is
demonstrated by convergence studies showing optimal rates and real world
examples in two and three dimensions.Comment: 32 pages, 27 figure
Recommended from our members
ALPHA_I, Remote Manufacturing, and Solid Freeform Fabrication
Alpha_l is a nonuniform rational B-spline (NURBs) based solid modeling system that
has been developed at the University of Utah over the past 10 years. In addition to being
useful in modeling objects that are described by simple rotation and extrusion operations,
the real power of Alpha_l is demonstrated in the modeling of complex parts with sculptured
surfaces. For the past several years, a major research thrust has been to use Alpha_l to
semi-automatically generate process plan information and numerical control code to manufacture
mechanical parts directly from the models. A long term goal is to support an on-line
remote manufacturing facility for producing prototype parts. Recently, a 3D Systems stereo
lithography machine has been added to the advanced manufacturing laboratory. The stereo
lithography process and other SFF techniques are of particular interest for supporting a
remote manufacturing facility in that these processes are inherently much safer than numerically
controlled machining. Special Alpha_l interfaces including a new slicing algorithm
are being developed for the SFF machine use. By generating a SFF part directly from
its NURBs description, Alpha_l should facilitate the manufacture of complex parts while
providing smoother surfaces.Mechanical Engineerin
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