439 research outputs found
A priori error for unilateral contact problems with Lagrange multiplier and IsoGeometric Analysis
In this paper, we consider unilateral contact problem without friction
between a rigid body and deformable one in the framework of isogeometric
analysis. We present the theoretical analysis of the mixed problem using an
active-set strategy and for a primal space of NURBS of degree and for
a dual space of B-Spline. A inf-sup stability is proved to ensure a good
property of the method. An optimal a priori error estimate is demonstrated
without assumption on the unknown contact set. Several numerical examples in
two- and three-dimensional and in small and large deformation demonstrate the
accuracy of the proposed method
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
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