4,967 research outputs found
Boundary-Conforming Free-Surface Flow Computations: Interface Tracking for Linear, Higher-Order and Isogeometric Finite Elements
The simulation of certain flow problems requires a means for modeling a free
fluid surface; examples being viscoelastic die swell or fluid sloshing in
tanks. In a finite-element context, this type of problem can, among many other
options, be dealt with using an interface-tracking approach with the
Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation. A
difficult issue that is connected with this type of approach is the
determination of a suitable coupling mechanism between the fluid velocity at
the boundary and the displacement of the boundary mesh nodes. In order to avoid
large mesh distortions, one goal is to keep the nodal movements as small as
possible; but of course still compliant with the no-penetration boundary
condition. Standard displacement techniques are full velocity, velocity in a
specific coordinate direction, and velocity in normal direction. In this work,
we investigate how the interface-tracking approach can be combined with
isogeometric analysis for the spatial discretization. If NURBS basis functions
of sufficient order are used for both the geometry and the solution, both a
continuous normal vector as well as the velocity are available on the entire
boundary. This circumstance allows the weak imposition of the no-penetration
boundary condition. We compare this option with an alternative that relies on
strong imposition at discrete points. Furthermore, we examine several coupling
methods between the fluid equations, boundary conditions, and equations for the
adjustment of interior control point positions.Comment: 20 pages, 16 figure
Isogeometric analysis applied to frictionless large deformation elastoplastic contact
This paper focuses on the application of isogeometric analysis to model frictionless large deformation contact between deformable bodies and rigid surfaces that may be represented by analytical functions. The contact constraints are satisfied exactly with the augmented Lagrangian method, and treated with a mortar-based approach combined with a simplified integration method to avoid segmentation of the contact surfaces. The spatial discretization of the deformable body is performed with NURBS and C0-continuous Lagrange polynomial elements. The numerical examples demonstrate that isogeometric surface discretization delivers more accurate and robust predictions of the response compared to Lagrange discretizations
Curve network interpolation by quadratic B-spline surfaces
In this paper we investigate the problem of interpolating a B-spline curve
network, in order to create a surface satisfying such a constraint and defined
by blending functions spanning the space of bivariate quadratic splines
on criss-cross triangulations. We prove the existence and uniqueness of the
surface, providing a constructive algorithm for its generation. We also present
numerical and graphical results and comparisons with other methods.Comment: With respect to the previous version, this version of the paper is
improved. The results have been reorganized and it is more general since it
deals with non uniform knot partitions. Accepted for publication in Computer
Aided Geometric Design, October 201
TVL<sub>1</sub> Planarity Regularization for 3D Shape Approximation
The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within.
This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy
The Influence of Quadrature Errors on Isogeometric Mortar Methods
Mortar methods have recently been shown to be well suited for isogeometric
analysis. We review the recent mathematical analysis and then investigate the
variational crime introduced by quadrature formulas for the coupling integrals.
Motivated by finite element observations, we consider a quadrature rule purely
based on the slave mesh as well as a method using quadrature rules based on the
slave mesh and on the master mesh, resulting in a non-symmetric saddle point
problem. While in the first case reduced convergence rates can be observed, in
the second case the influence of the variational crime is less significant
Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory
In this paper, we present an effectively numerical approach based on
isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT)
for geometrically nonlinear analysis of laminated composite plates. The HSDT
allows us to approximate displacement field that ensures by itself the
realistic shear strain energy part without shear correction factors. IGA
utilizing basis functions namely B-splines or non-uniform rational B-splines
(NURBS) enables to satisfy easily the stringent continuity requirement of the
HSDT model without any additional variables. The nonlinearity of the plates is
formed in the total Lagrange approach based on the von-Karman strain
assumptions. Numerous numerical validations for the isotropic, orthotropic,
cross-ply and angle-ply laminated plates are provided to demonstrate the
effectiveness of the proposed method
Optimal-order isogeometric collocation at Galerkin superconvergent points
In this paper we investigate numerically the order of convergence of an
isogeometric collocation method that builds upon the least-squares collocation
method presented in [1] and the variational collocation method presented in
[2]. The focus is on smoothest B-splines/NURBS approximations, i.e, having
global continuity for polynomial degree . Within the framework of
[2], we select as collocation points a subset of those considered in [1], which
are related to the Galerkin superconvergence theory. With our choice, that
features local symmetry of the collocation stencil, we improve the convergence
behaviour with respect to [2], achieving optimal -convergence for odd
degree B-splines/NURBS approximations. The same optimal order of convergence is
seen in [1], where, however a least-squares formulation is adopted. Further
careful study is needed, since the robustness of the method and its
mathematical foundation are still unclear.Comment: 21 pages, 20 figures (35 pdf images
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