Application of Cubic B-Spline Curves for Hull Meshing

This paper describes the development of a regular hull meshing code using cubic B-Spline curves. The discretization procedure begins by the definition of B-Spline curves over stations, bow and stern contours of the hull plan lines. Thus, new knots are created applying an equal spaced subdivision procedure on defined B-spline curves. Then, over these equal transversal space knots, longitudinal B-spline curves are defined and subdivided into equally spaced knots, too. Subsequently, new transversal knots are created using the longitudinal equally spaced knots. Finally, the hull mesh is composed by quadrilateral panels formed by these new transversal and longitudinal knots. This procedure is applied in the submerged Wigley hulls Series 60 Cb=0.60. Their mesh volumes are calculated using the divergence theorem, for mesh quality evaluation.

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Parametric Generation, Modeling, and Fairing of Simple Hull Lines With the Use of Nonuniform Rational B-Spline Surfaces

Journal of Ship Research ◽

10.5957/jsr.2008.52.1.1 ◽

2008 ◽

Vol 52 (01) ◽

pp. 1-15

Author(s):

F. L. Pérez ◽

J. A. Clemente ◽

J. A. Suárez ◽

J. M. González

Keyword(s):

Parametric Design ◽

Design Method ◽

Surface Modeling ◽

Affine Transformations ◽

Parametric Generation ◽

B Spline ◽

Ship Hulls ◽

Spline Curves ◽

Definition Of ◽

Fairing Process

This paper deals with the use of a simple parametric design method applied to simple hull lines, such as sailing ship hulls and round bilge hulls. The described method allows the generation of hull lines that meet hydrodynamic coefficients imposed by the designer, obtaining more flexibility than with normal affine transformations of a parent hull. First, a wire model of the ship stations is made with the use of explicit curves. The method is completed with an automatic surface modeling of the previ¬ously generated offsets. The construction of spline curves and their application in the definition of ship lines are reviewed. Approximation of spline curves fitting the data on the stations is made, with special emphasis on the choice of parametrization, which is relevant to increasing the accuracy of the splines. B-spline surface modeling of the hull and the fairing process adapted to maintain certain ship characteristics are described. Some examples of the generation, lofting, and fairing process are pre¬sented.

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Automatic Unstructured Mesh Generation Around Two-Dimensional Domains Described by B-Spline Curves

Volume 1: 21st Computers and Information in Engineering Conference ◽

10.1115/detc2001/cie-21269 ◽

2001 ◽

Author(s):

Horacio Flórez Guzmán ◽

Raúl Manzanilla Morillo

Keyword(s):

Grid Generation ◽

Computer Code ◽

Two Dimensional ◽

B Spline ◽

Piecewise Polynomials ◽

Spline Curves ◽

Interpolation Problems ◽

Interpolation Procedure ◽

Definition Of ◽

Unstructured Mesh Generation

Abstract A computer code for the generation of unstructured two-dimensional triangular meshes around arbitrary complex geometries has been developed. The code is based on Delaunay triangulation with an automatic point insertion scheme and a smoothing technique. The geometrical definition of the domain to be meshed is prescribed by means of B-spline curves obtained from two approaches of interest in Computer-Aided Geometric Design named inverse design and interpolation problems. The presented scheme is based on an interpolation procedure along a B-spline curve proposed by the author in a recent paper. This technique prevents that the resulting grid may overlap convex portions of the boundaries. The main goal is to study the possibility of extend the methodology of unstructured grid generation beginning with boundaries described by polylines to other in which they are prescribed by piecewise polynomials curves capable to drive more realistic problems. Several figures and examples from Computational Fluid Dynamics have been included to show the various steps of the algorithm. The results show that the code is able to solve the problem of automatic grid generation in a robust manner opening new perspectives for the development of a black-box grid generator.

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B-Splines Geometric Modeling for Dynamic Analysis Behaviour in Offshore Systems

Volume 2: Ocean Engineering and Polar and Arctic Sciences and Technology ◽

10.1115/omae2006-92091 ◽

2006 ◽

Author(s):

Fa´bio G. T. de Menezes ◽

Prota´sio Dutra Martins

Keyword(s):

Geometric Modeling ◽

Floating Body ◽

Design Work ◽

Oil Drilling ◽

B Spline ◽

B Splines ◽

Hydrodynamic Behaviour ◽

Spline Curves ◽

Definition Of ◽

Floating Systems

This work reports a study of B-Spline curves and surfaces applied to the geometric definition of hulls of ships and oil drilling and production platforms. The research aims at defining mathematically the floating body surface in suitable formats for the analysis of functional behaviour of the design object with sophisticated methods and tools. The WAMIT system was chosen as a reference in the research due to its reliability as a professional tool for hydrodynamic behaviour of floating systems in practice. The B-Spline model is input to the WAMIT system in the required format for the analysis of hull motion response to waves. The quality of the results obtained with B-Splines modeling was compared the ones obtained with flat panels. B-Splines have shown to be an effective approach, more efficient in computing terms when compared with the flat panels approach and suitable to optimization scripts. It revealed itself as a more adequate procedure to the design work as it simplifies the hull form mathematical definition of floating systems.

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