scholarly journals A novel shape optimization method using knot insertion algorithm in B-spline and its application to transonic airfoil design

2011 ◽  
Vol 6 (27) ◽  
Author(s):  
P. A. Sherar,
Keyword(s):  
Shape Optimization ◽  
Optimization Method ◽  
Knot Insertion ◽  
B Spline ◽  
Insertion Algorithm ◽  
Transonic Airfoil ◽  
Transonic Airfoil Design

Isogeometric Shape Optimization on Triangulations

2016 ◽  
Author(s):  
Cunfu Wang ◽  
Songtao Xia ◽  
Xilu Wang ◽  
Xiaoping Qian
Keyword(s):  
Shape Optimization ◽  
Optimization Method ◽  
Coarse Mesh ◽  
Mesh Quality ◽  
Numerical Accuracy ◽  
B Spline ◽  
Fine Mesh ◽  
Complex Topology ◽  
Physical Fields ◽  
Bézier Triangles

The paper presents an isogeometric shape optimization method that is based on Bézier triangles. Bézier triangles are used to represent both the geometry and physical fields. For a given physical domain defined by B-spline boundary, triangular Bézier parameterization can be automatically generated. This shape optimization method is thus applicable to structures of complex topology. Due to the use of B-spline parameterization of the boundary, the optimized shape can be compactly represented with a relatively small number of optimization variables. In order to ensure mesh validity during shape optimization, we adopt a bi-level mesh representation, where the coarse mesh is used to maintain mesh quality through positivity of Jacobian ordinates of the Bézier triangles. The fine mesh is used in isogeometric analysis for numerical accuracy. Numerical examples are presented to demonstrate the efficacy of the proposed method.

Approximate Merging B-Spline Curves via Least Square Approximation

2014 ◽  
Vol 556-562 ◽  
pp. 3496-3500 ◽  
Author(s):  
Si Hui Shu ◽  
Zi Zhi Lin
Keyword(s):  
Approximation Error ◽  
Least Square ◽  
Error Tolerance ◽  
Knot Insertion ◽  
Least Squares Approximation ◽  
B Spline ◽  
Spline Curve ◽  
Spline Curves ◽  
Insertion Algorithm ◽  
Approximate Merging

An algorithm of B-spline curve approximate merging of two adjacent B-spline curves is presented in this paper. In this algorithm, the approximation error between two curves is computed using norm which is known as best least square approximation. We develop a method based on weighed and constrained least squares approximation, which adds a weight function in object function to reduce error of merging. The knot insertion algorithm is also developed to meet the error tolerance.

Another knot insertion algorithm for B-spline curves

1992 ◽  
Vol 9 (3) ◽  
pp. 175-183 ◽  
Author(s):  
Phillip J. Barry ◽  
Rui-Feng Zhu
Keyword(s):  
Knot Insertion ◽  
B Spline ◽  
Spline Curves ◽  
Insertion Algorithm

scholarly journals A Tidal Level Prediction Approach Based on BP Neural Network and Cubic B-Spline Curve with Knot Insertion Algorithm

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Wenjuan Wang ◽  
Hongchun Yuan
Keyword(s):  
Neural Network ◽  
Storm Surge ◽  
Bp Neural Network ◽  
Knot Insertion ◽  
Tidal Level ◽  
B Spline ◽  
Spline Curve ◽  
Tide Level ◽  
Insertion Algorithm ◽  
Prediction Approach

Tide levels depend on both long-term astronomical effects that are mainly affected by moon and sun and short-term meteorological effects generated by severe weather conditions like storm surge. Storm surge caused by typhoons will impose serious security risks and threats on the coastal residents’ safety in production, property, and life. Due to the challenges of nonperiodic and incontinuous tidal level record data and the influence of multimeteorological factors, the existing methods cannot predict the tide levels affected by typhoons precisely. This paper targets to explore a more advanced method for forecasting the tide levels of storm surge caused by typhoons. First, on the basis of successive five-year tide level and typhoon data at Luchaogang, China, a BP neural network model is developed using six parameters of typhoons as input parameters and the relevant tide level data as output parameters. Then, for an improved forecasting accuracy, cubic B-spline curve with knot insertion algorithm is combined with the BP model to conduct smooth processing of the predicted points and thus the smoothed prediction curve of tidal level has been obtained. By using the data of the fifth year as the testing sample, the predicted results by the two methods are compared. The experimental results have shown that the latter approach has higher accuracy in forecasting tidal level of storm surge caused by typhoons, and the combined prediction approach provides a powerful tool for defending and reducing storm surge disaster.

Geometric Design and Fabrication of Developable Bezier and B-spline Surfaces

1994 ◽  
Vol 116 (4) ◽  
pp. 1042-1048 ◽  
Author(s):  
R. M. C. Bodduluri ◽  
B. Ravani
Keyword(s):  
Spline Interpolation ◽  
Geometric Design ◽  
Developable Surface ◽  
Knot Insertion ◽  
B Spline ◽  
Developable Surfaces ◽  
Spline Surfaces ◽  
Insertion Algorithm ◽  
Cad Cam ◽  
Type Construction

In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop a direct representation of developable surfaces in terms of plane geometry. It uses control planes to determine a surface which is a Bezier or a B-spline interpolation of the control planes. In the Bezier case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In the B-spline case, de Boor type construction for the geometric design of the developable surface and Boehm type knot insertion algorithm are presented. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.

Conformal and G1 Continuous Connection of NURBS Curves

2013 ◽  
Vol 756-759 ◽  
pp. 3826-3830
Author(s):  
Pei Sen Deng ◽  
Shao Ping Chen ◽  
Jun Cheng Shen
Keyword(s):  
Knot Insertion ◽  
Nurbs Curve ◽  
Nurbs Curves ◽  
Insertion Algorithm ◽  
Vector Rotation

This paper converts a NURBS curve to piecewise rational Bézier curves by knot insertion algorithm, and then discusses the algorithm of continuous connection of NURBS curves. Meanwhile, explores the method to keep the same shape of the NURBS curves after connecting through the point translation and vector rotation theory. Finally, gives an instance to verify the validity of the algorithm.

Comprehensive Design Method for Open or Ducted Propellers for Underwater Vehicles

2021 ◽  
Author(s):  
Spyros A. Kinnas ◽  
Kyungjung Cha ◽  
Seungnam Kim
Keyword(s):  
Design Method ◽  
A Priori ◽  
Optimization Method ◽  
Underwater Vehicles ◽  
Current Approach ◽  
Lattice Method ◽  
B Spline ◽  
Effective Wake ◽  
Propeller Thrust ◽  
Ducted Propellers

A comprehensive method which determines the most efficient propeller blade shapes for a given axisymmetric hull to travel at a desired speed, is presented. A nonlinear optimization method is used to design the blade, the shape of which is defined by a 3-D B-spline polygon, with the coordinates of the B-spline control points being the parameters to be optimized for maximum propeller efficiency, for given effective wake and propeller thrust. The performance of the propeller within the optimization scheme is assessed by a vortex-lattice method (VLM). To account fully for the hull/propeller interaction, the effective wake to the propeller and the hull resistance are determined by analyzing the designed propeller geometry by the VLM, coupled with a Reynolds-Averaged Navier-Stokes (RANS) solver. The optimization method re-designs the optimum blade with the updated effective wake and propeller thrust (taken to be equal to the updated hull resistance), and the procedure continues until convergence of the propeller performance. The current approach does not require knowledge of the wake fraction or the thrust deduction factor, both of which must be estimated a priori in traditional propeller design. The method is applied for a given hull to travel at a desired speed, and the optimum blades are designed for various combinations of propeller diameter and RPM, in the case of open and ducted propellers with provided duct shapes. The effects of the propeller diameter and RPM on the designed propeller thrust, torque, propeller efficiency, and required power are presented and compared with each other in the case of open and ducted propellers. The present approach is shown to provide guidance on the design of propulsors for underwater vehicles, and is applicable to the design of propulsors for surface ships.

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