scholarly journals Modeling technology of curved surface development for puffer fish

2020 ◽  
Vol 12 (4) ◽  
pp. 168781402091602
Author(s):  
Honggen Zhou ◽  
Jie Cui ◽  
Guizhong Tian ◽  
Yesheng Zhu ◽  
Changfeng Jia
Keyword(s):  
Three Dimensional ◽  
Least Square ◽  
Curved Surface ◽  
B Spline ◽  
Implicit Equation ◽  
Moving Least Square ◽  
Average Value ◽  
Modeling Technology ◽  
Surface Development ◽  
Puffer Fish

The drag reduction mechanism of puffer epidermis was closely related to its real geometry. In order to solve the modeling problem of epidermal spines on the puffer surface, a modeling method for the expansion of puffer shape was proposed. The three-dimensional scanning and non-uniform rational B-spline surface modeling technology was used to reconstruct the puffer model. According to the curvature characteristics, the surface mathematical equations including exponential, logarithmic, and sinusoidal functions were established based on the multinomial function. The surface was generated by a mathematical equation, and the surface was divided into several non-uniform rational B-spline patches according to curvature. After discretization, the point cloud Gaussian curvature and average value were calculated based on the implicit equation of moving least square surface, and whether the surface is approximately extensible or not was judged. Finally, the puffer surface was divided into 46 curved patches. In this article, the surface expansion algorithm gave priority to ensure the area unchanged, and four feature surfaces were selected according to the epidermal spines arrangement of the puffer surface. The results showed that the technique can simply and efficiently unfold the curved surface of the puffer fish, thus the mapping relationship between the epidermal spines on the surface and the plane was determined, which established a foundation for the accurate arrangement and modeling of the epidermal spines on the surface.

USE OF B-SPLINE FUNCTION IN ELEMENT FREE GALERKIN METHOD FOR NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATION

2009 ◽  
Vol 06 (03) ◽  
pp. 349-360
Author(s):  
K. SANDEEP ◽  
K. KAMAL KUMAR
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Spline Function ◽  
Least Square ◽  
Partial Differential ◽  
Order Continuity ◽  
B Spline ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free

The paper presents application of a B-spline function in place of a shape function obtained by using moving least square approximant with B-spline weight and linear basis. The piecewise polynomial function of B-spline with C2 and lower order continuity is efficiently used in element free Galerkin (EFG) method to generate a new fast algorithm for the solution of one-dimensional partial differential equation. The support of B-spline function is assumed as the domain of influence of EFG method. The results of bar deflection are compared with those obtained by other researchers.

Square Cracks in Three-Dimensional Transversely Isotropic Solids

2012 ◽  
Vol 487 ◽  
pp. 617-621
Author(s):  
Ya Dong Bian ◽  
Yu Zhou Sun
Keyword(s):  
Crack Opening ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Least Square ◽  
Weight Functions ◽  
Opening Displacement ◽  
Moving Least Square ◽  
Moving Least Square Approximation ◽  
Fracture Damage

This paper presents a study for the square crack in a three-dimensional infinite transversely isotropic medium, which can model the fracture damage of rock that displays transversely isotropic behavior. The study is based on a newly derived boundary integral equation. To carry out the numerical simulation, the crack opening displacement is first expressed as the product of the weight functions and the characteristic terms, and the unknown weight is approximated with the moving least-square approximation. A boundary type numerical scheme is established, and the effect of the orientation of the principle axis on the stress intensity factor is studied. The interaction between two coplanar square cracks are also modeled and discussed.

THREE-DIMENSIONAL ANALYSIS OF THICK PLATES BY MLS-RITZ METHOD

2008 ◽  
Vol 08 (01) ◽  
pp. 77-101 ◽  
Author(s):  
L. ZHOU ◽  
W. X. ZHENG
Keyword(s):  
Mixed Boundary ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Least Square ◽  
3D Analysis ◽  
Displacement Fields ◽  
Linear Elasticity Theory ◽  
Thick Plates ◽  
Moving Least Square

This paper presents a three-dimensional (3D) moving least-square Ritz (MLS-Ritz) formulation for the free vibration analysis of homogeneous elastic thick plates with mixed boundary constraints. The analysis is based on the linear elasticity theory. The Ritz trial functions are established through the moving least-square technique for the displacement fields of the plates. Vibration frequencies for thick square plates and right-angled isosceles triangular plates are obtained by the MLS-Ritz method. The reliability and accuracy of the presented method are examined by extensive convergence and comparison studies and it is established herein that the MLS-Ritz method is a powerful and effective numerical method for the 3D analysis of thick plates.

Research of 3D EFG of Limiting Nodal Point Number and Applied for Three-Dimensional Elastic Problem

2006 ◽  
Vol 306-308 ◽  
pp. 721-726 ◽  
Author(s):  
Dun Fu Zhang ◽  
Wei Shen Zhu ◽  
Shu Cai Li
Keyword(s):  
Nodal Point ◽  
Three Dimensional ◽  
Least Square Method ◽  
Variable Domain ◽  
Least Square ◽  
Global Approximation ◽  
Energy Principle ◽  
Moving Least Square ◽  
Nodal Points ◽  
Point Number

The formulation and implementation of three-dimensional element free Galerkin method (3D EFG) are developed. A simple and efficient scheme for a variable domain of influence stipulates that a constant number of nodal points are visible from each integration location is proposed. This method significantly increases the efficiency of the variable domain of influence by limiting the size of the least-square problem that is solved when computing approximate functions. The 3D EFG methods based on moving least square method use only nodal points to built local and global approximation. Discrete model of the 3D EFG for three-dimensional elastic problems is derived by least potential energy principle. Reference to the 2D EFG, in the 3D EFG, it is enforced to meet displacements boundary conditions by use of limiting nodal point number method and penalty method. The stress concentration of a small column-shaped cavity in a cube subjected to uniaxial uniform tension at two opposing faces in far field. Compared the approximation solutions with theory ones, the results indicate that the 3D EFG is validity in solving three-dimensional elastic problems and the limiting nodal point number method is validity.

Study on the Online Ink Testing with CCD Based on Calabro-Mercatucci Model

2010 ◽  
Vol 174 ◽  
pp. 195-198
Author(s):  
Zhen Liu ◽  
Hua Yang
Keyword(s):  
Film Thickness ◽  
Three Dimensional ◽  
Least Square ◽  
Curved Surface ◽  
Surface Model ◽  
Printing Quality ◽  
Set Up ◽  
The Relationship ◽  
Black Color ◽  
Rgb Values

With the increasing of press’ speed and the people’s requirement, online testing of printed stock becomes to the development direction. The ink metering control is an important part of printing quality control. So this paper sets up a three-dimensional curved surface model of the CCD’s RGB values and the best ink film thicknesses based on Calabro-Mercatucci model, which can be applied to the online ink testing with CCD. Firstly, we printed cyan magenta yellow black color bitches of different ink film thicknesses and got their optical densities and RGB values with measuring tools. Afterwards, we got the parameters in Calabro-Mercatucci model with the experimental data through the least square algorithm and then got the scale of the best ink film thickness. Last, we set up the three-dimensional curved surface model of the CCD’s RGB values and the best ink film thicknesses through ‘v4’ algorithm in matlab tools. With this three-dimensional curved surface model, we can judge whether the thickness corresponding to the RGB values is in the range of the best ink film thickness. It is proved that this method can indicate the relationship between CCD’s RGB values and the ink film thickness and be applied to detect the ink metering after tested.

B-Spline Curve Approximation with Nearly Arc-Length Parameterization

2014 ◽  
Vol 513-517 ◽  
pp. 3372-3376 ◽  
Author(s):  
Si Hui Shu ◽  
Zi Zhi Lin ◽  
Yun Ding
Keyword(s):  
Three Dimensional ◽  
Smooth Curve ◽  
Least Square ◽  
Arc Length ◽  
Key Factors ◽  
B Spline ◽  
Spline Curve ◽  
Curve Approximation ◽  
Fitting Algorithm ◽  
Data Points

An algorithm of B-spline curve approximation with the three-dimensional data is presented in this paper. In this algorithm, we will get a smooth curve which is nearly arc-length parameterization. The smoothness and uniform parameterization are key factors of the approximating curve, specifically in skinning surface and surface approximation. Firstly, the data points are fitted using local interpolation, this local fitting algorithm yields n Bezier segments, each segment having speed equal to 1 at their end and midpoints. Then segments are composed of a C1 continuous cubic B-spline curve which named controlling curve. But the controlling curves control points are redundancy, so we find another curve to approximate the controlling curve using least square approximation with smoothness

Sign in / Sign up

Export Citation Format

Share Document