Applications of Angular Basis Function (Abf) Method Containing Cracklets and Stokeslets to Solve the Crack and Stokes Flow Problems.

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Project title

Code/計畫編號

MOST108-2221-E019-048

Translated Name/計畫中文名

含cracklets與Stokeslets之角度基底函數法於裂縫及斯托克斯流問題之應用

Project Coordinator/計畫主持人

Jeng-Tzong Chen

Funding Organization/主管機關

National Science and Technology Council

Co-Investigator(s)/共同執行人

李家瑋

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=13128147

Year

2019

Start date/計畫起

01-08-2019

Expected Completion/計畫迄

01-07-2020

Bugetid/研究經費

1180千元

ResearchField/研究領域

機械工程

Laplace方程式的複數型的閉合型基本解ln（z）可以分解為徑向基底函數（RBF）和角度基底函數（ABF）兩部分。在本報告中，不僅是RBF,亦引入ABF來求解含橢圓孔洞之螺旋差排問題。螺旋差排將透過ABF之分離核來呈現。而邊界值問題則透過RBF來求解。由於幾何形狀是橢圓形，分離核在橢圓坐標以級數形式展開，而未知邊界密度則以傅立葉級數展開。結合分離核與零場積分方程，可以很容易地解析求解邊界值問題。成功地將先前圓的例子推展到橢圓。最後，BIEM的結果與複變之結果進行比較，一致吻合。The complex-valued fundamental solution ln(z) can be decomposed into the radial basis function (RBF) and the angular basis function (ABF). In this report, not only RBF but also ABF are employed to solve the screw dislocation problem with an elliptic hole. The screw dislocation is represented by the ABF in terms of degenerate kernel. The BVP is solved by the RBF and boundary integral equation. Since the geometric shape is an ellipse, the degenerate kernel is firstly expanded to a series form under the elliptic coordinates, while the unknown boundary densities are expanded to Fourier series. By combining the degenerate kernel and the null-field integral equation, the boundary value problem can be easily solved. We extend our previous success of a circular case to an elliptic case. Finally, the results of BIEM were also compared with those of complex variables.

Keyword(s)

角度項基底函數
徑向基底函數
Stokeslet
cracklet
柯西-黎曼
多值函數
基本解法
angular basis function
radial basis function
Stokeslet
cracklet
Cauchy-Riemann
multi-valued function
method of fundamental solution

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Applications of Angular Basis Function (Abf) Method Containing Cracklets and Stokeslets to Solve the Crack and Stokes Flow Problems.

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