A Systematic Approach for Solving Laplace, Helmholtz and Biharmonic Equations Using Degenerate Kernels (III)

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簡歷

基本資料

Project title

Code/計畫編號

NSC96-2221-E019-041

Translated Name/計畫中文名

以退化核求解拉普拉斯、赫姆茲與雙諧和方程式之系統性解法(III)

Project Coordinator/計畫主持人

Jeng-Tzong Chen

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=1440799

Year

2007

Start date/計畫起

01-08-2007

Expected Completion/計畫迄

01-07-2008

Bugetid/研究經費

832千元

ResearchField/研究領域

土木水利工程

本計劃利用零場積分方程配合傅利葉級數及退化核來求解含圓形邊界之雙諧和問題。其中，我們利用場源點分離的技巧將核函數展成以內外域表示的退化核型式，藉此可避開不適當的邊界積分。而未知的邊界密度則展成傅立葉級數型式，再搭配選點法，可輕易的將未知的傅立葉係數計算出來。最後，我們使用薄板與史托克斯流的問題來驗證此方法的可行性，並與有限元素法軟體(ABAQUS)與前人所做之研究結果做一比對。The null-field integral equation method in conjunction with Fourier series and degenerate kernels are proposed to solve the biharmonic problems with circular boundaries. The degenerate kernels in the BIEM are expanded by using the technique of separating the field point and source point. The improper boundary integrals are novelly avoided since the appropriate interior and exterior expansions of degenerate kernels are used. The unknown boundary densities are expressed in terms of Fourier series and the unknown Fourier coefficients can be easily determined by using the collocation method. Finally, the numerical solutions for problems of plate and Stokes flow are compared with the data of finite element solution (ABAQUS) and previous results to demonstrate the validity of the present method.

Keyword(s)

雙諧和方程
退化核
零場積分方程
傅立葉級數
史托克斯流
Kirchhoff板
biharmonic equation
degenerate kernel
null-field integral equation
Fourier series
Stokes flow
Kirchhoff plate

DSpace CRIS

A Systematic Approach for Solving Laplace, Helmholtz and Biharmonic Equations Using Degenerate Kernels (III)

基本資料

Description