Null-Field Integral Equations and Their Engineering Applications

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基本資料

Project title

Code/計畫編號

NSC97-2221-E019-015-MY3

Translated Name/計畫中文名

零場積分方程及工程應用

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=1685776

Year

2008

Start date/計畫起

01-08-2008

Expected Completion/計畫迄

01-07-2009

Bugetid/研究經費

843千元

ResearchField/研究領域

土木水利工程

基於以往三年零場積分方程推導的成功經驗，本三年計畫，將應用零場積分方程來求解一些工程問題。首先，我們將使用一些數學技巧，如：退化核與傅立葉級數，結合零場積分方程來建構這些問題的數學模式與數值驗證。我們擬採用場源點分離的想法，將基本解推展成退化核形式。針對圓形邊界問題，我們使用傅立葉級數來近似邊界未知密度函數。而使用自適性觀察座標系統、退化核與傅立葉級數，我們可不需計算主値且輕易求得邊界積分。藉由邊界佈點來滿足邊界條件後，我們可將零場積分方程輕易化簡成一個線性代數系統。使用超奇異式來計算偏心圓的勢能導微時，須採用向量分解技巧小心處理。第一年計畫，將專注於求解含理想與非理想界面扭轉問題。我們將計算扭轉剛度與文獻中的結果來做比較，來驗證我們方法的準確性。我們也將分析在扭轉桿的應力分布狀況。同時，也會一併探討此法在扭轉問題是否會有退化尺度的問題產生，並且提供解決方案。第二年的計畫，將研究水波問題。本年度的計畫著重於柱體表面受力分析。受柱體影響後的整體勢能場分布狀況也將一併作探討。針對入射波的角度、週波數與柱體尺寸大小的影響，我們也會做相關的參數分析。而是否有解非唯一性的陷阱模態問題產生，我們也將做深入的探討。最後一年的計畫，我們將推廣到彈性力學問題。受力後的應力與應變分析、含多圓洞與夾雜的應力集中問題，將是我們觀察的重點。而其退化尺度的現象也是我們興趣所在。最後，我們將提出幾個數值算例來驗證此方法的可行性與正確性。 Following the success of the null-field integral formulation in the past three years, the null-field integral equations will be extended to deal with some engineering applications including (I) torsion, (II) water wave and (III) elasticity problems in the three-years project. In the mathematical model, some mathematical tools, e.g. degenerate kernel (separable kernel) and Fourier series, will be employed in the null-field integral equations. The fundamental solution will be extended into separable form based on the concept of separating the source point and field point. For the circular boundary, the boundary densities will be approximated by Fourier series. By using the adaptive observer system in conjunction with degenerate kernels, all boundary integrals in the null-field integral equations will be calculated easily and analytically free of the sense of principal values. Null-field integral equation yields the linear algebraic system after matching the boundary conditions. For the eccentric case, the vector decomposition technique for the potential gradient in the hypersingular formulation will be considered carefully for the radial and tangential derivatives. For the first-year project, we will focus on the torsion problems including perfect and imperfect interfaces. The torsional rigidity will be calculated and will be compared with the results in the literature. The stress distribution on the torsion bar will also be analyzed. The degenerate scale and its treatments in the present method will be studied analytically and numerically on the torsion problem. For the second-year project, the water wave problem will be studied. Forces on surfaces of the cylinders will be determined. Also, the interacting potentials by cylinders will be solved. Parameter study of wave number of water wave, impinging angle and size of cylinders will be discussed. Whether the nonuniqueness problem exists of trap mode or not will be discussed in detail. For the third-year project, elasticity problems will be considered. Stress concentration factor of multiple holes and/or inclusions are our main concern. Also, the degenerate scale may occur and is still our interest. Several examples will be tested to see the accuracy and efficiency of the present method after comparing with other available methods.

Keyword(s)

扭轉
水波
彈性力學
退化核
傅立葉級數
torsion
water wave
elasticity
degenerate kernel
Fourier series

DSpace CRIS

Null-Field Integral Equations and Their Engineering Applications

基本資料

Description