Semi-Analytical Approach for Torsion Problems of a Circular Bar with Multiple Holes and/or Cracks

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基本資料

Project title

Code/計畫編號

MOST103-2221-E019-011

Translated Name/計畫中文名

半解析法求解含多孔洞與裂縫之圓形桿件扭轉問題

Project Coordinator/計畫主持人

Ying-Te Lee

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=8360923

Year

2014

Start date/計畫起

01-08-2014

Expected Completion/計畫迄

01-07-2015

Bugetid/研究經費

558千元

ResearchField/研究領域

土木水利工程

本計劃使用一套由零場積分方程法結合退化核函數的半解析法來處理含圓形孔洞、橢圓形孔洞與裂縫之扭轉問題。為了充分發揮橢圓形幾何特性，關鍵之處在於透過橢圓座標系統搭配加法定理來將閉合型基本解展成退化核。而橢圓邊界上的邊界密度函數則利用特徵函數展開法來進行模擬。值得注意的是我們使用極限的方式將橢圓孔洞的短軸長近似於零來模擬裂縫行為。另外，我們也透過讓橢圓的長軸長近似於短軸長的方式來模擬圓形邊界。接著，藉由邊界佈點來滿足邊界條件後，我們可輕易地建構出一套線性代數系統來計算未知的特徵函數係數。本法可被視為是一套半解析法，由於誤差源自於特徵函數展開法中項數擷取多寡並且本法為指數階收斂優於傳統邊界元素法的線性階收斂。最後，我們使用幾個數值算例來驗證本法的可行性與正確性。我們也計算扭轉剛度與應力強度因子來與文獻中的結果做比對，並獲得與文獻上ㄧ致的結果。 A semi-analytical approach of the null-field integral equation in conjunction with the degenerate kernels is used to deal with the torsion problems of a circular bar with circular or elliptic holes and/or line cracks. In order to fully capture the elliptic geometry, the use of the addition theorem in terms of the elliptic coordinates plays an important role to expand the fundamental solution into the degenerate form. The boundary densities are expressed by the eigenfunction expansion for elliptic boundary. It is worthy of noting that the model of elliptic hole in companion with the limiting process of approaching the length of the semi-minor axis to zero is adopted to simulate the line cracks in this work. Besides, we also make the length of the semi-major axis close to the length of the semi-minor axis to approximate the circular boundary. By collocating the observation point exactly on the real boundary and matching the boundary conditions, a linear algebraic system is easily constructed to determine the unknown eigenfucntion coefficients. This approach can be seen as a semi-analytical manner since error purely attributes to the truncation of eigenfunction expansions and the convergence rate of exponential order is better than the linear order of the conventional boundary element method. Finally, several numerical examples of a circular bar with circular or elliptic holes and/or line cracks are employed to show the feasibility and validity of the proposed approach. Not only the torsional rigidity but also the stress intensity factors are calculated to compare with the available results in literature, and good agreements are made in this project.

Keyword(s)

扭轉剛度
應力強度因子
零場積分方程
退化核
扭曲函數
裂縫
torsional rigidity
stress intensity factor
null-field integral equation
degenerate kernel
warping function
crack

DSpace CRIS

Semi-Analytical Approach for Torsion Problems of a Circular Bar with Multiple Holes and/or Cracks

基本資料

Description