Study on the Interaction of Sh Waves with a Kink-Tipped Semi-Infinite Crack

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簡歷

基本資料

Project title

Code/計畫編號

NSC102-2221-E019-044

Translated Name/計畫中文名

前端折角半無限長裂縫與SH波互制之研究

Project Coordinator/計畫主持人

Deng-How Tsaur

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=3115365

Year

2013

Start date/計畫起

01-08-2013

Expected Completion/計畫迄

31-07-2014

Bugetid/研究經費

423千元

ResearchField/研究領域

土木水利工程

"在實際的構造體中，微裂縫伴生於主裂縫前端的情況常發生，因此，在過去文獻中，前端折角之半無限長裂縫是頗受歡迎的一個簡化模型。然而，關於它承受 SH波作用後所引致的散射問題，至今仍然不容易得到正確解析解。從數學的角度來看，其所對應的外域 Helmholtz邊界值問題，要以波函數展開法直接求得一對一的閉合解析表達式，幾乎是不可能的，這是由於此模型之幾何形狀，並不符合任一個可分離之座標系統的緣故。因此，本年度(102年)計畫，擬以《前端折角半無限長裂縫與 SH波互制之研究》為主軸，從理論解析的方向下手處理。透過「領域媒親技巧」和「波函數展開法」的使用，且引入考慮裂縫尖端之應力奇異行為的「奇異基底函數」，即可推導出頻率域的級數解。預計將針對裂縫折角改變時，入射波以不同頻率及角度入射，對裂縫開口位移、近場位移分佈及動應力強度因子的影響做一系列分析與探討。本計畫成果將可提供給其他數值方法作為驗證比對之用，亦可作為相關研究之參考。 " "In real structures, the tips of main cracks usually accompany micro-cracks. Hence, the simplified model pertaining to a kink-tipped semi-infinite crack is a very popular one in the literature. However, the exact analytical solution to the problem of scattering induced by such a barrier subjected to SH-wave incidence is not easily acquired so far. From the mathematical viewpoint, for the corresponding exterior Helmholtz boundary-value problem, it is nearly impossible to determine a one-to-one closed-form analytical expression by directly using the method of wavefuncion expansions. This is because the geometry of the model does not conform to any one of separate coordinate systems. In view of this point, the main purpose of this project is to explore the interaction of SH waves with a kink-tipped semi-infinite crack. A theoretical analysis, applying the region-matching technique and the method of wavefuncion expansions, is executed. Singular basis functions are introduced to take into account the singular behavior in stress fields. A frequency-domain series solution to the problem under consideration is derived. Herein, the effects of the tilted angle of kinked crack, wave frequency, and angle of incidence on the crack open displacement, the near-field displacement, and the dynamic stress intensity factor will be evaluated and discussed. Besides, the computed results presented may serve as a cross-reference for other numerical approximation methods and pertinent studies. "

Keyword(s)

SH波
裂縫
散射
波函數
奇異基底
SH waves
crack
scattering
wavefunction
singular basis

DSpace CRIS

Study on the Interaction of Sh Waves with a Kink-Tipped Semi-Infinite Crack

基本資料

Description