Null-Field Integral Equation Approach for Magnetoelectroelastic Problems with Circular and Elliptic Inclusions

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Project title

Code/計畫編號

NSC102-2218-E019-005

Translated Name/計畫中文名

零場積分法求解含圓形與橢圓形置入物之磁電彈問題

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=8014464

Year

2013

Start date/計畫起

01-10-2013

Expected Completion/計畫迄

31-07-2014

Bugetid/研究經費

509千元

ResearchField/研究領域

土木水利工程

本報告使用零場積分方程法結合退化核函數來處理含任意圓形與橢圓形置入物之磁電彈問題。為了充分利用圓形與橢圓形幾何邊界，關鍵點在於極座標系統與橢圓座標系統下加法定理的使用，以及利用傅立葉級數與特徵函數展開法來模擬圓形與橢圓形邊界密度函數。本法僅需邊界佈點而無須在邊界上切割元素。因此，本法本法可被視為是一種無網格法。而誤差則源自於傅立葉級數或特徵函數展開法項數擷取多寡且本法為指數階收斂優於傳統邊界元素法的線性階收斂。針對含單圓置入物或單橢圓置入物問題，我們使用本法來導得解析解。此外，我們也發展一套數值程式來求解含任意數目多顆圓形或橢圓形置入物問題。最後，我們使用一個含兩圓形置入物的數值算例來驗證我們所提方法的可行性。 In this report, we use the null-field integral equation in conjunction with the degenerate kernel to deal with the magnetoelectroelastic problems containing arbitrary circular and/or elliptic inclusions. In order to fully capture the circular and elliptic geometry, the key point is the use of the addition theorem in terms of the polar and elliptic coordinates to expand the fundamental solution into the degenerate kernel and boundary densities are simulated by the Fourier series and eigenfunction expansion. In the proposed approach, only boundary nodes are required instead of boundary elements. Therefore, it belongs to one kind of meshless methods. Approximation error stems from the number of truncation terms of the Fourier series or eigenfunction expansion and the convergence rate of exponential order is better than the linear order of the conventional boundary element method. For the problem containing single circular or single elliptic inclusion, the analytical solutions are derived by using our approach. Besides, a numerical program is also developed for solving the problems containing arbitrary number of circular and/or elliptic inclusions. We will detect its magnetoelectric coupling coefficient or coupling effect by considering various material parameters of piezomagnetic and piezoelectric materials. Finally, a numerical example of solving the problem containing two circular inclusions is used to demonstrate the feasibility of our approach.

Keyword(s)

磁電彈性
圓形置入物
橢圓形置入物
反平面剪力
平面電場
平面磁場
magneto-electro-elasticity
circular inclusion
elliptic inclusion
anti-plane shear
in-plane electric field
in-plane magnetic field

DSpace CRIS

Null-Field Integral Equation Approach for Magnetoelectroelastic Problems with Circular and Elliptic Inclusions

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