A Nonsingular Boundary Collocation Method for the Inverse Problems in Elasticity

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Project title

Code/計畫編號

MOST104-2221-E019-027

Translated Name/計畫中文名

無奇異邊界佈點法求解彈性力學反算問題

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=11573029

Year

2015

Start date/計畫起

01-08-2015

Expected Completion/計畫迄

01-07-2016

Bugetid/研究經費

706千元

ResearchField/研究領域

土木水利工程

本報告中我們建構一套無奇異邊界佈點法來求解彈性力學中奈維爾(Navier)方程的反算問題。本法屬於一種邊界型式的無網格法。不同於基本解法之處在於本法使用無奇異的核函數來取代基本解。因此，可將源點與場點同時分佈於真實問題的邊界上，而無須擔心當場點與源點座落於同一位置時所需面對的奇異積分或主值計算問題。此計畫關鍵之處在於我們透過霍曼得(Hörmander)法來導得奈維爾方程中的無奇異核函數，再藉由求解正算的彈性力學邊界值問題來驗證所導得的無奇異核函數的正確性與可行性。進一步，我們延伸至求解部分邊界條件完全已知，但另ㄧ部分邊界條件則完全未知的柯西(Cauchy)反算問題。最後，我們舉幾個數值算例來展現此法的簡易性、效率性與精確性。 In this report, a nonsingular boundary collocation scheme is used to solve the inverse problems in elasticity governed by the Navier equation. This method belongs to one kind of boundary-type meshless methods. It differs from the method of fundamental solutions, since the source point and collocation point can be both located on the real boundary at the same time. The purposed method uses the non-singular functions to substitute the fundamental solutions. As a result, it does not worry to face singular integral or calculate principal value, because there is no singularity when the source point and collocation point coincide together. The non-singular functions for the Navier equation, which is the key point of the proposed approach, are derived by using the Hormander method. First, we employ the non-singular kernel functions to solve the boundary value problems for verifying the feasibility and validity of solutions. Then we extend the proposed approach to deal with the inverse problem, or called Cauchy problem, that the boundary conditions are overprescribed on a portion of boundary and others are unknown. Finally, several examples are used to show the simplicity, efficiency and accuracy of the proposed approach.

Keyword(s)

無奇異邊界佈點法
奈維爾方程
霍曼得法
反算問題
柯西問題
無網格法
nonsingular boundary collocation method
Navier equation
Hörmander method
inverse problem
Cauchy problem
meshless method

DSpace CRIS

A Nonsingular Boundary Collocation Method for the Inverse Problems in Elasticity

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