Development of meshless boundary element method for inhomogeneous materials and its application to material propertiy identification

非均匀材料无网格边界元方法的发展及其在材料性能识别中的应用

• 批准号: 15560068
• 负责人: MATSUMOTO Toshiro
• 金额: $ 1.92万
• 依托单位: Nagoya University (2004)Shinshu University (2003)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15560068/
• 关键词: Boundary Element Method; Inhomogeneous Material; Dual Reciprocity Method; Thermal Conductivity; Source Identification; Inverse Problem; Temperature Dependency; Meshless Approach

The meshless-type boundary element method is a novel boundary element method which can be applied to inhomogeneous media and nonlinear problems. In this method, the domain integral term originated from inhomogeneous term for body foroes, etc., is transformed to boundary integral terms by means of the dual reciprocity method(DRM). Therefore, no domain mesh is needed in the numerical analyses, only the boundary mesh and internal collocation points are required. Generating internal collocation points are much easier than discretizing the domain into mesh, hence the meshless-type boundary element method is more efficient than the conventional boundary element method in preparing the data.In this research project, we applied the meshless-type boundary element method to the inverse problems for inhomogeneous materials. First, we developed some new accurate numerical integration schemes when the source point of the fundamental solution is located at an internal collocation point near the boundary. Then, we formulated the boundary element method for transient thermal problems and thermoelasticity problems with temperature dependent material properties and arbitrary inhomogeneities. The effectiveness of the formulation has been demonstrated through numerical test examples obtained by using the developed boundary element code. The inhomogeneous term is treated as a equivalent source/body-force term. It is approximated with a linear combination of the radial basis functions. Therefore, identifying inhomogeneous material properties results in idenfications of the unknown coefficients of the linear combination. The inverse analysis algorithm to identify the inhomogeneous thermal conductivity distribution has been finally developed and its effectiveness has also been demonstrated through some numerical test examples.

无网格型边界元方法是一种适用于非均匀介质和非线性问题的新型边界元方法。该方法利用对偶互易方法(DRM)将体孔等非齐次项产生的区域积分项转化为边界积分项。因此，数值分析不需要区域网格，只需要边界网格和内部配置点。生成内部配置点比将区域离散成网格容易得多，因此无网格型边界元方法在数据准备方面比传统的边界元方法更有效。首先，当基本解的源点位于边界附近的内部配置点时，我们发展了一些新的精确数值积分格式。在此基础上，建立了求解材料性质随温度变化的、任意非均匀的瞬变热问题和热弹性问题的边界元方法。利用所开发的边界元程序进行了数值试验，验证了该公式的有效性。非均匀项被视为等效源/体力项。它用径向基函数的线性组合来逼近。因此，识别不均匀的材料属性会导致线性组合的未知系数的确定。最后提出了识别非均匀导热系数分布的反分析算法，并通过数值算例验证了该算法的有效性。

项目成果

Boundary element method for nonlinear thermoelasticity with temperature dependent material properties

具有温度相关材料特性的非线性热弹性的边界元法

• 发表时间: 2004
• 期刊: 計算数理工学論文集 4
• 作者: Toshiro Matsumoto;Artur Guzik;Masataka Tanaka
• 通讯作者: Masataka Tanaka

Identification of point sources using DRM based boundary element method

使用基于 DRM 的边界元方法识别点源

• 发表时间: 2004
• 期刊: Advances in Boundary Element Techniques V (Ed. V.M.A.Leitao and M.H.Aliabadi)
• 作者: Toshiro Matsumoto;Masataka Tanaka;Tomoki Tsukamoto
• 通讯作者: Tomoki Tsukamoto

二重相反法に基づくBEMを用いた非均質材料の熱伝導率同定解析

基于双互易法的非均质材料热导率边界元辨识分析

• 发表时间: 2004
• 期刊: 計算数理工学論文集 4
• 作者: 松本敏郎;田中正隆;末吉耕平;Artur Guzik
• 通讯作者: Artur Guzik

Identifications of thermal conductivity distribution in inhomogeneous materials by means of DRM-based BEM

利用基于 DRM 的边界元法识别非均质材料的导热率分布

• 发表时间: 2004
• 期刊: Transactions of JASCOME Vol.4
• 作者: Toshiro Matsumoto;Masataka Tanaka;Kohei Sueyoshi;Artur Guzik
• 通讯作者: Artur Guzik

松本敏郎, 田中正隆: "2次元BEMにおける境界点近傍のソース点に対する境界積分の変数変換による評価法"境界要素法論文集. 20巻. 87-92 (2003)

Toshiro Matsumoto、Masataka Tanaka：“二维 BEM 中边界点附近源点的边界积分的变量变换的评估方法”边界元方法论文。 20. 87-92 (2003)