Thermoelastic analysis based on hypersingular boundary integral representation

基于超奇异边界积分表示的热弹性分析

• 批准号: 11650083
• 负责人: MATSUMOTO Toshiro
• 金额: $ 2.11万
• 依托单位: Shinshu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11650083/
• 关键词: Hypersingularity; Computational Mechanics; Thermal Stress; Thermoelasticity; Dual Reciprocity Method; Boundary Stress; Integral Equation; Numerical Analysis; 感度係数; エネルギ解放率; 積分方程式

Although the boundary element method can give us boundary displacements and tractions very accurately as the direct boundary solutions, boundary stress components are less accurate since they are calculated indirectly from the traction components and tangential derivatives of the displacement components. In the present research, we used a hypersingular boundary integral representation for the boundary displacement gradients in order to improve the accuracy of the boundary stress components in thermoelastic problems. A direct numerical evaluation scheme of the hypersingular boundary integral representation has been derived by considering the thermal strains. A boundary integral treatment of the domain integral term for the thermal strains based on the dual reciprocity method is also discussed. The numerical results have shown that the present approach could give very accurate boundary stress results.Singular treatment of the boundary integral equation is also useful in fracture mechanics application. Stress intensity factors of bimaterial interface cracks are evaluated based on the interaction energy release rates. The interaction energy release rate is defined based on the energy release rates of a cracked body, corresponding to two independent loading conditions, and is related to a boundary integral of the sensitivity coefficients of the displacement and the traction, with respect to the crack length: The boundary element sensitivity analyzes are used to calculate these quantities accurately. Some numerical demonstrations show that the present method can give accurate results for the stress intensity factors of various bimaterial interface cracks under coarse mesh discretizations

虽然边界元法可以非常精确地给出边界位移和边界力作为直接边界解，但边界应力分量不太精确，因为它们是由位移分量的切向导数和边界力分量间接计算的。在本研究中，我们使用了超奇异边界积分表示的边界位移梯度，以提高在热弹性问题的边界应力分量的精度。考虑热应变，导出了超奇异边界积分表示的直接数值计算格式。讨论了基于对偶互易法的热应变区域积分项的边界积分处理。数值结果表明，本文方法可以给出非常精确的边界应力结果，边界积分方程的奇异性处理在断裂力学应用中也是有用的。基于交互作用能量释放率计算了双材料界面裂纹的应力强度因子。相互作用能量释放率是基于裂纹体的能量释放率定义的，对应于两个独立的加载条件，并且与位移和牵引的灵敏度系数的边界积分有关，相对于裂纹长度：边界元灵敏度分析用于精确地计算这些量。数值计算表明，在粗网格离散下，本文方法可以给出各种双材料界面裂纹应力强度因子的精确结果

项目成果

岡山瞬,松本敏郎,田中正隆: "熱弾性問題における二重相反境界要素法に関する検討"境界要素法論文集. Vol.17. 7-10 (2000)

冈山舜、松本俊郎、田中正孝：“热弹性问题的双倒数边界元法研究”边界元法论文集 17. 7-10 (2000)。

岡山瞬,松本敏郎,田中正隆: "応力感度解析における境界積分方程式の評価法"境界要素法論文集. 第16巻. 93-96 (1999)

Shun Okama、Toshiro Matsumoto、Masataka Tanaka：“应力敏感性分析中的边界积分方程的评估方法”边界元方法论文第 16 卷。93-96 (1999)

岡山 瞬, 松本敏郎, 田中正隆: "熱弾惟問題における二重相反境界要素法に関する検討"境界要素法論文集. Vol.17. 7-10 (2000)

冈山俊、松本敏郎、田中正孝：“热弹问题的双倒数边界元法研究”边界元法论文第 17 卷 7-10 (2000)。

松本敏郎,田中正隆,徳田良輔: "非定常熱伝導問題の時間領域境界要素法における初期条件の取り扱いに関する-考察"BTEC論文集. Vol.10. 29-32 (2000)

Toshiro Matsumoto、Masataka Tanaka、Ryosuke Tokuda：“非稳态热传导问题的时域边界元方法中初始条件的处理研究”BTEC Proceedings Vol. 10. 29-32 (2000)。

岡山 瞬, 松本敏郎, 田中正隆: "重調和方程式のTrefftz関数とThin Plate Splineを用いた多重相反法"計算工学講演会論文集. 第5巻・第1号. 313-314 (2000)

Shun Okama、Toshiro Matsumoto、Masataka Tanaka：“使用双调和方程和薄板样条的 Trefftz 函数的多重倒数方法”计算工程会议论文集，第 5 卷，第 1. 313-314 期（2000 年）。