| 固体力学边界元法中若干数学与理论问题的分析 |
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| 引用本文： | 潘安福. 固体力学边界元法中若干数学与理论问题的分析[J]. 武汉大学学报(工学版), 1987, 0(5) |
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| 作者姓名： | 潘安福 |
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| 作者单位： | 武汉水利水电学院水利水电工程建筑及施工系 |
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| 摘 要： | 本文对固体力学边界元法中二维奇异积分方程的可解性进行了分析。证明二维纳维叶奇异积分方程的“符号行列式”为△=ν(2-3ν)/(1-ν)~2。对一般工程材料的ν而言(0<ν≤1/2),△>0,奇异积分算子的“指数”为零,因而这奇异积分方程是可解的。同时,证明了其解的存在与唯一性。其次,从纳维叶算子的边界积分方程出发,由边界元直接法公式可导出不同的间接法公式,这说明边界元法的直接法与间接法在理论上是等价的。通过实例,对直接法与间接法进行比较与分析。最后,指出了它们之间的差别。
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| 关 键 词： | 奇异积分方程 可解 等价 边界元法 |
Analysis of some Mathematical and Theoretical Problems in Boundary Element Method of Solid Mehanics |
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| Pan Anfu. Analysis of some Mathematical and Theoretical Problems in Boundary Element Method of Solid Mehanics[J]. Engineering Journal of Wuhan University, 1987, 0(5) |
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| Authors: | Pan Anfu |
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| Abstract: | Firstly, this paper has analysed the solvability of two dimenisonal singular integral equations of boundary element method in solid mechanics. The existence and uniqueness of the solutions to this singular integral equation have been demonstrated. Secondly,it proves that the direct and indirect methods in boundary element method are equivalence in theory. By calculating engineering examples, the direct and indirect methods are compared, discussed and analysed. |
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| Keywords: | singular integral equation solvability equivalence boundary element method |
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