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| 各向异性全平面包含多边形夹杂的非均匀问题内部弹性场的近似算法 | |
| 引用本文： | 高峰,徐凯宇,潘尔年.各向异性全平面包含多边形夹杂的非均匀问题内部弹性场的近似算法[J].上海大学学报(自然科学版),2012(2):203-208. |
| 作者姓名： | 高峰 徐凯宇 潘尔年 |
| 作者单位： | 1. 上海大学上海市应用数学和力学研究所,上海200072 2. 上海大学理学院,上海200444 3. 阿克伦大学土木工程系,俄亥俄州OH44325 3905,美国 |
| 基金项目： | 国家自然科学基金资助项目(10772106,11072138) |
| 摘 要： | 对于各向异性全平面中包含多边形夹杂的非均匀问题,提出一种精确的闭型解和简单的迭代方法.基于特征应变等效体力的概念,首先,用沿着夹杂物边界的格林函数的线积分表示诱导弹性场;然后,将此闭形解应用到各向异性全平面中包含多边形夹杂的模型中,迭代计算夹杂为正方形和三角形量子线模型的内部弹性场;最后,将数值结果与边界元方法计算的结果进行对比.研究表明,两种算法的结果比较吻合. |
| 关 键 词： | Eshelby问题 非均匀 特征应变 格林函数 迭代法 |
Approximate Algorithms for Inner Elastic Field of Polygonal Inhomogeneity in Anisotropic Full-Planes |
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| GAO Feng,XU Kai-yu,PAN Er-nian.Approximate Algorithms for Inner Elastic Field of Polygonal Inhomogeneity in Anisotropic Full-Planes[J].Journal of Shanghai University(Natural Science),2012(2):203-208. | |
| Authors: | GAO Feng XU Kai-yu PAN Er-nian |
| Institution: | 1.Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,China; 2.College of Sciences,Shanghai University,Shanghai 200444,China; 3.Department of Civil Engineering,University of Akron,OH44325-3905,USA) |
| Abstract: | This paper presents an exact closed-form solution and a simple iteration method for polygonal inhomogeneity in anisotropic full planes.Based on the equivalent body-force concept of eigenstrain,the induced elastic fields are first expressed in terms of the line integral on the boundary of the inclusion with the integrand being the Green’s functions.The exact closed-form solutions are then applied to a polygonal wire within an anisotropic full-plane.Using the iteration method we have developed,we compute the inner elastic fields of a square-shaped and a triangle-shaped wire within an anisotropic full-plane,and compare them with the results obtained with boundary element method(BEM).The results show that they are close to each other. |
| Keywords: | Eshelby problem inhomogeneity eigenstrain Green’s function iteration method |
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