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

Approximate Algorithms for Inner Elastic Field of Polygonal Inhomogeneity in Anisotropic Full-Planes

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.

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.