On the Solution of an Elliptical Inhomogeneity in Plane Elasticity by the Equivalent Inclusion Method
On the Solution of an Elliptical Inhomogeneity in Plane Elasticity by the Equivalent Inclusion Method
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DOI：
10.1007/s10659-012-9423-0
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发表时间：
2014
影响因子：
2
通讯作者：
Xiaoqing Jin;Zhanjiang Wang;Qinghua Zhou;L. Keer;Q. Wang
中科院分区：
文献类型：
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作者：
Xiaoqing Jin;Zhanjiang Wang;Qinghua Zhou;L. Keer;Q. Wang
无限大各向同性弹性平面内椭圆形夹杂的应力分析是经典的弹性力学问题，通常采用复变函数法求解。在这项工作中，我们证明了这样一个问题的解决方案的替代方法，通过等效包含方法，可能是更方便和直接的，而不求助于复杂的潜力或曲线坐标。通过简单的代数运算可以得到显式解析解，但在平面应变情况下，纵向本征应变分量应小心处理。由于椭圆夹杂的外部Eshelby张量是可用在封闭的形式，本研究提供了一个在笛卡尔坐标系中表示的全场应力解。面内应力分量用Dundurs参数表示。所提出的应力集中的求解方法和计算公式，对工程设计人员制定设计评价基准具有一定的实用价值。
Stress analysis of an elliptical inhomogeneity in an infinite isotropic elastic plane is a classical elasticity problem, which is usually solved by means of the complex variable formulation. In this work, we demonstrate that an alternative method of solution for such a problem, via the equivalent inclusion method, may be more convenient and straightforward without recourse to complex potentials or curvilinear coordinates. The explicit analytical solution can be derived through simple algebraic manipulation, although the longitudinal eigenstrain component should be handled with care in the case of plane strain. Since the exterior Eshelby tensor for an elliptical inclusion is available in closed-form, the present study provides a full field stress solution expressed in Cartesian coordinates. Furthermore, the in-plane stress components are represented in terms of Dundurs’ parameters. The solution methodology and the convenient formulae of the stress concentration may be of practical use to the engineers in developing benchmarks for design evaluation.