椭圆类夹杂分析的杂交应力有限元方法

A HYBRID-STRESS FEM FOR ELLIPTICAL INCLUSION PROBLEMS

论文给出了一种分析椭圆类夹杂周边应力场的新型杂交应力有限元方法.基于弹性力学中平面问题的Muskhelishvili复势方法,应用保角变换映射技术,以Laurent级数和Faber级数为工具,借助Hellinger-Reissner原理构建一个能够反映椭圆类夹杂周边弹性现象同时包含椭圆夹杂的多边形超级单元.将该超级单元与标准的4结点杂交应力单元耦合在一起即可建立一种分析椭圆类夹杂周边弹性场的新型特殊杂交应力有限元方法.文中考核算例表明:该文方法不但使用简单、有效,而且精度高、单元少.作为论文方法的一个拓展应用,文章最后给出了一个分析含二个椭圆夹杂无限大各向同性板在远场均布载荷作用下椭圆夹杂周边弹性场的算例,并讨论了椭圆夹杂间距和弹性刚度比对应力集中系数的影响.

This paper presents a novel hybrid-stress finite element method for solving elastic fields a- round elliptical inclusions. A super polygonal-sided element containing an inclusion is constructed to reflect elastic behavior around the inclusion in terms of the variational principle of modified Hellinger-Reissner functionals. Displacement and stress fields in the element are expressed as complex series with Laurent series and Faber series by using the Muskhelishvili complex potential method and the eonformal transformation technique. The super element is in conjunction with standard 4-node hybrid-stress elements to establish a new hybrid-stress finite element method. Benchmark example in the paper shows present method is rather general and efficient, as well as yields numerical results with higher accuracy and fewer elements. As an extended application of the method, an infinite isotropic plate containing two inclusions is analyzed under remote tension load. Effects of two inclusion span and elastic stiffness ratio on stress concentration coefficient are also discussed.