偶应力问题的杂交／混合元分析

将弹性力学中Hellinger—Reissner交分原理推广到偶应力理论中，并以罚函数的形式引入其约束条件，提出了一种有效的杂交／混合单元。文中分别分析了带中心小孔平板在轴向均匀加载时的应力集中情况，以及含中问裂纹的无限平板单轴拉伸时的位移场和应力场。算例表明，该单元计算效率高，精度好，即使在材料本征长度很小时，仍然能够得到相当理想的结果。

Hybrid/mixed finite element analysis of couple-stress problems

In this paper the Hellinger Reissner variational principle in classical elastic i ty is extended to couple stress theory.Based on the generalized variational pri n ciple,a new effective hybrid/mixed finite element method for couple stress theo r y is put forward and its constraint is introduced by a penalty function techniqu e.In addition,the single element stability conditions and its patch stability te st are discussed.Farther the verification for the element eigenvalues makes sure that th e present mothod is reliable.Two numerical examples are given: the stress concen tration around a central circular hole in a uniformly axially loaded field,and t he displacement and stress fields around a crack in an infinite plate of uni ax i al tension.The numerical results show that the present method has high efficienc y and good accuracy.The considerably satisfying results can be obtained, even if the characteristic length is very small.