平面Cosserat模型有限元分析的4和8节点单元与分片试验研究

经典连续体理论不包括物质内部尺度，当考虑应变软化问题时，有限元结果对网格具有很强的依赖性。与经典连续介质力学理论不同，Cosserat连续体模型在传统平动自由度的基础上添加了一独立的旋转自由度，在本构模型中引入了内尺度参数。本文研究了基于Cosserat理论的平面4和8节点等参元以及8（4）节点线、角位移混合插值等参单元，给出Cosserat单元分片试验的实施过程。最后将单元运用到小孔应力集中问题的分析当中，通过计算结果与理论解的比较，表明了4和8节点以及8（4）节点等参元的适用性，为问题的非线性分析打下基础。

4-And 8-node isoparametric elements for finite element analysis of plane cosserat bodies

Internal scale of material is not included in the classic continuum theory.It has been found that the finite element results suffer from the pathological mesh dependence in numerical computations while strain-softening models are employed.To overcome the difficulties,Cosserat continuum model,where a rotation degree of freedom and internal length scale parameter are introduced in the classical continuum model,was developed in the past years.In this paper,4-node,8-node and 8(4)-node rectangular isoparametric elements for the solution of boundary value problems in linear isotropic Cosserat elasticity is proposed.Principle and execution of the patch tests for these three kinds of elements are discussed in detail.Patch test for the Cosserat theory is described and applied to validate the finite elements developed.Finally,a more realistic engineering application,i.e.the stress concentration problem around a circular hole in plane strain condition,is computed to test the accuracy of the new kinds of finite elements.