论文标题
根据一致的夫妇应力理论，有限元的新的混合配方和网状依赖性
New mixed formulation and mesh dependency of finite elements based on the consistent couple stress theory
论文作者
论文摘要
这项工作提出了一种基于六个视场变异原理的一般有限元公式，该原理结合了一致的夫妇应力理论。涵盖弹性材料和非弹性材料的简单，高效和本地迭代的无迭代解决程序被得出以最大程度地减少计算成本。通过适当的插值，提出了各种节点的膜元素作为示例。实施的有限元素用于进行数值实验，以研究一致的夫妇应力理论引入的平面内钻孔自由度的性能。还使用弹性和非弹性材料研究了网格依赖性问题。结果表明，与凯奇理论相比，一致的夫妇应力理论提供了旋转的客观定义，但是需要其他正则化（或其他技术）来克服与软化或裂缝相关的问题中的网格/大小依赖性。在硬化连续性问题和/或较大的特征长度的情况下，所提出的配方和元素为模拟自由度转化和旋转程度的结构提供了更可靠的方法。
This work presents a general finite element formulation based on a six--field variational principle that incorporates the consistent couple stress theory. A simple, efficient and local iteration free solving procedure that covers both elastic and inelastic materials is derived to minimise computation cost. With proper interpolations, membrane elements of various nodes are proposed as the examples. The implemented finite elements are used to conduct numerical experiments to investigate the performance of the in-plane drilling degrees of freedom introduced by the consistent couple stress theory. The mesh dependency issue is also studied with both elastic and inelastic materials. It is shown that the consistent couple stress theory provides an objective definition of rotation compared with the Cauchy theory but additional regularisation (or other techniques) is required to overcome mesh/size dependency in softening or fracture related problems. In the case of hardening continuum problems and/or large characteristic lengths, the proposed formulation and elements offer a more reliable approach to model structures with both translational and rotational degrees of freedom.
