Unsymmetric enhanced assumed strain elements for solid and structural mechanics

固体力学的有限元方法已经发展了四十多年。尽管如此，仍有很大的改进空间。本文的目标是显著提高低阶有限元的性能。本文的方法是将混合有限元方法与非对称有限元方法的最新发展相结合。特别提出了非对称增强假设应变法（EAS）。新方法有可能显著增加当前EAS方法的吸引力。EAS方法可以看作是不相容模态方法的推广，并且已知具有出色的数值近似性质。然而，EASelements的适用性目前存在一些不良的副作用，随着新方法的建立，这些副作用将在很大程度上被消除。

Finite element methods for solid mechanics have been developed for more than four decades. Despite of this, there is still much room for improvement.The goal of the present proposal is to significantly enhance the performance of low-order finite elements. The present approach consists of combining mixed finite element methods with recent developments in the field of unsymmetric finite element methods. In particular, the unsymmetric enhanced assumed strain (EAS) method is newly proposed. The new approach has the potential to significantly increase the attractivity of the current EAS method. The EAS method can be viewed as generalization of the method of incompatible modes and is known to possess outstanding numerical approximation properties. However, the applicability of EASelements is currently plagued with several undesirable side effects which shall be removed to a large extend with the establishment of the newly proposed method.