Two‐ and three‐dimensional transition element families for adaptive refinement analysis of elasticity problems

Abstract

AbstractIn this paper, new enhanced assumed strain (EAS) and hybrid stress transition element families are developed for 2D and 3D adaptive refinement analysis of elasticity problems. The EAS element families are based on some existing incompatible transition element families. By using the EAS method and the previous incompatible modes, the B‐matrix columns associated with the EAS modes can be directly designed such that their domain integrals vanish automatically and they can be computed more efficiently. For 2D hybrid stress transition element families, it is possible to derive different stress fields that lead to rank‐sufficient transition elements. However, the task becomes intractable for 3D hybrid stress transition elements in which many combinations of mid‐side and mid‐face nodes are possible. This paper proposes to use hybrid stress transition element families in which the assumed stress fields are linearly complete. The new 2D element family is more accurate than the 2D rank‐sufficient element family. The new 3D element family is more accurate than the one with additional bilinear stress modes. Numerical examples reveal that the most accurate transition element families are the newly developed hybrid stress families followed by the EAS families, the incompatible families and then the compatible families. Copyright © 2008 John Wiley & Sons, Ltd.