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Structural Engineering and Mechanics
  Volume 43, Number 3, August10 2012 , pages 349-370

Variable-node element families for mesh connection and adaptive mesh computation
Jae Hyuk Lim, Dongwoo Sohn and Seyoung Im

    Variable-node finite element families, termed (4 + k + l + m + n)-node elements with an arbitrary number of nodes (k, l, m, and n) on each of their edges, are developed based on the generic point interpolation with special bases having slope discontinuities in two-dimensional domains. They retain the linear interpolation between any two neighboring nodes, and passes the standard patch test when subdomain-wise 2 x 2 Gauss integration is employed. Their shape functions are automatically generated on the master domain of elements although a certain number of nodes are inserted on their edges. The elements can provide a flexibility to resolve nonmatching mesh problems like mesh connection and adaptive mesh refinement. In the case of adaptive mesh refinement problem, so-called \"1-irregular node rule\" working as a constraint in performing mesh adaptation is relaxed by adopting the variable-node elements. Through several examples, we show the performance of the variable-node finite elements in terms of accuracy and efficiency.
Key Words
    variable-node finite elements; transition elements; nonmatching meshes; adaptive mesh refinement; 1-irregular node rule; mesh connection
Jae Hyuk Lim: Satellite Structure Department, Korea Aerospace Research Institute (KARI), 169-84 Gwahak-ro, Yuseong-gu, Daejeon 305-806, Korea
Dongwoo Sohn: Division of Mechanical and Energy Systems Engineering, College of Engineering, Korea Maritime University, 727 Taejong-ro, Yeongdo-gu, Busan 606-791, Korea
Seyoung Im: Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Korea

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