Computational Mechanics

, Volume 63, Issue 1, pp 69–98 | Cite as

Numerical procedure to couple shell to solid elements by using Nitsche’s method

  • Takeki YamamotoEmail author
  • Takahiro Yamada
  • Kazumi Matsui
Original Paper


This paper presents a numerical procedure to couple shell to solid elements by using the Nitsche’s method. The continuity of displacements can be satisfied approximately with the penalty method, which is effective in setting the penalty parameter to a sufficiently large value. When the continuity of only displacements on the interface is applied between shell and solid elements, an unreasonable deformation may be observed near the interface. In this work, the continuity of the stress vector on the interface is considered by employing the Nitsche’s method, and hence a reasonable deformation can be obtained on the interface. The authors propose two types of shell elements coupled with solid elements in this paper. One of them is the conventional MITC4 shell element, which is one of the most popular elements in engineering applications. This approach shows the capability of discretizing the domain of the structure with the different types of elements. The other is the shell element with additional degrees of freedom to represent thickness–stretch developed by the authors. In this approach, the continuity of displacements including the deformation in the thickness direction on the interface can be considered. Several numerical examples are presented to examine the fundamental performance of the proposed procedure. The behavior of the proposed simulation model is compared with that of the whole domain discretized with only solid elements.


Nitsche’s method Combined modeling Shell element Solid element 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringTohoku UniversitySendaiJapan
  2. 2.Graduate School of Environment and Information ScienceYokohama National UniversityYokohamaJapan

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