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

Takeki Yamamoto, Takahiro Yamada, Kazumi Matsui

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)69-98
Number of pages30
JournalComputational Mechanics
Issue number1
Publication statusPublished - 2019 Jan 15


  • Combined modeling
  • Nitsche’s method
  • Shell element
  • Solid element

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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