Three-dimensional numerical manifold method based on hexahedron element with full first-order cover function and its application in underground excavation

Y. H. Zhang, Q. Sheng, Yung Ming Cheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)


In this paper, three-dimensional(3D) Numerical Manifold Method (NNM) based on hexahedron element cover with full first-order cover function is proposed and the shape function of C8 isoparametric element in FEM is used as the cover weight function. All sub-matrices in equilibrium equations, including stiffness matrix, initial stress matrix, point force matrix, surface force matrix, body force matrix, inertia force matrix, contact matrix and friction matrix, are derived. Different with 2D contact, the direction of shear stiffness and friction force can not be easily defined in 3D contact. A new iterative method based on vector theory to detect the contact direction is developed. The application of 3D NMM in underground excavation is also presented and show good agreement with real engineering.
Original languageEnglish
Pages (from-to)365-370
Number of pages6
JournalKey Engineering Materials
Volume340-341 I
Publication statusPublished - 16 Apr 2007


  • 3D contact
  • First-order function
  • Hexahedron element
  • Manifold method
  • Underground excavation

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

Cite this