Hierarchical multi-layered element of assembled timoshenko beams

K. Wisniewski, B. A. Schrefler

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


A procedure of assembling Timoshenko beam elements into a hierarchical multi-layered element is presented. Using a linear approximation of the tangent displacement u in the thickness direction the traditionally used unknowns w,u, θ are replaced by w, u+, u-, where u+ and u- denote tangent displacements at the top and bottom surfaces of a layer. Then the compatibility conditions at layer interfaces are written and layers are aggregated, leading to a layer-wise model. The hierarchical model is obtained by using a Taylor or Chebyshev expansion of the tangent displacements in the thickness direction. The degree of the expansion can be arbitrarily chosen, and its coefficients are the new independent parameters. A finite element based on the presented procedure has been developed. A layer-wise model, and a single-layer model with an arbitrary order of approximation can be obtained as special cases. Accuracy and versatility of this element are confirmed on several numerical examples.

Original languageEnglish (US)
Pages (from-to)255-261
Number of pages7
JournalComputers and Structures
Issue number2
StatePublished - Jul 17 1993

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Modeling and Simulation
  • Materials Science(all)
  • Mechanical Engineering
  • Computer Science Applications


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