A finite-strain solid–shell using local Löwdin frames and least-squares strains

P. Areias, C. A.Mota Soares, T. Rabczuk, J. Garção

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of-reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced-assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

Original languageEnglish
Pages (from-to)112-133
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2016 Nov 1

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.


  • Assumed-strains
  • Finite-strain solid–shell
  • Least-squares
  • Singular value decomposition

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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