Nonlinear bending of microarchitectural thin beams within strain gradient elasticity

Loc Tran, Jarkko Niiranen

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientific


This paper investigates the bending behaviour of beams by taking into account (1)material length scales according to Mindlin’s strain gradient elasticity theory of form II, (2) small strains but moderate displacements based on the von Kármán strain assumptions. The principle of virtual work is used to derive the nonlinear governing equations in form of a sixth-order partial differential equation. Thereafter, a conforming Galerkin method based on an isogeometric approach is adopted to naturally fulfill the stringent C2-continuity required by the beam model. Through numerical benchmarks, the accuracy and validity of the present theoretical formulations at linear and nonlinear regimes are confirmed.
Original languageEnglish
Title of host publicationProceedings of the 32nd Nordic Seminar on Computational Mechanics
EditorsA.H. Niemi, H. Koivurova
ISBN (Electronic)978-952-62-2420-6
Publication statusPublished - 2019
MoE publication typeB3 Non-refereed article in conference proceedings
EventNordic Seminar on Computational Mechanics - Oulu, Finland
Duration: 24 Oct 201925 Oct 2019
Conference number: 32

Publication series

NameRaportti / Oulun yliopisto, Konetekniikka
PublisherOulun yliopisto
ISSN (Print)2342-2599


SeminarNordic Seminar on Computational Mechanics
Abbreviated titleNSCM
Internet address


  • beam
  • strain gradient elasticity
  • isogeometric analysis
  • geometrical nonlinearity


Dive into the research topics of 'Nonlinear bending of microarchitectural thin beams within strain gradient elasticity'. Together they form a unique fingerprint.

Cite this