### Abstract

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 language | English |
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Title of host publication | Proceedings of the 32nd Nordic Seminar on Computational Mechanics |

Editors | A.H. Niemi, H. Koivurova |

Pages | 158-159 |

ISBN (Electronic) | 978-952-62-2420-6 |

Publication status | Published - 2019 |

MoE publication type | B3 Non-refereed article in conference proceedings |

Event | Nordic Seminar on Computational Mechanics - Oulu, Finland Duration: 24 Oct 2019 → 25 Oct 2019 Conference number: 32 https://www.oulu.fi/construction/nscm32 |

### Publication series

Name | Raportti / Oulun yliopisto, Konetekniikka |
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Publisher | Oulun yliopisto |

Number | 9 |

ISSN (Print) | 2342-2599 |

### Seminar

Seminar | Nordic Seminar on Computational Mechanics |
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Abbreviated title | NSCM |

Country | Finland |

City | Oulu |

Period | 24/10/2019 → 25/10/2019 |

Internet address |

### Keywords

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

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## Cite this

Tran, L., & Niiranen, J. (2019). Nonlinear bending of microarchitectural thin beams within strain gradient elasticity. In A. H. Niemi, & H. Koivurova (Eds.),

*Proceedings of the 32nd Nordic Seminar on Computational Mechanics*(pp. 158-159). (Raportti / Oulun yliopisto, Konetekniikka ; No. 9).