### Abstract

We formulate a linear elastic beam problem by employing Saint Venant’s principle so that end eﬀects do not appear in the beam. Then the elasticity solution to the formulated interior problem is presented. By using mid-surface variables derived

from the solution, a nodally-exact beam element is formulated by a force-based approach. A ﬁnite element calculation example is presented. In addition to the beam element, elasticity-based circular and rectangular plate elements may be developed on the basis of similar approaches founded on 2D stress functions or 3D displacement potentials.

from the solution, a nodally-exact beam element is formulated by a force-based approach. A ﬁnite element calculation example is presented. In addition to the beam element, elasticity-based circular and rectangular plate elements may be developed on the basis of similar approaches founded on 2D stress functions or 3D displacement potentials.

Original language | English |
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Title of host publication | Proceedings of 29th Nordic Seminar on Computational Mechanics – NSCM29 |

Editors | Ragnar Larsson |

Place of Publication | Göteborg |

Publisher | Chalmers University of Technology |

Publication status | Published - 2016 |

MoE publication type | A4 Article in a conference publication |

Event | Nordic Seminar on Computational Mechanics - Stockholm, Sweden Duration: 22 Oct 2014 → 24 Oct 2014 Conference number: 27 |

### Publication series

Name | Department of Applied Mechanics: Research report |
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Publisher | Department of Applied Mechanics, Chalmers University of Technology |

Number | 2016:04 |

ISSN (Electronic) | 1652-8549 |

### Seminar

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

Country | Sweden |

City | Stockholm |

Period | 22/10/2014 → 24/10/2014 |

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## Cite this

Karttunen, A., von Hertzen, R., Reddy, J., & Romanoff, J. (2016). Closed-form finite element solutions for beams and plates. In R. Larsson (Ed.),

*Proceedings of 29th Nordic Seminar on Computational Mechanics – NSCM29*(Department of Applied Mechanics: Research report ; No. 2016:04). Göteborg : Chalmers University of Technology.