# Closed-form finite element solutions for beams and plates

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

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**Closed-form finite element solutions for beams and plates.** / Karttunen, Anssi; von Hertzen, Raimo; Reddy, Junthula; Romanoff, Jani.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

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*Proceedings of 29th Nordic Seminar on Computational Mechanics – NSCM29.*Department of Applied Mechanics: Research report , no. 2016:04, Chalmers University of Technology, Göteborg , Nordic Seminar on Computational Mechanics, Stockholm, Sweden, 22/10/2014.

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

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TY - GEN

T1 - Closed-form finite element solutions for beams and plates

AU - Karttunen, Anssi

AU - von Hertzen, Raimo

AU - Reddy, Junthula

AU - Romanoff, Jani

PY - 2016

Y1 - 2016

N2 - 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 derivedfrom 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.

AB - 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 derivedfrom 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.

UR - http://publications.lib.chalmers.se/publication/244480-proceedings-of-29th-nordic-seminar-on-computational-mechanics-nscm29

M3 - Conference contribution

T3 - Department of Applied Mechanics: Research report

BT - Proceedings of 29th Nordic Seminar on Computational Mechanics – NSCM29

A2 - Larsson, Ragnar

PB - Chalmers University of Technology

CY - Göteborg

ER -

ID: 9591694