Closed-form finite element solutions for beams and plates

Anssi Karttunen, Raimo von Hertzen, Junthula Reddy, Jani Romanoff

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review


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.
Original languageEnglish
Title of host publicationProceedings of 29th Nordic Seminar on Computational Mechanics – NSCM29
EditorsRagnar Larsson
Place of PublicationGöteborg
PublisherChalmers University of Technology
Publication statusPublished - 2016
MoE publication typeA4 Article in a conference publication
EventNordic Seminar on Computational Mechanics - Stockholm, Sweden
Duration: 22 Oct 201424 Oct 2014
Conference number: 27

Publication series

NameDepartment of Applied Mechanics: Research report
PublisherDepartment of Applied Mechanics, Chalmers University of Technology
ISSN (Electronic)1652-8549


SeminarNordic Seminar on Computational Mechanics
Abbreviated titleNSCM


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