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 -