@inproceedings{50e365042a44424b821b34a430c34640, title = "Closed-form finite element solutions for beams and plates", 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 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.", author = "Anssi Karttunen and {von Hertzen}, Raimo and Junthula Reddy and Jani Romanoff", year = "2016", language = "English", series = "Department of Applied Mechanics: Research report", publisher = "Chalmers University of Technology", number = "2016:04", editor = "Ragnar Larsson", booktitle = "Proceedings of 29th Nordic Seminar on Computational Mechanics – NSCM29", }