“Computational Civil Engineering - "Intersections" International Journal

22 A.G. Popa, H.L. CucuFigure 10. Normal stresses at level 1 [kN/m 2 ], meshwork U 2 , loading case (c)3. CONCLUSIONSNumerical tests performed with the incompatible plane element with three degreesof freedom per node PLAN-12 have revealed a good behavior in all the loadingcases and especially for restrained torsion.The mean deviation of the displacements is less than 2% with respect to theanalytical solutions. For stresses and internal actions, the gap between the twosolutions, analytical and numerical, is greater but still in technically acceptedlimits. It has been mentioned that finite elements used in the analysis have quitelarge dimensions and the solutions are improving with the refining of the meshes.The above considerations lead to the conclusion that the plane incompatible finiteelement with three degrees of freedom per node is efficient in the analysis of thethin-walled bars with open section.References1. Kolbrunner, C.F. and Hajdiu N., Dünnwändige Stäbe, Springer Verlag, Berlin 1975.2. Chen, B. and Hu, Y., A Consistent Theory for Torsion of Thin-walled Bars, Thin-walledStructures, nr.7, 1988.3. El-Hammasi, A.S., Numerical Method for Analysing Open Thin-walled Structures underInteraction of Bending and Torsion, Computer & Structures, vol.37, 1990.4. Marţian, I., Teoria elasticităţii si plasticităţii pentru constructori, Universitatea Tehnică dinCluj-Napoca, 1999, (in Romanian).5. Roberts, T.M. and Achour, B., Torsion and Bending of Braced Thin-walled Open Sections,Journal of Structural Engineering, vol.116, 1990.