Shear deformable shell elements for large strains and rotations

Well-known Þnite element concepts like the Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) techniques are combined to derive e¦cient and reliable Þnite elements for continuum based shell formulations. In the present study two aspects are covered: The Þrst aspect focuses on the classical 5-parameter shell formulation with ReissnerÐMindlin kinematics. The above-mentioned combinations, already discussed by AndelÞnger and Ramm1 for the linear case of a four-node shell element, are extended to geometrical non-linearities. In addition a nine-node quadrilateral variant is presented. A geometrically non-linear version of the EAS-approach is applied which is based on the enhancement of the GreenÐLagrange strains instead of the displacement gradient as originally proposed by Simo and Armero.2 In the second part elements are derived in a similar way for a higher order, so-called 7-parameter non-linear shell formulation which includes the thickness stretch of the shell (Bu¬ chter and Ramm3). In order to avoid artiÞcial sti¤ening caused by the three dimensional displacement Þeld and termed Ôthickness lockingÕ, special provisions for the thickness stretch have to be introduced