Optimal 4-node shell and 3d-shell finite elements for nonlinear analysis

Abstract

Summary First we shortly present several low-order (4-node) shellfinite element formu-lations (based on Reissner-Mindlin kinematics) that allow for accurate and effi-cient (with coarse and distortedmeshes) analysis of shell-likestructures subjectedto large deformations and rotations. The formulations are based on mixed varia-tionalprinciple,enhancedassumedstrain(EAS)method(basedonGreen-Lagrangestrains) and assumed natural strain (ANS) method. The EAS method is used in allformulations in order to improve both membrane and bending behavior of the 4-node element (the formulationsdiffer from one another by the number of assumedEAS parameters), and the ANS method is used to avoid shear locking. An optimalnumber of membrane/bending EAS parameters is then identified by comparing re-sults of a set of characteristic numerical examples (in this paper we only presentresults of two illustrativeexamples). Thus an optimal 4-node EAS/ANS nonlinearshell element is derived. In the second part of the paper we shortly present en-hancement of the previously derived optimal shell element leading to an optimallow-order (4-node) nonlinear 3d-shell element; i.e. an element that accounts forthrough-the-thickness stretching. The enhancement, which introduces incompati-bleGreen-Lagrangestrainsinthethrough-the-thicknessdirection,isbasedonEASmethod. Thederived3d-shellelementlooksas asurface(withextensibledirectors)from the outside but it can build fully 3d stress and 3d strain states. Finally, wepresent a numerical example, which illustrates performance of an optimal 4-nodeEAS/ANS 3d-shellelement.