Enhanced one-point quadrature shell element for nonlinear applications

This work is an extension to nonlinear applications of a previously published work (Int. J. Numer. Meth. Engng 2006; 66:214-249) about membrane and transverse shear improvement for one-point quadrature shell elements. A new formulation based on the enhanced assumed strain method and reduced integration techniques, called iCYSE-E6 (improved Cardoso and Yoon shell element with 6 enhanced parameters) was suggested by Cardoso et al. to improve membrane and transverse shear performances under the framework of linear applications. It was proven that the proposed linear formulation gives accurate responses, even with extremely coarse meshes. The proposed extension of this work is then performed in such a way that the resulting new finite element can be applied in general simulations with nonlinearities in geometry, material and contact. The interaction among hourglass and enhanced assumed strain stiffness matrices and internal force vectors is taken into account in the present formulation. Special emphasis is given for the construction of nonlinear hourglass terms such that excessive hourglass energy in elastoplastic applications can be controlled efficiently. The finite element matrices are constructed in resultant form, allowing a much simpler and effective formulation for the hourglass terms, and also for the coupling between the constant and the enhanced strain-displacement matrices. It is shown that the present formulation is accurate in demanding problems, even for the cases of relatively large coarse mesh structures. The paper presents several nonlinear examples to assess the element's performance.