A nonlinear extensible 4-node shell element based on continuum theory and assumed strain interpolations

Summary A quadrilateral continuum-basedC ⁰ shell element is presented, which relies on extensible director kinematics and incorporates unmodified three-dimensional constitutive models. The shell element is developed from the nonlinear enhanced assumed strain (EAS) method advocated by Sino & Armero [1] and formulated in curvilinear coordinates. Here, the EAS-expansion of the material displacement gradient leads to the local interpretation of enhanced covariant base vectors that are superposed on the compatible covariant base vectors. Two expansions of the enhanced covariant base vectors are given: first an extension of the underlying single extensible shell kinematic and second an improvement of the membrane part of the bilinear element. Furthermore, two assumed strain modifications of the compatible covariant strains are introduced such that the element performs well even in the case of very thin shells. This paper is dedicated to the memory of Juan C. Simo In honour of Professor Juan Simo who had significant collaboration with our institute and contributed important insights to our research work. This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan Simo.