One-point quadrature ANS solid-shell element based on a displacement variational formulation Part I – Geometrically linear assessment

A demonstration of a computationally efficient, physically stabilised one point-quadrature solid-shell finite element in pure displacement variational formulation and within the context of hierarchical displacement modes is presented in this paper. The displacement field of the 24 degree of freedom 8-node solid finite element is enhanced by a hierarchical, thickness-wise, quadratic displacement field and associated single displacement degree of freedom. The displacement enhancements expand the covariant element strain space resolving thickness locking and in combination with the assumed natural strain approach, attenuates shear and trapezoidal locking in thin shell simulations. Formulated within the recent framework of the reduced integration element technology and hourglass physical stabilisation, a locking free, 8-node solid-shell element for general three dimensional shell analysis is obtained. The theoretical relevance and applicability of the proposed displacement-kinematics 8-node solid-shell element offering comparable accuracy and performance flexibility as physically stabilised reduced integration solid-shell elements based on mixed and EAS variational statements is demonstrated in selected linear numerical benchmark problems.