Physically stabilised displacement-based ANS solid-shell element

• A reduced integration, displacement-degree-of-freedom-only solid-shell is presented.
• Three hierarchical freedoms compliment the 8-node element trilinear displacement field.
• ANS enforcement on shear and normal strains improves mesh distortion tolerance.
• A single element-layer through the shell thickness was used with full constitutive laws.
• The displacement-variational element was comparable in accuracy to EAS elements.

A robust reduced integration solid-shell finite element in irreducible variational formulation is demonstrated in this paper. To enable shell element-like performance using a single through-shell-thickness element layer, we apply element technologies isotropically, introducing local tri-quadratic hierarchical displacement modes thereafter systematically projected to the global coordinate frame. We also enforce uniform, bilinear and linear ANS interpolations to all local normal and shear strains respectively, imposing identical in-plane and out-of-plane element response for robust 3D thin shell deformation behaviour in non-regular, trapezoidal-shaped meshes. The hierarchical strains realised improve the element performance by complementing the locking alleviating actions of the ANS-modified membrane and shear strain fields in reduced numerical integration scheme performed along the designated shell thickness. We restrict our initial numerical investigations to geometrically linear beams, plates and shell problems solely for preliminary assessment of the element's in-plane and out-of-plane behaviour in response to the uniform modification of strains and hierarchical displacement modes introduced. To this end, the results indicate robust behaviour and comparable accuracy in comparison to mixed variational, enhanced assumed strain elements in full and in reduced integration in all structural problem classes undertaken.