Description:
<jats:title>Abstract</jats:title><jats:p>A hybrid-mixed ANS four-node shell element by
using the sampling surfaces (SaS) technique is developed.
The SaS formulation is based on choosing inside the nth
layer In not equally spaced SaS parallel to the middle surface
of the shell in order to introduce the displacements
of these surfaces as basic shell variables. Such choice of
unknowns with the consequent use of Lagrange polynomials
of degree In − 1 in the thickness direction for each
layer permits the presentation of the layered shell formulation
in a very compact form. The SaS are located inside
each layer at Chebyshev polynomial nodes that allows one
to minimize uniformly the error due to the Lagrange interpolation.
To implement the efficient analytical integration
throughout the element, the enhanced ANS method
is employed. The proposed hybrid-mixed four-node shell
element is based on the Hu-Washizu variational equation
and exhibits a superior performance in the case of coarse
meshes. It could be useful for the 3D stress analysis of thick
and thin doubly-curved shells since the SaS formulation
gives the possibility to obtain numerical solutions with a
prescribed accuracy, which asymptotically approach the
exact solutions of elasticity as the number of SaS tends to
infinity.</jats:p>