Discrete Kirchhoff-Love shell quadrilateral finite element designed from cubic Hermite edge curves and Coons surface patch

We present a nonlinear discrete Kirchhoff-Love four-node shell finite element that is based on the cubic Hermite edge curves and the bilinear Coons surface patch spanning the surface between them. The cubic Hermite edge curves are constructed by minimizing the bending curvature of a spatial curve connecting two adjacent nodes of the element. The G(1)-continuity is obtained at each node of the finite element mesh. Namely, the tangent vectors of the set of the edge curves attached to a given node of the mesh share the same tangent plane to the shell mid-surface for any configuration. To avoid the membrane locking, common in shell elements with higher-order interpolations, the assumed natural strains are adopted, solving the plate compatibility equation. The derived element has 5 degrees of freedom per node, 3 mid-surface displacements and 2 rotations of the mid-surface normal vector, which also rotate the corresponding mid-surface tangent plane. Several numerical examples illustrate its performance in linear and nonlinear tests, for both regular and distorted meshes.