Subdivision surfaces: a new paradigm for thin-shell finite-element analysis

We develop a new paradigm for thin-shell nite-element analysis based on the use of subdivision surfaces for (i) describing the geometry of the shell in its undeformed con guration, and (ii) generating smooth interpolated displacement elds possessing bounded energy within the strict framework of the Kirchho {Love theory of thin shells. The particular subdivision strategy adopted here is Loopʹs scheme, with extensions such as required to account for creases and displacement boundary conditions. The displacement elds obtained by subdivision are H2 and, consequently, have a nite Kirchho {Love energy. The resulting nite elements contain three nodes and element integrals are computed by a one-point quadrature. The displacement eld of the shell is interpolated from nodal displacements only. In particular, no nodal rotations are used in the interpolation. The interpolation scheme induced by subdivision is non-local, i.e. the displacement eld over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements. However, the use of subdivision surfaces ensures that all the local displacement elds thus constructed combine conformingly to de ne one single limit surface. Numerical tests, including the Belytschko et al. [10] obstacle course of benchmark problems, demonstrate the high accuracy and optimal convergence of the method.