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

We develop a new paradigm for thin-shell finite-element analysis based on t he use of subdivision surfaces for (i) describing the geometry of the shell in its undeformed configuration, and (ii) generating smooth interpolated d isplacement fields possessing bounded energy within the strict framework of the Kirchhoff-Love theory of thin shells. The particular subdivision strat egy adopted here is Loop's scheme, with extensions such as required to acco unt for creases and displacement boundary conditions. The displacement fiel ds obtained by subdivision are H-2 and, consequently, have a finite Kirchho ff-Love energy. The resulting finite elements contain three nodes and eleme nt integrals are computed by a one-point quadrature. The displacement field 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 field over one element depend on the nodal displacements of the element nodes and all node s of immediately neighbouring elements. However, the use of subdivision sur faces ensures that all the local displacement fields thus constructed combi ne conformingly to define one single limit surface. Numerical tests, includ ing the Belytschko er al. [10] obstacle course of benchmark problems, demon strate the high accuracy and optimal convergence of the method. Copyright ( C) 2000 John Wiley & Sons, Ltd.