Subdivision Shells

Abstract

Subdivision elements, as originally introduced by Cirak, Ortiz, and Schröder [5], provide a new paradigm for thin-shell finite-element analysis based on the use of subdivision surfaces for (i) describing the geometry of the shell in its undeformed configuration, and (ii) generating smooth interpolated displacement fields. The displacement fields obtained by subdivision are H 2 and, consequently, have a finite Kirchhoff-Love energy. The displacement field of the shell is interpolated from nodal displacements only and no nodal rotations are used. The interpolation scheme induced by subdivision is nonlocal, i.e. the displacement field over one element depends on the nodal displacements of the three element nodes and all nodes of immediately neighboring elements. However, the use of subdivision schemes ensures that all the local displacement fields combine conformingly to define one single limit surface. Numerical tests, demonstrate the high accuracy and optimal convergence of the method even in highly nonlinear problems [4]. Furthermore, because of the unification of representations for mechanics and geometric modeling (i.e. CAD: Computer Aided Design), subdivision elements are ideally suited to applications in shape optimization [3]. Recently, specialized cohesive elements have been developed that account for in-plane tearing, shearing, and hinge modes of shell fracture [1]; and methods for coupling subdivision shells to gas dynamics [2].

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