Title: Interrogation of spline surfaces with application to isogeometric design and analysis of lattice-skin structures,
Abstract: A novel surface interrogation technique is proposed to compute the
intersection of curves with spline surfaces in isogeometric analysis. The
intersection points are determined in one-shot without resorting to a
Newton-Raphson iteration or successive refinement. Surface-curve intersection
requires usually the solution of a system of nonlinear equations. It is assumed
that the surface is given in form of a spline, such as a NURBS, T-spline or
Catmull-Clark subdivision surface, and is convertible into a collection of
Bézier patches. First, a hierarchical bounding volume tree is used to
efficiently identify the Bézier patches with a convex-hull intersecting the
convex-hull of a given curve segment. For ease of implementation convex-hulls
are approximated with k-dops (discrete orientation polytopes). Subsequently,
the intersections of the identified Bézier patches with the curve segment are
determined with a matrix-based implicit representation leading to the
computation of a sequence of small singular value decompositions (SVDs). As an
application of the developed interrogation technique the isogeometric design
and analysis of lattice-skin structures is investigated. Current additive
manufacturing technologies make it possible to produce up to metre size parts
with designed geometric features reaching down to submillimetre scale. The skin
is a spline surface that is usually created in a computer-aided design (CAD)
system and the periodic lattice to be fitted consists of unit cells, each
containing a small number of struts. The lattice-skin structure is generated by
projecting selected lattice nodes onto the surface after determining the
intersection of unit cell edges with the surface. For mechanical analysis, the
skin is modelled as a Kirchhoff-Love thin-shell and the lattice as a
pin-jointed truss. The two types of structures are coupled with a standard
Lagrange multiplier approach.