Delaunay meshing of NURBS models

Nov 2019 - Current

As is known to the CAD community, NURBS representations have a topological deficiency in trimmed regions, which poses a challenge to the isogeometric analysis as well as the meshing of NURBS models. A novel approach to meshing NURBS models is proposed, which does not rely on the parameterisation of individual trimmed NURBS surfaces. The trimmed regions are firstly protected with spheres, inside which implicit surfaces are defined to approximate the smooth trimmed regions. The meshing process is performed on the entire NURBS model, not individual NURBS surfaces as in conventional mesh generators. The topological inconsistency between adjacent trimmed NURBS surfaces can be automatically repaired in the output Delaunay mesh. In addition, the mesh will be no longer segmented by trimming curves.

Key words: Delaunay meshing; Trimmed NURBS; Protecting spheres; Topology repair.

CAD-compatible structural optimisation

2019

An automated and topologically robust method was proposed to generate parametric CAD models from voxelised topology optimisation results, pipelining topology design and manufacturing. In conventional topology optimisation, the optimised structure is usually represented as a voxelised model, which cannot be used in manufacturing without converting it to a CAD model beforehand. Instead of a manual conversion process which inevitably changes the original optimisation result, a topologically identical voxel chain is firstly extracted with the skeletionisation algorithm from digital topology. An initial structural skeleton is derived from the voxel chain, and a sequence of size and shape optimisation are applied to the skeleton until it becomes optimal. The optimised skeleton can be readily converted to a CAD model with primitive objects.

Key words: Topology optimisation; Digital topology; Homotopic skeletonisation.

Implicit matrix representation of curves and surfaces

2018

The need to compute the intersections between a line and a high-order curve or surface arises in many finite element and geometry applications. This can be easy to formulate but hard to solve robustly. A non-iterative method for computing intersections by solving a SVD and an eigenvalue problem was proposed. All intersection points and corresponding parametric coordinates are determined using only standard linear algebra techniques. The technique is far more robust than the widely used Newton-Raphson method or its variants.

A C++ implementation of the method is available at Nitro project.

Key words: Implicitisation; Algebraic geometry; Higher-order finite elements.

Isogeometric analysis and optimisation of lattice-skin structures

2014 - 2018

A novel approach for the structural analysis of lattice-skin structures was proposed. The skin is a spline surface that is usually created in a CAD system, and the infill lattice is generated automatically by interrogating the skin surface. The surface interrogation is applied on the exact geometry of the skin, which is also used in the structural analysis, avoiding the inaccurate geometric representation in the analysis. The lattice is modelled as a truss and the skin as a Kirchhoff-Love thin-shell. The two types of structures are coupled with a standard Lagrange multiplier approach.

Key words: Isogeometric analysis; Surface interrogation; Subdivision surfaces; Freeform deformation.