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FEA-driven Geometric Modelling for Meshless Methods
(Springer Paris, 2005-11) Ruíz, Óscar; Granados, Miguel; Cadavid, Carlos; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Optimized Boolean Operations against orthogonal Fixed Grids (FG) for 2-manifold construction in quasi-meshless methods for Finite Element Analysis are presented -- A Piecewise Linear (PL) or Boundary Representation (B-Rep) B is assumed to be the boundary of a solid S ⊂ R3 -- On the other hand, R3 is partitioned into a 3-dimensional array of cubic, uniform cells Ci,j,k . Cells Ci,j,k with Ci,j,k ∩ S ≠Φ and Ci,j,k ∩ S ≠ Ci,j,k are particularly important for FG applications -- These are the cells Ci,j,k intersecting B, which happen to be Neither Inside nor Outside (NIO) of B -- The boundary ∂(Ci,j,k ∩ S ) of Ci,j,k ∩ S must be calculated from ∂Ci,j,k and B for a large number of cells Ci,j,k , which makes the normal boolean operations unpractical -- The article illustrates with examples the immersion of B-Rep models in Fixed Grids, visits the downstream results of the stress-strain calculations using FG and explains how this approach is used in Product Design Optimization