Computing intersections between non-compatible curves and finite elements

• Published in: Computational mechanics Vol. 56; no. 3; pp. 463 - 475
• Main Authors: Durand, Raul, Farias, Márcio M., Pedroso, Dorival M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-09-2015; Springer
• Subjects: Algorithms; Analysis; Classical and Continuum Physics; Computation; Computational Science and Engineering; Curved; Engineering; Finite element method; Intersections; Mathematical analysis; Mathematical models; Original Paper; Theoretical and Applied Mechanics; Three dimensional; Embedded technique; Mesh intersection; Finite element mesh; Curve elements
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-015-1181-y

This paper presents a method to find all intersections between curved lines such as structural line elements and finite element meshes with intentions to generate smaller, non-compatible, line cells (e.g. bar elements) between crossings. The intersection finding algorithm works for two and three-dimensional meshes constituted by linear, quadratic or higher order elements. Using the proposed algorithm, meshes can then be automatically prepared for finite element analyses with techniques for embedding elements within others or analyses that require lines within solids. The application of the method is demonstrated by a number of numerical examples illustrating its capabilities in handling complex geometries, relative speed and convenience.