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A density field parametrization for topology optimization using Bernstein elements
Author(s) -
Lambe Andrew B.,
Czekanski Aleksander
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5843
Subject(s) - bernstein polynomial , mathematics , interpolation (computer graphics) , parametrization (atmospheric modeling) , polygon mesh , topology (electrical circuits) , finite element method , lagrange polynomial , topology optimization , field (mathematics) , boundary (topology) , mathematical optimization , mathematical analysis , geometry , computer science , pure mathematics , polynomial , frame (networking) , physics , combinatorics , quantum mechanics , radiative transfer , telecommunications , thermodynamics
Summary A new way of describing the density field in density‐based topology optimization is introduced. The new method uses finite elements constructed from Bernstein polynomials rather than the more common Lagrange polynomials. Use of the Bernstein finite elements allows higher‐order elements to be used in the density‐field interpolation without producing unrealistic density values, ie, values lower than zero or higher than one. Results on several test problems indicate that using the higher‐order Bernstein elements produces optimal designs with sharper estimates of the optimal boundary on coarse design meshes. However, higher‐order elements are also required in the structural analysis to prevent the appearance of unrealistic material distributions. The Bernstein element density interpolation can be combined with adaptive mesh refinement to further improve design accuracy even on design domains with complex geometry.