Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 331, Issue -, Pages 585-622Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2017.11.032
Keywords
Isogeometric shape optimization; Bezier triangles; Distance constraints; Coarse and fine mesh; Material design; Negative Poisson's ratio
Funding
- National Science Foundation [1435072, 1404665]
- ARO grant [W911NF-17-1-0020]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1435072] Funding Source: National Science Foundation
- Div Of Chem, Bioeng, Env, & Transp Sys
- Directorate For Engineering [1404665] Funding Source: National Science Foundation
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The paper presents a Bezier triangle based isogeometric shape optimization method. Bezier triangles are used to represent both the geometry and physical fields. For a given physical domain defined by B-spline boundary, a coarse Bezier triangular parameterization is automatically generated. This coarse mesh is used to maintain parameterization quality and move mesh by solving a pseudo linear elasticity problem. Then a fine mesh for isogeometric analysis is generated from the coarse mesh through degree elevation and refinement. As the fine mesh retains the same geometric map as the coarse mesh, we can guarantee mesh validity with the coarse mesh only. This bi-level mesh allows us to achieve high numerical accuracy of isogeometric analysis and lower computational cost on mesh validity control and mesh movement. Due to the use of B-spline boundary, the optimized shape can be compactly represented with a relatively small number of optimization variables. Due to the use Bezier triangles, this shape optimization method is applicable to structures of complex topology and allows for local refinement for analysis. By representing the squared distance between two Bezier curves as a Bezier form, a distance check scheme is also introduced to prevent intersections of design boundaries and control the thickness of structural connections. Numerical examples on minimal compliance design and design of negative Poisson ratios are presented to demonstrate the efficacy of the proposed method. (C) 2017 Elsevier B.V. All rights reserved.
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