Isogeometric shape optimization of trimmed shell structures

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In most of structural analyses and optimizations using the conventional isogeometric analysis, handling of trimmed or topologically complex geometries is difficult and awkward. A trimmed or topologically complex geometry is normally modeled with multiple untrimmed patches due to the tensor-product form of a Non-Uniform Rational B-Spline (NURBS) surface, and then the patches are put together for analysis. In the present work, the isogeometric shape optimization of trimmed shell structures using the information of trimmed NURBS surfaces is proposed. To treat the trimmed shell structures efficiently, two-dimensional Trimmed Surface Analysis (TSA) which is the isogeometric approach for treating a topologically complex geometry with a single patch is extended and adopted to the analysis and optimization of shell structures. Not only the coordinates of shell surface control points, but also the coordinates of trimming curve control points are chosen as design variables so that the curvatures of shell surface as well as the trimmed boundaries can be varied during the optimization. The degenerated shell based on Reissner-Mindlin theory is formulated with exact direction vectors and their analytic derivatives. Method of Moving Asymptotes (MMA) is used as the optimization algorithm, and the shape sensitivities with respect to the coordinates of surface control points and trimming curve control points are formulated with exact direction vectors and their analytic derivatives. The developed sensitivity formulations are validated by comparing with the results of Finite Difference Method (FDM), and they show excellent agreements. Numerical examples are treated to confirm the ability of the proposed approach
Publisher
SPRINGER
Issue Date
2016-04
Language
English
Article Type
Article
Keywords

TOPOLOGY OPTIMIZATION; FINITE-ELEMENTS; DESIGN; NURBS; FORM; FORMULATION; SURFACES; SOLIDS; LAYOUT; CAD

Citation

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, v.53, no.4, pp.825 - 845

ISSN
1615-147X
DOI
10.1007/s00158-015-1361-6
URI
http://hdl.handle.net/10203/208740
Appears in Collection
ME-Journal Papers(저널논문)
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