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Shape Design Sensitivity Analysis Using Isogeometric Approach  

Ha, Seung-Hyun (서울대학교 조선해양공학과)
Cho, Seon-Ho (서울대학교 조선해양공학과)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.20, no.3, 2007 , pp. 339-345 More about this Journal
Abstract
In this paper, a variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions for response analysis are generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Furthermore, the solution space for the response analysis can be represented in terms of the same functions to represent the geometry, which enables to provide a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling and analyze arbitrarily shaped structures without re-meshing. In this paper, a continuum-based adjoint sensitivity analysis method using the isogeometric approach is extensively derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of geometry In the isogeometric analysis, however, the geometric properties are already embedded in the B-spline basis functions and control points so that it has potential capability to overcome the aforementioned difficulties. Through some numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.
Keywords
shape design sensitivity; isogeometric analysis; adjoint sensitivity analysis; NURBS;
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