Isogeometric shape design optimization: exact geometry and enhanced sensitivity

By Seonho Cho, Seung-Hyun Ha. 2009

225 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/aa8287575c709e53772968034f277a224db6ea3c

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Isogeometric design of elastic arches for maximum fundamental frequency (2011, background): “The isogeometric framework delineated thus far facilitates the evaluation of design sensitivities analytically, which yields consistent sensitivity information of enhanced accuracy (Cho and Ha 2009) and reduces computational time, leading to significant performance improvements.”
Isogeometric Shape Optimization of Vibrating Membranes (2011, background): “…with the situations when domain families parametrized by only a few variables are consedered (such as, for example, a circle of a varying radius [11, 24], or a family of super-elliptical shapes [17, 18]), or when only certain parts of the boundary are allowed to vary locally [10, 13, 24, 25].”
Topology optimization approaches (2013, background): “…are allowed to move independently (with some regularization) (Le et al. 2011; Arnout et al. 2012), partly due to great interest in applications of isogeometric approaches (Wall et al. 2008; Cho and Ha 2009; Seo et al. 2010) and partly due to the need of explicit mesh-resolved boundary conditions.”
Implementation of regularized isogeometric boundary element methods for gradient‐based shape optimization in two‐dimensional linear elasticity (2016, methodology): “The application of IGA in shape optimization can be found in [47, 48, 49, 50, 51].”
Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, methodology): “Isogeometric Analysis has already been introduced successfully and discussed for shape optimization in [29, 50, 70, 105] and we believe that it also represents a potentially effective numerical approximation method for topology optimization problems.”
Numerical method for shape optimization using T-spline based isogeometric method (2010, methodology): “Since then, an isogeometric analysis, which handles an exact geometry with the NURBS basis function, was developed by Hughes et al. (2005). A robust way to define a basis function and its property was detailed.”
Full analytical sensitivities in NURBS based isogeometric shape optimization (2010, methodology): “Isogeometric analysis has recently been successfully applied in structural shape optimization [11, 12] where, again, only analytical sensitivities for positions of control points are given.”
Shape optimization of continua using NURBS as basis functions (2013, methodology): “[11,14] presented a numerical method for computing the derivatives of cost functions with respect to the coordinates of control points by using the velocity field due to the variation of each control point in the formulae of shape derivatives for domain and boundary integrals.”