Isogeometric structural shape optimization

By Wolfgang A. Wall, M. Frenzel, C. Cyron. 2008

546 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/5bb8e68e2af59c5a65904a3c83618fbe030a2a58

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

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].”
Shape optimization of continua using NURBS as basis functions (2013, methodology): “[40] demonstrated the numerical solvability of a shape optimization problem formulated by selecting the coordinates of control points as design variables.”
A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM (2010, unknown): “Additional benefits may include higher order accuracy [2, 8, 9, 10, 11, 12, 13, 14], C(1) or higher continuity, and increased robustness [15].”
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.”
Isogeometric contact analysis using mortar method (2012, methodology): “The isogeometric concept has been applied to structural shape [13] and topology optimizations [14] for an integrated framework of structural design with CAD.”
Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations (2017, methodology): “Please cite this article as: D. Toshniwal, H. Speleers, T.J.R. Hughes, Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations, Comput.”
Static, free vibration, and buckling analysis of laminated composite Reissner–Mindlin plates using NURBS‐based isogeometric approach (2012, methodology): “For structural mechanics, isogeometric analysis has been extensively studied for nearly incompressible linear and non-linear elasticity and plasticity problem [58], structural vibrations [59], the Reissner–Mindlin shell [60], the Kirchhoff–Love shell [61, 62], the large deformation with rotation-fre”
Topology optimization in B-spline space (2013, methodology): “It is also worth noting that, although the use of B-splines for density parametrization has not been explored much in topology optimization, in shape optimization the use of B-splines to avoid shape oscillation and to ensure existence of solution has been used as early as 1980s [26], and as recent a”
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].”
Bounding the influence of domain parameterization and knot spacing on numerical stability in Isogeometric Analysis (2014, methodology): “In [23] [24] [25] [26] the authors discuss various methods for shape optimization of different domains .”