Fundamental aspects of shape optimization in the context of isogeometric analysis

DOI10.1016/j.cma.2014.12.028zbMath1425.65159OpenAlexW1989038951MaRDI QIDQ1798893

D. Fußeder, Bernd Simeon, Anh-Vu Vuong

Publication date: 23 October 2018

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2014.12.028

zbMATH Keywords

shape optimizationisogeometric analysisNURBSadjoint approachweight optimization

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Topological methods for optimization problems in solid mechanics (74P15) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (19)

The embedded isogeometric Kirchhoff-Love shell: from design to shape optimization of non-conforming stiffened multipatch structures ⋮ Higher-Order Moving Mesh Methods for PDE-Constrained Shape Optimization ⋮ A performance study of NURBS-based isogeometric analysis for interior two-dimensional time-harmonic acoustics ⋮ Isogeometric gradient‐free proportional topology optimization (<scp>IGA‐PTO</scp>) for compliance problem ⋮ Tangled finite element method for handling concave elements in quadrilateral meshes ⋮ On the computation of analytic sensitivities of eigenpairs in isogeometric analysis ⋮ A computationally efficient isoparametric tangled finite element method for handling inverted quadrilateral and hexahedral elements ⋮ Volumetric embedded entities for the isogeometric analysis of complex structures ⋮ Shape optimization for natural frequency with isogeometric Kirchhoff-love shell and sensitivity mapping ⋮ A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis ⋮ Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures ⋮ Inverse homogenization using isogeometric shape optimization ⋮ Multiresolution Shape Optimisation with Subdivision Surfaces ⋮ Algorithmic Aspects of Isogeometric Shape Optimization ⋮ Isogeometric collocation methods for Cosserat rods and rod structures ⋮ A framework for parametric design optimization using isogeometric analysis ⋮ Exact and efficient isogeometric reanalysis of accurate shape and boundary modifications ⋮ Isogeometric shape optimization for nonlinear ultrasound focusing ⋮ Tensor train based isogeometric analysis for PDE approximation on parameter dependent geometries

Uses Software

• NLopt

Cites Work

• A Riemannian view on shape optimization
• Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting
• A subdivision-based implementation of the hierarchical b-spline finite element method
• Full analytical sensitivities in NURBS based isogeometric shape optimization
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• A level-set method for vibration and multiple loads structural optimization
• Isogeometric structural shape optimization
• Shapes and Geometries
• An optimal control approach to a posteriori error estimation in finite element methods
• Optimization with PDE Constraints
• Introduction to Shape Optimization
• A priorierror estimates for finite element discretizations of a shape optimization problem
• On Convergence in Elliptic Shape Optimization
• A practical guide to splines.
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