An integrated approach to shape optimization and mesh adaptivity based on material residual forces

DOI10.1016/j.cma.2014.06.010zbMath1423.74915OpenAlexW2166636141MaRDI QIDQ1667350

Stefan Riehl, Paul Steinmann

Publication date: 28 August 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.2014.06.010

zbMATH Keywords

shape optimizationadaptive finite elementstraction methodmaterial force method

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Topological methods for optimization problems in solid mechanics (74P15) Sensitivity analysis for optimization problems on manifolds (49Q12)

Related Items

Level set based shape optimization using trimmed hexahedral meshes ⋮ A staggered approach to shape and topology optimization using the traction method and an evolutionary-type advancing front algorithm

Uses Software

• deal.ii

Cites Work

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• The \texttt{deal.II} library, version 8.4
• Shape optimization of continua using NURBS as basis functions
• Goal-oriented \(r\)-adaptivity based on variational arguments in the physical and material spaces
• On material forces and finite element discretizations
• On a solution strategy for energy-based mesh optimization in finite hyperelastostatics
• Energy-based r-adaptivity: a solution strategy and applications to fracture mechanics
• Variational design sensitivity analysis in the context of structural optimization and configurational mechanics
• On boundary potential energies in deformational and configurational mechanics
• A combined \(r-h\) adaptive strategy based on material forces and error assessment for plane problems and bimaterial interfaces
• On variational sensitivity analysis and configurational mechanics
• Adaptive finite element methods for shape optimization of linearly elastic structures
• Computational methods for inverse finite elastostatics
• Application of material forces to hyperelastostatic fracture mechanics. I: Continuum mechanical setting
• On the discrete variant of the traction method in parameter-free shape optimization
• Use of material forces in adaptive finite element methods
• An ALE formulation based on spatial and material settings of continuum mechanics. I: Generic hyperelastic formulation
• An ALE formulation based on spatial and material settings of continuum mechanics. II: Classification and applications
• A SMOOTHING METHOD FOR SHAPE OPTIMIZATION: TRACTION METHOD USING THE ROBIN CONDITION
• Configurational variations for the primal and dual problem in elasticity
• On the numerical implementation of variational arbitrary Lagrangian–Eulerian (VALE) formulations
• deal.II—A general-purpose object-oriented finite element library
• On configurational forces in the context of the finite element method
• Adaptive finite element method for shape optimization
• The gradient of the finite element variational indicator with respect to nodal and applications in fracture mechanics and mesh optimization
• A variational r‐adaption and shape‐optimization method for finite‐deformation elasticity
• Solution to shape optimization problems of viscous flow fields
• The force on an elastic singularity
• Application of material forces to hyperelastostatic fracture mechanics. II: Computational setting.