Adaptive finite element methods for shape optimization of linearly elastic structures

DOI10.1016/0045-7825(86)90071-XzbMath0578.73081OpenAlexW2079140771MaRDI QIDQ1066724

John E. Taylor, Toshikazu Torigaki, Noboru Kikuchi, Kyoon Yang Chung

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1016/0045-7825(86)90071-x

zbMATH Keywords

optimal shape designremeshinginterpolation errornecessary conditionlinearly elastic structuresdesign changeGrid adaptive methods combined with means of automatic remeshingobjective function that reflects the discretization errorperformed at intermediate stages of the overall solution processquantitative effect of element distortion

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Optimization problems in solid mechanics (74P99)

Related Items

Generalized implicit function theorems and problems with a free boundary ⋮ Generating optimal topologies in structural design using a homogenization method ⋮ State space Newton's method for topology optimization ⋮ An integrated approach to shape optimization and mesh adaptivity based on material residual forces ⋮ Shape optimization in laminated composite plates ⋮ Relaxed error control in shape optimization that utilizes remeshing ⋮ Nonparametric gradient-less shape optimization for real-world applications ⋮ A gradient-based, parameter-free approach to shape optimization ⋮ Large-scale stochastic topology optimization using adaptive mesh refinement and coarsening through a two-level parallelization scheme ⋮ An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations ⋮ A fictitious energy approach for shape optimization ⋮ Integrated topology and boundary shape optimization of 2-D solids ⋮ A structural optimization method based on the level set method using a new geometry-based re-initialization scheme ⋮ Optimal shape design in biomimetics based on homogenization and adaptivity ⋮ Shape optimization of elasto-plastic structures and continua ⋮ Sensitivity analysis of linear elastic systems using domain parameterization and a mixed mutual energy principle

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Variational approach by means of adjoint systems to structural optimization and sensitivity analysis. I. Variation of material parameters within fixed domain
• Adaptive grid-design methods for finite element analysis
• Variational approach by means of adjoint systems to structural optimization and sensitivity analysis. II. Structure shape variation
• Error estimates for the combined h and p versions of the finite element method
• On optimal structural remodeling
• Numerical solution of the quasilinear Poisson equation in a nonuniform triangle mesh
• A procedure to obtain a fully stressed shape of elastic continuum
• Multiparameter shape optimization of elastic bars in torsion
• Two-dimensional shape optimal design by the finite element method
• The synthesis of near-optimum finite element meshes with interactive computer graphics
• On the rates of convergence of the finite element method
• The hierarchical concept in finite element analysis
• On the optimum shape of fillets in plates subjected to multiple in‐plane loading cases
• An optimization procedure for stress concentrations by the finite element technique
• Error Estimates for Adaptive Finite Element Computations