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Shape and topology optimization (Q2235778)

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Language	Label	Description	Also known as
English	Shape and topology optimization	scientific article

Statements

scholarly article

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Shape and topology optimization (English)

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Grégoire Allaire

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Charles Dapogny

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François Jouve

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publication date

21 October 2021

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zbMATH Keywords

shape optimization

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topology optimization

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partial differential equations

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level set method

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Hadamard method

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mesh deformation

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mesh modification

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1016/bs.hna.2020.10.004

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Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes

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Shape optimization by the homogenization method

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Optimal treatment of structures

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A linearized approach to worst-case design in parametric and geometric shape optimization

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A deterministic approximation method in shape optimization under random uncertainties

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Multi-phase structural optimization<i>via</i>a level set method

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Structural optimization under overhang constraints imposed by additive manufacturing technologies

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Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh

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Shape optimization with a level set based mesh evolution method

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Topology optimization of modulated and oriented periodic microstructures by the homogenization method

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Taking into account thermal residual stresses in topology optimization of structures built by additive manufacturing

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A level-set method for vibration and multiple loads structural optimization

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Minimum stress optimal design with the level set method

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A level-set method for shape optimization.

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Structural optimization using sensitivity analysis and a level-set method.

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Damage and fracture evolution in brittle materials by shape optimization methods

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Structural optimization with FreeFem++

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An optimal design problem with perimeter penalization

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Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

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Analysis of a level set method for topology optimization

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A new algorithm for topology optimization using a level-set method

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A notion of compliance robustness in topology optimization

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A consistent relaxation of optimal design problems for coupling shape and topological derivatives

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Efficient topology optimization in MATLAB using 88 lines of code

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Shape deformation analysis from the optimal control viewpoint

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Image Segmentation Using Active Contours: Calculus of Variations or Shape Gradients?

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Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains

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Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations

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Generating optimal topologies in structural design using a homogenization method

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Material interpolation schemes in topology optimization

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Phase-field Approaches to Structural Topology Optimization

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Filters in topology optimization

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Design-dependent loads in topology optimization

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Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations

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Variational methods in shape optimization problems

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An accurate anisotropic adaptation method for solving the level set advection equation

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A framework for the construction of level set methods for shape optimization and reconstruction

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Incorporating topological derivatives into level set methods.

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Phase‐Field Relaxation of Topology Optimization with Local Stress Constraints

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Cut topology optimization for linear elasticity with coupling to parametric nondesign domain regions

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Representation of equilibrium solutions to the table problem for growing sandpiles

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Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût

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A discrete level-set topology optimization code written in Matlab

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Level set topology optimization of fluids in Stokes flow

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A density result in two-dimensional linearized elasticity, and applications

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Level set based robust shape and topology optimization under random field uncertainties

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On the existence of a solution in a domain identification problem

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Topology optimization using a reaction-diffusion equation

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Computing minimal surfaces via level set curvature flow

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Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems

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Computation of the signed distance function to a discrete contour on adapted triangulation

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Robust shape and topology optimization of nanophotonic devices using the level set method

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Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization

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Shape and topology optimization of the robust compliance<i>via</i>the level set method

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Isogeometric analysis for topology optimization with a phase field model

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Shapes and Geometries

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Shape-topology optimization of Stokes flow via variational level set method

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Shape optimization of a coupled thermal fluid-structure problem in a level set mesh evolution framework

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A variational formulation for computing shape derivatives of geometric constraints along rays

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Phase-field based topology optimization with polygonal elements: a finite volume approach for the evolution equation

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The Topological Asymptotic for PDE Systems: The Elasticity Case

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3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method

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Achieving minimum length scale in topology optimization using nodal design variables and projection functions

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Confidence structural robust design and optimization under stiffness and load uncertainties

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Robust structural topology optimization considering boundary uncertainties

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Explicit feature control in structural topology optimization via level set method

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Shape variation and optimization. A geometrical analysis

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Comparison of approximate shape gradients

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Level set based method for design of compliant mechanisms

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Computing geodesic paths on manifolds

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Topology optimization with geometric uncertainties by perturbation techniques

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Robust optimal shape design for an elliptic PDE with uncertainty in its input data

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The flexible, extensible and efficient toolbox of level set methods

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Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations

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High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations

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Level set methods for optimization problems involving geometry and constraints. I: Frequencies of a two-density inhomogeneous drum

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Sensitivity of the heat equation to jumps of conductivity

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A Post-Treatment of the Homogenization Method for Shape Optimization

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A new scheme for imposing a minimum length scale in topology optimization

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A computational framework for the regularization of adjoint analysis in multiscale PDE systems.

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Fast Sweeping Methods for Eikonal Equations on Triangular Meshes

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Sparse monolithic compliant mechanisms using continuum structural topology optimization

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A review of level set methods to model interfaces moving under complex physics: Recent challenges and advances

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A Riemannian view on shape optimization

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Fast Marching Methods

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Structural boundary design via level set and immersed interface methods

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On the Topological Derivative in Shape Optimization

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Topological derivatives for elliptic problems

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Semi-Lagrangian methods for level set equations

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On optimal shape design

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Shape and topology optimization based on the phase field method and sensitivity analysis

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Review of options for structural design sensitivity analysis. I: Linear systems

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Density and level set-XFEM schemes for topology optimization of 3-D structures

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On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming

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On projection methods, convergence and robust formulations in topology optimization

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``Color'' level sets: A multi-phase method for structural topology optimization with multiple materials.

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A level set method for structural topology optimization.

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A fast sweeping method for Eikonal equations

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A variational level set method for the topology optimization of steady-state Navier-Stokes flow

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Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives

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Identifiers

zbMATH Open document ID

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10.1016/bs.hna.2020.10.004

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2235778

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