Shape sensitivity analysis for elastic structures with generalized impedance boundary conditions of the Wentzell type -- application to compliance minimization

DOI10.1007/s10659-018-9692-3zbMath1428.35573OpenAlexW2614393551WikidataQ129251692 ScholiaQ129251692MaRDI QIDQ2424203

Djalil Kateb, Fabien Caubet, Frédérique Le Louër

Publication date: 24 June 2019

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10659-018-9692-3

zbMATH Keywords

linear elasticityasymptotic analysisgeneralized impedance boundary conditionsshape sensitivity analysiscompliance minimizationshape calculusWentzell conditions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Classical linear elasticity (74B05) Asymptotic expansions of solutions to PDEs (35C20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Optimization of shapes other than minimal surfaces (49Q10) Compliance or weight optimization in solid mechanics (74P05) PDEs in connection with mechanics of deformable solids (35Q74) Sensitivity analysis for optimization problems on manifolds (49Q12)

Related Items

Shape sensitivity of eigenvalue functionals for scalar problems: computing the semi-derivative of a minimum, Reilly-type inequalities for Paneitz and Steklov eigenvalues, Thin layer approximations in mechanical structures: the Dirichlet boundary condition case, An Inverse Parameter Problem with Generalized Impedance Boundary Condition for Two-Dimensional Linear Viscoelasticity, Shape Derivative for Some Eigenvalue Functionals in Elasticity Theory

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Electromagnetic inverse shape problem for coated obstacles
• Shape derivatives of boundary integral operators in electromagnetic scattering. I: Shape differentiability of pseudo-homogeneous boundary integral operators
• Non-reflecting boundary conditions
• Optimal treatment of structures
• Topological sensitivity analysis for three-dimensional linear elasticity problem
• Functional analysis, Sobolev spaces and partial differential equations
• Effective boundary conditions for laminar flows over periodic rough boundaries
• Structural optimization using sensitivity analysis and a level-set method.
• Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness
• Shape variation and optimization. A geometrical analysis
• Topological derivatives in shape optimization
• Effective Boundary Conditions for Thin Ferromagnetic Layers: The One-Dimensional Model
• The Topological Asymptotic for PDE Systems: The Elasticity Case
• A notion of compliance robustness in topology optimization
• Effective transmission conditions for thin-layer transmission problems in elastodynamics. The case of a planar layer model
• Generalized impedance boundary conditions and shape derivatives for 3D Helmholtz problems
• On Simultaneous Identification of the Shape and Generalized Impedance Boundary Condition in Obstacle Scattering
• Simultaneous reconstruction of shape and generalized impedance functions in electrostatic imaging
• A domain derivative-based method for solving elastodynamic inverse obstacle scattering problems
• Generalized impedance boundary condition at high frequency for a domain with thin layer: the circular case
• Direct Methods in the Theory of Elliptic Equations
• GENERALIZED IMPEDANCE BOUNDARY CONDITIONS FOR SCATTERING PROBLEMS FROM STRONGLY ABSORBING OBSTACLES: THE CASE OF MAXWELL'S EQUATIONS
• Inequalities of Korn's type, uniform with respect to a class of domains
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• A nonlinear elliptic boundary value problem related to corrosion modeling
• Introduction to Shape Optimization
• Shape optimization for Navier–Stokes flow
• Integral equation methods for the inverse obstacle problem with generalized impedance boundary condition
• New development in freefem++
• A deterministic approximation method in shape optimization under random uncertainties
• New transmission condition accounting for diffusion anisotropy in thin layers applied to diffusion MRI
• Shape optimization methods for the inverse obstacle problem with generalized impedance boundary conditions
• A Macroscopic Model Including Membrane Exchange for Diffusion MRI
• The Effect of a Thin Coating on the Scattering of a Time-Harmonic Wave for the Helmholtz Equation
• Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
• GENERALIZED IMPEDANCE BOUNDARY CONDITIONS FOR SCATTERING BY STRONGLY ABSORBING OBSTACLES: THE SCALAR CASE
• On the roughness-induced effective boundary conditions for an incompressible viscous flow
• Acoustic and electromagnetic equations. Integral representations for harmonic problems
• Shape optimization by the homogenization method