Topological sensitivity analysis and Kohn-Vogelius formulation for detecting a rigid inclusion in an elastic body

DOI10.11650/tjm/190705zbMath1439.49077OpenAlexW2967728672MaRDI QIDQ1988615

Mourad Hrizi

Publication date: 23 April 2020

Published in: Taiwanese Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.twjm/1565337621

zbMATH Keywords

linear elasticityshape optimizationtopological optimizationKohn-Vogelius functionaltopological sensitivity analysis

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Inverse problems for PDEs (35R30) Optimization of shapes other than minimal surfaces (49Q10) Topological methods for optimization problems in solid mechanics (74P15) Inverse problems in optimal control (49N45) Sensitivity analysis for optimization problems on manifolds (49Q12)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the detection of several obstacles in 2D Stokes flow: topological sensitivity and combination with shape derivatives
• Topological optimization of structures subject to von Mises stress constraints
• Application of the topological gradient to image restoration and edge detection
• Topological sensitivity analysis of inclusion in two-dimensional linear elasticity
• A new method for inverse electromagnetic casting problems based on the topological derivative
• Damage and fracture evolution in brittle materials by shape optimization methods
• On a Kohn-Vogelius like formulation of free boundary problems
• Detecting rigid inclusions, or cavities, in an elastic body
• Boundary integral equations
• Time domain topological gradient and time reversal analogy: an inverse method for ultrasonic target detection
• Topological optimization method for a geometric control problem in Stokes flow
• Nondestructive cavity identification in structures
• Complete asymptotic expansions of solutions of the system of elastostatics in the presence of an inclusion of small diameter and detection of an inclusion
• Identification of material properties and cavities in two-dimensional linear elasticity
• Identification of cavities inside two-dimensional heterogeneous isotropic elastic bodies
• Optimization algorithms for identification inverse problems with the boundary element method
• Topological derivatives in shape optimization
• On the first-order shape derivative of the Kohn-Vogelius cost functional of the Bernoulli problem
• The direct method of fundamental solutions and the inverse Kirsch-Kress method for the reconstruction of elastic inclusions or cavities
• A new algorithm for topology optimization using a level-set method
• The Topological Asymptotic for PDE Systems: The Elasticity Case
• Boundary Integral Formulae for the Reconstruction of Imperfections of Small Diameter in an Elastic Medium
• Localization of small obstacles in Stokes flow
• Topological Sensitivity Analysis for the Location of Small Cavities in Stokes Flow
• The topological asymptotic for the Navier-Stokes equations
• Identification of a spheroidal defect in an elastic solid using a reciprocity gap functional
• Theoretical Numerical Analysis
• Uniqueness and stability in determining a rigid inclusion in an elastic body
• Relaxation of a variational method for impedance computed tomography
• On the Topological Derivative in Shape Optimization
• A boundary element formulation for the inverse elastostatics problem (iesp) of flaw detection
• Identification of Lame Parameters by Boundary Measurements
• The Topological Asymptotic for the Helmholtz Equation
• Detecting an Inclusion in an Elastic Body by Boundary Measurements
• Topological Sensitivity and Shape Optimization for the Stokes Equations
• Numerical size estimates of inclusions in elastic bodies
• Inverse problems in elasticity
• The topological asymptotic expansion for the Maxwell equations and some applications
• The Topological Asymptotic Expansion for the Dirichlet Problem
• A new spatial regularization scheme for the identification of the geometric shape of an inclusion in a finite body
• Weak solutions for the exterior Stokes problem in weighted Sobolev spaces
• A new reconstruction method for a parabolic inverse source problem
• The topological asymptotic expansion for the Quasi-Stokes problem
• A new reconstruction method for the inverse source problem from partial boundary measurements
• Shape optimization by the homogenization method