Topological sensitivity analysis and Kohn-Vogelius formulation for detecting a rigid inclusion in an elastic body
type: Item
instance of: scholarly article
title: Topological sensitivity analysis and Kohn-Vogelius formulation for detecting a rigid inclusion in an elastic body
zbMATH Open document ID: 1439.49077
author: Mourad Hrizi
published in: Taiwanese Journal of Mathematics
publication date: 2020-04-23T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.twjm/1565337621
review text: The author explores a now classical method to detect a rigid inclusion immersed in an isotropic elastic body from a single pair of Cauchy data on the boundary of a two-dimensional domain \(\Omega\). To solve this inverse problem, the author introduces a functional à la Kohn-Vogelius, which measures the difference between the solutions of two auxiliary problems. He also computes the so-called topological derivative and propose a non-iterative reconstruction algorithm based on this derivative. More precisely, the aim is to reconstruct the location and shape of a rigid inclusion \(\omega\), with Dirichlet boundary condition on its boundary thanks to over-determined data (given traction and measured displacement field) on the boundary of \(\Omega\). The state equation is the classical linear elasticity with a given traction acting on the boundary \(\partial\Omega\). The theoretical part consists in computing rigorously the topological derivative of the functional using precise asymptotic analysis. In the numerical algorithm, the unknown rigid inclusion is defined by a level curve of a scalar function. The efficiency of the proposed algorithm is illustrated by some numerical examples.
Mathematics Subject Classification ID: 49Q10
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 49Q12
Mathematics Subject Classification ID: 74P15
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 49N45
zbMATH DE Number: 7192943
zbMATH Keywords: shape optimization
zbMATH Keywords: topological optimization
zbMATH Keywords: topological sensitivity analysis
zbMATH Keywords: linear elasticity
zbMATH Keywords: Kohn-Vogelius functional
reviewed by: Antoine Henrot
MaRDI profile type: Publication
OpenAlex ID: W2967728672
cites work: Topological Sensitivity Analysis for the Location of Small Cavities in Stokes Flow
cites work: Topological optimization method for a geometric control problem in Stokes flow
cites work: Numerical size estimates of inclusions in elastic bodies
cites work: Detecting an Inclusion in an Elastic Body by Boundary Measurements
cites work: Shape optimization by the homogenization method
cites work: Damage and fracture evolution in brittle materials by shape optimization methods
cites work: Weak solutions for the exterior Stokes problem in weighted Sobolev spaces
cites work: Boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium
cites work: The direct method of fundamental solutions and the inverse Kirsch-Kress method for the reconstruction of elastic inclusions or cavities
cites work: Complete asymptotic expansions of solutions of the system of elastostatics in the presence of an inclusion of small diameter and detection of an inclusion
cites work: The topological asymptotic for the Navier-Stokes equations
cites work: A new algorithm for topology optimization using a level-set method
cites work: Q5323150
cites work: Topological optimization of structures subject to von Mises stress constraints
cites work: Identification of cavities inside two-dimensional heterogeneous isotropic elastic bodies
cites work: Theoretical Numerical Analysis
cites work: On the first-order shape derivative of the Kohn-Vogelius cost functional of the Bernoulli problem
cites work: Application of the topological gradient to image restoration and edge detection
cites work: A boundary element formulation for the inverse elastostatics problem (iesp) of flaw detection
cites work: Inverse problems in elasticity
cites work: A new reconstruction method for the inverse source problem from partial boundary measurements
cites work: A new method for inverse electromagnetic casting problems based on the topological derivative
cites work: On the detection of several obstacles in 2D Stokes flow: topological sensitivity and combination with shape derivatives
cites work: Localization of small obstacles in Stokes flow
cites work: Q3993273
cites work: Time domain topological gradient and time reversal analogy: an inverse method for ultrasonic target detection
cites work: On a Kohn-Vogelius like formulation of free boundary problems
cites work: The topological asymptotic for PDE systems: The elasticity case
cites work: Topological sensitivity analysis of inclusion in two-dimensional linear elasticity
cites work: The Topological Asymptotic Expansion for the Dirichlet Problem
cites work: Topological Sensitivity and Shape Optimization for the Stokes Equations
cites work: The topological asymptotic expansion for the Quasi-Stokes problem
cites work: Q5323159
cites work: A new reconstruction method for a parabolic inverse source problem
cites work: Boundary integral equations
cites work: Nondestructive cavity identification in structures
cites work: Relaxation of a variational method for impedance computed tomography
cites work: A new spatial regularization scheme for the identification of the geometric shape of an inclusion in a finite body
cites work: Identification of material properties and cavities in two-dimensional linear elasticity
cites work: The topological asymptotic expansion for the Maxwell equations and some applications
cites work: Q4216744
cites work: Detecting rigid inclusions, or cavities, in an elastic body
cites work: Uniqueness and stability in determining a rigid inclusion in an elastic body
cites work: Identification of Lame Parameters by Boundary Measurements
cites work: Topological derivatives in shape optimization
cites work: Optimization algorithms for identification inverse problems with the boundary element method
cites work: The Topological Asymptotic for the Helmholtz Equation
cites work: Identification of a spheroidal defect in an elastic solid using a reciprocity gap functional
cites work: On the Topological Derivative in Shape Optimization
DOI: 10.11650/TJM/190705
description: scientific article; zbMATH DE number 7192943