Cavity identification in linear elasticity and thermoelasticity

DOI10.1002/mma.772zbMath1118.35064OpenAlexW1973442249MaRDI QIDQ5293184

Benjamin Hackl, Martin Burger, Hend Ben Ameur

Publication date: 26 June 2007

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.772

zbMATH Keywords

uniquenessiterative regularizationshape derivativesshape identificationstability estimatesleast-squares formulation

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Inverse problems for PDEs (35R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (12)

Land-sea interface identification and submarine groundwater exchange (SGE) estimation ⋮ Defect detection using Cauchy data on a part of outer boundary of an elastic body ⋮ An energy gap functional: cavity identification in linear elasticity ⋮ A phase-field approach for detecting cavities via a Kohn–Vogelius type functional ⋮ Identification of cavities and inclusions in linear elasticity with a phase-field approach ⋮ Cavity identification in elastic structures by explicit domain mapping and boundary mode sensitivity analysis ⋮ Recovering elastic inclusions by shape optimization methods with immersed finite elements ⋮ Shape optimization approach to defect-shape identification with convective boundary condition via partial boundary measurement ⋮ A practical meshfree inverse method for identification of thermo-mechanical fracture load of a body by examining the crack path in the body ⋮ Shape sensitivity analysis for identification of voids under Navier's boundary conditions in linear elasticity ⋮ Reconstruction of an ellipsoidal defect in anisotropic elastic solid, using results of one static test ⋮ Cavities identification in linear elasticity: energy-gap versus L²-gap cost functionals

Cites Work

• Unnamed Item
• Inverse acoustic and electromagnetic scattering theory.
• A framework for the construction of level set methods for shape optimization and reconstruction
• A level set method for inverse problems
• An Introduction to Classical Inverse Eigenvalue Problems
• Shapes and Geometries
• Level set methods for geometric inverse problems in linear elasticity
• Schiffer's theorem in inverse scattering theory for periodic structures
• Examples of instability in inverse boundary-value problems

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