On the second order topological asymptotic expansion

DOI10.1007/s00158-009-0436-7zbMath1274.74382OpenAlexW2024377381MaRDI QIDQ381339

Jairo Rocha de Faria, Antonio André Novotny

Publication date: 15 November 2013

Published in: Structural and Multidisciplinary Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00158-009-0436-7

zbMATH Keywords

topological asymptotic expansionfirst order topological derivativesecond order topological derivative

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Topological methods for optimization problems in solid mechanics (74P15)

Related Items

High Order Topological Asymptotics: Reconciling Layer Potentials and Compound Asymptotic Expansions ⋮ Higher order topological derivatives in elasticity ⋮ Topological derivatives of shape functionals. part III: second-order method and applications ⋮ Topological sensitivity analysis for elliptic differential operators of order \(2{m}\) ⋮ Pollution sources reconstruction based on the topological derivative method ⋮ A new method for inverse electromagnetic casting problems based on the topological derivative ⋮ Topological derivative for the inverse conductivity problem: a Bayesian approach

Cites Work

• Unnamed Item
• Unnamed Item
• The elastic energy-momentum tensor
• Topological sensitivity analysis
• The shape and topological optimizations' connection
• Reconstruction of small inhomogeneities from boundary measurements
• Configuration forces as basic concepts of continuum physics
• An introduction to continuum mechanics
• Second order topological sensitivity analysis
• Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction
• On the Topological Derivative in Shape Optimization
• High-Order Terms in the Asymptotic Expansions of the Steady-State Voltage Potentials in the Presence of Conductivity Inhomogeneities of Small Diameter
• The Topological Asymptotic Expansion for the Dirichlet Problem