Topological Derivatives in Shape Optimization

• Main Authors: Novotny, Antonio André (Author), Sokołowski, Jan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Series: Interaction of Mechanics and Mathematics,
• Subjects: Engineering.; Mathematical physics.; Computer mathematics.; Mechanics.; Mechanics, Applied.; Theoretical and Applied Mechanics.; Computational Science and Engineering.; Mathematical Applications in the Physical Sciences.

The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, t...

Table of Contents:

• Domain Derivation in Continuum Mechanics
• Material and Shape Derivatives for Boundary Value Problems
• Singular Perturbations of Energy Functionals
• Configurational Perturbations of Energy Functionals
• Topological Derivative Evaluation with Adjoint States
• Topological Derivative for Steady-State Orthotropic Heat Diffusion Problems
• Topological Derivative for Three-Dimensional Linear Elasticity Problems
• Compound Asymptotic Expansions for Spectral Problems
• Topological Asymptotic Analysis for Semilinear Elliptic Boundary Value Problems
• Topological Derivatives for Unilateral Problems.