Asymptotic Analysis, Polarization Matrices, and Topological Derivatives for Piezoelectric Materials with Small Voids

DOI10.1137/08073367XzbMath1204.35158arXiv0910.1474OpenAlexW3104945382MaRDI QIDQ3060374

Giuseppe Cardone, Sergueï A. Nazarov, Jan Sokolowski

Publication date: 3 December 2010

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.1474

zbMATH Keywords

asymptotic analysis shape optimization optimum design electric enthalpy piezoelectricity topological derivative polarization matrix

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Optimization of shapes other than minimal surfaces (49Q10) Electromagnetic theory (general) (78A25) Existence theories for optimal control problems involving partial differential equations (49J20) Optimization problems in optics and electromagnetic theory (78M50) Topological and monotonicity methods applied to PDEs (35A16)

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One-Sided Derivative of Parametrized Minima for Shape and Topological Derivatives ⋮ Spectral gaps for periodic piezoelectric waveguides ⋮ On shape optimization for an evolution coupled system ⋮ Topological derivatives of shape functionals. I: Theory in singularly perturbed geometrical domains ⋮ Spectra of open waveguides in periodic media ⋮ Sensitivity analysis of hyperbolic optimal control problems ⋮ The Eshelby theorem and its variants for piezoelectric media ⋮ Energy change to insertion of inclusions associated with a diffusive/convective steady-state heat conduction problem ⋮ Topological sensitivity analysis in heterogeneous anisotropic elasticity problem. Theoretical and computational aspects ⋮ On topological derivatives for contact problems in elasticity

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