Optimal control of inclusion and crack shapes in elastic bodies

DOI10.1007/s10957-012-0053-2zbMath1287.49046OpenAlexW2021591700MaRDI QIDQ1934639

Günter R. Leugering, Maria Specovius-Neugebauer, Alexandr Mikhailovich Khludnev

Publication date: 29 January 2013

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-012-0053-2

zbMATH Keywords

variational inequalityoptimal control problemrigid inclusionnonpenetration conditioninclusion shape

Mathematics Subject Classification ID

Variational inequalities (49J40) Optimization of shapes other than minimal surfaces (49Q10) Existence theories for optimal control problems involving partial differential equations (49J20) Sensitivity analysis for optimization problems on manifolds (49Q12)

Related Items (14)

Optimal control of rigidity parameters of thin inclusions in composite materials ⋮ A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media ⋮ Crack growth control based on the topological derivative of the Rice's integral ⋮ First‐order and second‐order sensitivity analyses for a body with a thin rigid inclusion ⋮ Necessary conditions of first-order for an optimal boundary control problem for viscous damage processes in 2D ⋮ Shape- and Topology Optimization for Passive Control of Crack Propagation ⋮ Shape sensitivity analysis of Timoshenko's plate with a crack under the nonpenetration condition ⋮ On crack propagations in elastic bodies with thin inclusions ⋮ Multimaterial topology optimization of contact problems using phase field regularization ⋮ Equilibrium problem for a Timoshenko plate with an oblique crack ⋮ First-order shape derivative of the energy for elastic plates with rigid inclusions and interfacial cracks ⋮ Rigidity parameter identification for thin inclusions located inside elastic bodies ⋮ A Shape-Topological Control Problem for Nonlinear Crack-Defect Interaction: The Antiplane Variational Model ⋮ Control of crack propagation by shape-topological optimization

Cites Work

• On the active control of crack growth in elastic media
• On the equilibrium of elastic bodies containing thin rigid inclusions
• On the control of crack growth in elastic media
• On safe crack shapes in elastic bodies
• Simulation of fracture in heterogeneous elastic materials with cohesive zone models
• On elastic bodies with thin rigid inclusions and cracks
• Optimal control of cracks in elastic bodies with thin rigid inclusions
• Optimal Shape Design Subject to Elliptic Variational Inequalities
• Relaxation of an optimal design problem in fracture mechanic: the anti-plane case
• Differentiation of Energy Functionals in Two-Dimensional Elasticity Theory for Solids with Curvilinear Cracks
• Derivatives of the energy functional for 2D-problems with a crack under Signorini and friction conditions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Optimal control of inclusion and crack shapes in elastic bodies