Shape Optimization for a Class of Semilinear Variational Inequalities with Applications to Damage Models

DOI10.1137/16M1057759zbMath1350.49063arXiv1601.04136MaRDI QIDQ2827753

Kevin Sturm, Christian Heinemann

Publication date: 21 October 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.04136

zbMATH Keywords

Banach spaceselasticityobstacle problemsshape optimizationsemilinear elliptic variational inequalitiesdamage phase field models

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Optimality conditions for problems involving partial differential equations (49K20) Variational inequalities (49J40) Optimization of shapes other than minimal surfaces (49Q10) Existence theories for problems in abstract spaces (49J27) Brittle damage (74R05) Elastic materials (74B99) Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators (35J87) Semilinear elliptic equations (35J61)

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Cites Work

• Shape optimization in 2D contact problems with given friction and a solution-dependent coefficient of friction
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• Variation and optimization of formes. A geometric analysis
• Existence results for diffuse interface models describing phase separation and damage
• Shape Optimization with Nonsmooth Cost Functions: From Theory to Numerics
• Shapes and Geometries
• Optimal Shape Design Subject to Elliptic Variational Inequalities
• First-Order Optimality Conditions for Elliptic Mathematical Programs with Equilibrium Constraints via Variational Analysis
• A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media
• Shape Optimization in Contact Problems with Coulomb Friction
• Shape Optimization in Contact Problems with Coulomb Friction and a Solution-Dependent Friction Coefficient
• Optimal Control in Some Variational Inequalities
• Numerical Solution of 2D Contact Shape Optimization Problems Involving a Solution-Dependent Coefficient of Friction
• Measure and integration theory
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