Boundary optimal control of a dynamic frictional contact problem
Zijia Peng, Piotr Gamorski, Stanisław Migórski
2020ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik17 citationsDOIOpen Access PDF
Abstract
Abstract In this paper we study boundary optimal control of an evolutionary system governed by a history‐dependent variational‐hemivariational inequality. The inequality is a weak formulation of a dynamic frictional contact problem for a viscoelastic body with a multivalued normal damped response condition and a simplified version of the Coulomb law of dry friction. A continuous dependence result for the solution map is proved and the existence of optimal solutions to the control problem is established.
Topics & Concepts
Variational inequalityBoundary (topology)ViscoelasticityCoulomb frictionOptimal controlMathematicsDry frictionCoulombBoundary value problemCoulomb's lawMathematical analysisControl (management)Classical mechanicsControl theory (sociology)Applied mathematicsMathematical optimizationPhysicsComputer scienceNonlinear systemMaterials scienceThermodynamicsQuantum mechanicsArtificial intelligenceComposite materialElectronContact Mechanics and Variational InequalitiesMechanical stress and fatigue analysisElasticity and Material Modeling