A variational characterization of a hyperelastic rod with hard self-contact

We consider an elastic rod, modeled as a curve in space with an impenetrable surrounding tube of radius  ρ , subject to a general class of boundary conditions. The impossibility of self-intersection is then imposed as a family of scalar constraints on the physical separation of nonlocal pairs of poi...

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Vydáno v:Nonlinear analysis Ročník 74; číslo 16; s. 5388 - 5401
Hlavní autoři: Hoffman, Kathleen A., Seidman, Thomas I.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier Ltd 01.11.2011
Elsevier
Témata:
Calculus of variations and optimal control
Contact
Derivation
Elastic rod
Energy of formation
Exact sciences and technology
Homotopy class
Mathematical analysis
Mathematical models
Mathematics
Non-smooth optimization
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Optimization
Regularity
Scalars
Sciences and techniques of general use
Tubes
Elastic rod
Homotopy class
Non-smooth optimization
Necessary condition
Homotopy
Nonlinear analysis
Optimization method
Optimality condition
Boundary condition
Mathematical model
ISSN:0362-546X, 1873-5215
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Popis
Shrnutí:We consider an elastic rod, modeled as a curve in space with an impenetrable surrounding tube of radius  ρ , subject to a general class of boundary conditions. The impossibility of self-intersection is then imposed as a family of scalar constraints on the physical separation of nonlocal pairs of points on the rod. Thus, the usual variational formulation of energy minimization is considered in a context of nonconvex, nonsmooth optimization. We show the existence of minimizers within suitably defined homotopy classes associated with both the centerline and the frame along the rod. The principle results are then concerned with derivation of first-order necessary conditions for optimality and some consequences of these for the contact forces and for regularity.
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2011.05.022