Approximation of an Elastic Rod with Self-Contact

Kathleen A. Hoffman () and Thomas I. Seidman ()
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Kathleen A. Hoffman: University of Maryland, Baltimore County
Thomas I. Seidman: University of Maryland, Baltimore County

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 3, No 10, 1021 pages

Abstract: Abstract The variational formulation of an elastic rod with an impenetrable surface surrounding the centerline corresponds to a nonsmooth optimization of cost functional $$\mathcal {J}$$ J with nonconvex inequality constraints and so presents many analytical and computational challenges in approximating the minima. We construct a sequence of approximate variational cost functionals $$\mathcal {J}_k$$ J k , corresponding to elastic rods with infinite energy barriers that enforce impenetrability constraints. Using this construction, we show strong convergence of minimizing configurations of $$\mathcal {J}_k$$ J k to the minimizer of $$\mathcal {J}$$ J and weak* convergence in $$[C(0,1)]^*$$ [ C ( 0 , 1 ) ] ∗ of contact forces induced by the repulsive potential to the contact forces of the minimizing configurations of $$\mathcal {J}$$ J .

Keywords: Elastic rod; Contact; Non-smooth optimization; Approximation; Forces; 49M30; 65K10; 74B20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02002-5

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