Simulation of constrained elastic curves and application to a conical sheet indentation problem

DOI10.1093/IMANUM/DRAB008zbMATH Open1502.65113arXiv2004.11089OpenAlexW3129285798MaRDI QIDQ5077056

Sören Bartels

Publication date: 17 May 2022

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Abstract: We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence. The stability of semi-implicit discretizations of gradient flows is investigated which provide a practical method to determine stationary configurations. A particular application of the considered models arises in the description of conical sheet deformations.

Full work available at URL: https://arxiv.org/abs/2004.11089

zbMATH Keywords

discretizationelasticityrodssurfacesconical sheets

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Elastic materials (74B99) PDEs in connection with mechanics of deformable solids (35Q74) PDE constrained optimization (numerical aspects) (49M41)

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