A homotopy method applied to elastica problems

DOI10.1016/0020-7683(81)90044-5zbMath0452.73071OpenAlexW2064082539MaRDI QIDQ1148732

Layne T. Watson, Chang Yi Wang

Publication date: 1981

Published in: International Journal of Solids and Structures (Search for Journal in Brave)

Full work available at URL: http://eprints.cs.vt.edu/archive/00000844/

zbMATH Keywords

inverse problemhomotopy methodincompressibleglobally convergent Chow-Yorke algorithmsimple, accurate, stable, and efficient

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Discrete approximations in optimal control (49M25)

Related Items (19)

Asymptotic expansions for the Bessel transformations with high oscillations by using the homotopy technique ⋮ Direct and inverse dynamics of a very flexible beam ⋮ Numerical approximations to integrals with a highly oscillatory Bessel kernel ⋮ Non-linear stochastic dynamics analysis of mechanical systems using non-intrusive polynomial chaos method: application to pole vaulting ⋮ Modern homotopy methods in optimization ⋮ Stability and equilibrium of the straight and curved elastica-finite element computation ⋮ Engineering applications of the Chow-Yorke algorithm ⋮ Overhang of a heavy elastic sheet ⋮ Parameter identification in dynamic systems using the homotopy optimization approach ⋮ Dynamics of a flexible beam and a system of rigid rods, with fully inverse (one-sided) boundary conditions ⋮ A TFC-based homotopy continuation algorithm with application to dynamics and control problems ⋮ Globally convergent homotopy methods: A tutorial ⋮ Asymptotic expansions of Bessel, Anger and Weber transformations ⋮ A simple method for determining large deflection states of arbitrarily curved planar elastica ⋮ Note on the homotopy perturbation method for multivariate vector-value oscillatory integrals ⋮ Effect of flexible joints on the stability and large deflections of a triangular frame ⋮ Numerical approximations for highly oscillatory Bessel transforms and applications ⋮ Free rotation of a circular ring about a diameter ⋮ Creep behaviour of butt-welded joints

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