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A bifurcation problem involving elastica

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Sommario

Si consideri un filo flessibile ed inestensibile di lunghezza assegnata, vincolato agli estremi con angoli prefissati ϑ, − ϑ; 0<ϑ<π.

Vengono determinate le infinite configurazioni del filo aventi momento nullo agli estremi; ognuna di queste è caratterizzata dal numero di volte con cui la curva elastica attraversa il segmento congiungente gli estremi del filo. Allorché la lunghezza del filo viene perturbata si dimostra che in corrispondenza di ogni configurazione con momento nullo agli estremi (denominata «inflexional elastica» in [4]) nascono due nuove configurazioni del filo aventi agli estremi momento diverso da zero (denominate «non inflexional elastica» in [4]).

Summary

A flexible inextensible elastica has been considered, with fixed end points and fixed equal end slopes, and varying length. The existence of at least one elastic curve has been proved when the elastica length is greater than the distance between the end points. A critical value of the length has been found, as a function of the given end slope only, corresponding to some elastic curves. From each of them two new elastic curves branch when the length is greater than the critical value.

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References

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Authors and Affiliations

  1. Researcher of Consiglio Nazionale delle Ricerche of Italy, at Istituto di Calcoli Numerici of Università di Torino, Italy

    B. Gabutti

Authors
  1. B. Gabutti
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  2. P. Lepora
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  3. G. Merlo
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Additional information

Member of Consiglio Nazionale delle Ricerche of Italy — Gruppo di Informatica Matematica.

Member of Consiglio Nazionale delle Ricerche of Italy — Gruppo di Informatica Matematica — Professor at Istituto Matematico del Politecnico di Torino.

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Gabutti, B., Lepora, P. & Merlo, G. A bifurcation problem involving elastica. Meccanica 15, 154–165 (1980). https://doi.org/10.1007/BF02128926

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  • DOI: https://doi.org/10.1007/BF02128926

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