Invariant solutions and constitutive laws for a nonlinear elastic rod of variable cross-section

Summary A group analysis approach is developed for the model describing a non linear elastic rod of variable cross-section. Thus, some sets of exact invariant solutions to the system of governing equations are obtained.Meanwhile, via the group theoretic methods considered herein, possible functional forms of the stress-strain laws as well as the cross-section area are characterized.

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Riassunto In questo lavoro si considera, nell'ambito della teoria dei gruppi di trasformazioni infinitesime, il modello che descrive una corda elastica non lineare di sezione variabile. In talmodo è possibile ottenere delle classi di soluzioni esatte per il sistema differenziale in esame. Inoltre la richiesta di invarianza del modello considerato rispetto a gruppi di transformazione consente di caratterizzare delle classi di legami costitutivi per lo stress e l'area.

     

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Theoretical and Mathematical Physics -     

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