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New Models for Bending and Torsion of Variable Cross Section Rods
Author(s) -
ÁlvarezDios J.A.,
ÁlvarezVázquez L.J.,
Viaño J.M.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199912)79:12<835::aid-zamm835>3.0.co;2-4
Subject(s) - uniqueness , torsion (gastropod) , rod , elasticity (physics) , linear elasticity , mathematics , mathematical analysis , stress field , section (typography) , structural engineering , physics , finite element method , computer science , engineering , medicine , alternative medicine , surgery , pathology , thermodynamics , operating system
In this paper we propose new models for variable cross section rods in both symmetric and nonsymmetric cases. These models have been obtained from the three‐dimensional linear elasticity model by using an asymptotic method where the small parameter is the area of the cross section. In this way we succeed in characterizing the first‐ and second‐order displacements and the first‐order stress field. We shall also prove existence, uniqueness, and convergence results for the solution of both limit models.