Affiliations: Departamento de Matemática Aplicada, Uniuersidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain, and Departamento de Matemáticas, Uniuersidad de La Coruña, Campus da Zapateira s/n, 15071 La Coruña, Spain | Departamento de Matemática Aplicada, Uniuersidad de Santiago de Compos tela, 15706 Santiago de Compostela, Spain
Note: [] This work is part of the project “Junctions in Elastic Multistructures” of the Programme “S.C.I.E.N.C.E.” of the Commission of the European Communities Contract No. SCI*0473-C (EDB).
Note: [] Correspondence to: J.A. Alvarez-Dios, Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain.
Abstract: We use asymptotic techniques on a re-scaled three-dimensional linear elasticity model to justify and generalise models describing the elastic behaviour of rods, taking into account the nonhomogeneity and anisotropy of the material they are made of. General bending models for nonhomogeneous anisotropic rods are obtained as the limit of the tridimensional elasticity model when the cross section area tends to zero. We also include convergence results mathematically justifying the method. Next, by identification of second-order terms in the asymptotic expansion we obtain a general theory for transversally nonhomogeneous isotropic rods taking into account Timoshenko and Saint Venant's effects.
