期刊
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
卷 2, 期 1, 页码 117-143出版社
IMPERIAL COLLEGE PRESS
DOI: 10.1142/S1758825110000500
关键词
Beam structures; Hierarchical modelling; Closed form solution
类别
资金
- Ministere de la Culture, de l'Enseignement Superieuer et de la Recherche of Luxembourg [TR-PDR BFR07-136]
This paper proposes several axiomatic refined theories for the linear static analysis of beams made of isotropic materials. A hierarchical scheme is obtained by extending plates and shells Carrera's Unified Formulation (CUF) to beam structures. An N-order approximation via Mac Laurin's polynomials is assumed on the cross-section for the displacement unknown variables. N is a free parameter of the formulation. Classical beam theories, such as Euler-Bernoulli's and Timoshenko's, are obtained as particular cases. According to CUF, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The governing differential equations are solved via the Navier type, closed form solution. Rectangular and I-shaped cross-sections are accounted for. Beams undergo bending and torsional loadings. Several values of the span-to-height ratio are considered. Slender as well as deep beams are analysed. Comparisons with reference solutions and three-dimensional FEM models are given. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and loading conditions.
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