Abstract
This paper proposes several axiomatic refined theories for the linear static analysis of beams made of functionally graded materials. A bi-directional variation upon the cross-section is accounted for. Via a unified formulation, a generic N-order approximation is assumed for the displacement unknown variables over the beam cross-section. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. A Navier type, closed form solution is adopted. Beams undergo bending and torsional loadings. Deep beams are investigated. Comparisons with three-dimensional finite element models are given. The numerical investigation shows that the proposed unified formulation yields the complete three-dimensional displacement and stress fields as long as the appropriate approximation order is considered.
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