In this paper, we study the nonlocal linear bending behavior of functionally graded beams subjected to distributed loads. A finite element formulation for an improved first-order shear deformation theory for beams with five independent variables is proposed. The formulation takes into consideration 3D constitutive equations. Eringen's nonlocal differential model is used to rewrite the nonlocal stress resultants in terms of displacements. The finite element formulation is derived by means of the principle of virtual work. High-order nodal-spectral interpolation functions were utilized to approximate the field variables, which minimizes the locking problem. Numerical results and comparisons of the present formulation with those found in the literature for typical benchmark problems involving nonlocal beams are found to be satisfactory and show the validity of the developed finite element model.

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado. / In this research, an improved first order formulation is presented to study the critical buckling load in functionally graded beams. The formulation has five independent variables in comparison with the Timoshenko theory that has three. The Trefftz criterion is utilized with incremental and fundamental states to define the stability analysis. Virtual work statements are derived for the finite element model where the field variables are interpolated by Lagrange polynomials. The numerical results are compared and verified with other formulations found in literature. Parametric studies are also carried out for buckling behavior due to different slenderness ratios, power-law indices and boundary conditions. Applications of the model to functionally graded materials show the validity of the present approach.