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 m...

In this paper, a three-dimensional numerical solution for the bending study of laminated composite doubly-curved shells is presented. The partial differential equations are solved analytically by the Navier summation for the midsurface variables; this method is only valid for shells with constant curvature where boundary conditions are considered simply supported. The partial differential equations present different coefficients, which depend on the thickness coordinates. A semi-analytical solution and the so-called Differential Quadrature Method are used to calculate an approximated derivative of a certain function by a weighted summation of the function evaluated in a certain grin domain. Each layer is discretized by a grid point distribution such as: Chebyshev-Gauss-Lobatto, Legendre, Ding and Uniform. As part of the formulation, the inter-laminar continuity conditions of displacement...

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado.

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado.

This study presents a static analysis of laminated composite doubly curved shells using a refined kinematic model with polynomial and non-polynomial functions. In particular Maclaurin, trigonometric, exponential and zig-zag functions are employed. Refined models are based on the Equivalent Single Layer theories and obtained by using Carrera Unified formulation. The shell model is subjected to different mechanical loading such as bi-sinusoidal, uniform and point load. The governing equations are derived from the principle of virtual displacement and solved via Navier-Type closed form solutions. The results are compared with Layer-wise and higher-order shear deformation solutions available in the literature. It is shown that refined models with non-polynomial terms are capable of accurately predicting the through-the-thickness displacements and stress distributions with a low computational...

This paper presents a static analysis of functionally graded single and sandwich beams by using an efficient 7DOFs quasi-3D hybrid type theory. The governing equations are derived by employing the principle of virtual works in a weak form and solved by means of the Finite Element Method (FEM). A C1 cubic Hermite interpolation is used for the vertical deflection variables while C0 linear interpolation is employed for the other kinematics variables. Convergence rates are studied in order to validate the finite element technique. Numerical results of the present formulation are compared with analytical and FEM solutions available in the literature.