Evaluation of stress distributions in the geometrical nonlinear regime of functionally graded structures

In this study, stresses distributions in the large deflection field of Functionally Graded (FG) structures are investigated. Numerical simulations are carried out using one-dimensional (1D) models combining the Finite Element Method (FEM) and Carrera Unified Formulation (CUF) to evaluate the three-dimensional (3D) displacement field over the cross-section, employing Lagrange and Taylor polynomials. Then, the geometrical nonlinear relations are solved with the Newton-Raphson linearization and constrained with an arc-length method. The nonlinear behavior of cantilever beams undergoing bending and compression loading conditions is calculated. The results show the influence of the adopted theory to approximate the displacement field over the cross-section on FG beams. According to the results of this study, it is emphasized that geometrical nonlinearities should be taken into consideration in the evaluation of stress distributions in FG structures.