Beam finite element for modal analysis of FGM structures

In this contribution, a homogenized beam finite element for modal analysis considering a double symmetric cross-section made of a Functionally Graded Material (FGM) is presented. The material properties in a real beam can vary continuously in longitudinal direction while the variation with respect to the transversal and lateral directions is assumed to be symmetric in a continuous or discontinuous manner. The shear force deformation effect and the effect of longitudinally varying inertia and rotary inertia are taken into account. Additionally, the longitudinally varying Winkler elastic foundation and the effect of internal axial forces are included in the finite element equations as well. Homogenization of spatially varying material properties to effective quantities with a longitudinal variation is done by extended mixture rules and the multilayer method (MLM). For the homogenized beam the 12 x 12 finite element matrix, consisting of the effective linearized stiffness and consistent mass inertia terms, is established. Numerical experiments are done considering modal analyses of single FGM beams and spatial beam structures with a spatial varying FGM to show the accuracy and effectiveness of the new FGM beam finite element. The finite beam element can also be used for static and buckling analysis of single beams and spatial beam structures, which will be presented in our future works. (C) 2016 Elsevier Ltd. All rights reserved.