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In this contribution, a homogenized beam finite element of double symmetric crosssection made of a Functionally Graded Material (FGM) is presented, which can be used for static, modal and buckling analysis of single beams and beam structures with three directional variation of material properties. The material properties in a real beam can vary continuously in longitudinal direction while the variation with respect 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 inertia and rotary inertia are taken into account. Additionally, the longitudinally varying Winkler elastic foundation and the effect of axial force are included by the finite element equations as well. Homogenization of spatially varying material properties to effective quantities with a longitudinal variation is done by the extended mixture rules and multilayer method (MLM). For the homogenized beam the 1212 finite element effective matrix, consisting of the linearized stiffness and consistent mass inertia terms, is established. Numerical experiments are made concerning static, modal and buckling analyses of single FGM beam and beam structures to show the accuracy and effectiveness of the proposed FGM beam finite element.

ELASTOSTATIC AND MODAL AND BUCKLING ANALYSIS OF SPATIAL FGM BEAM STRUCTURES