## Abstract

In this contribution, results of elastostatic analysis of spatial composite beam structures are presented using our new beam finite element of double symmetric cross-section made of a Functionally Graded Material (FGM). Material properties of the real beams vary continuously in the longitudinal direction while variation with respect to the transversal and lateral directions is assumed to be symmetric in a continuous or discontinuous manner. Continuously longitudinal varying spatial Winkler elastic foundations (except the torsional foundation) and the effect of axial and shear forces are considered as well. Homogenization of spatially varying material properties to effective quantities with a longitudinal variation is done by the multilayer method (MLM). For the homogenized beam finite element the local stiffness matrix is established by means of the transfer matrix method. By the conventional finite element procedure, the global element stiffness matrix and the global system of equation for the beam structure are established for calculation of the global displacement vector. The secondary variables (internal forces and moments) are then calculated by means of the transfer relations on the real beams. Further, the mechanical stress in the real beams are calculated. Finally, the numerical experiments are carried out concerning the elastic-static analysis of the single FGM beams and beam structures in order to show the possibilities of our approach.

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