Abstract
In this paper we employ the direct approach to the theory of rods and beams, which is based on the deformable curve model with a triad of rotating directors attached to each point. We show that this model (also called directed curve) is an efficient approach for analyzing the deformation of elastic beams with a complex material structure. Thus, we consider non-homogeneous, composite and functionally graded beams made of isotropic or orthotropic materials and we determine the effective stiffness properties in terms of the three-dimensional elasticity constants. We present general analytical expressions of the effective stiffness coefficients, valid for beams of arbitrary cross-section shape. Finally, we apply this method for FGM beams made of metal foams and compare our analytical results with the numerical results obtained by a finite element analysis.
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