Functionally graded rod with small concentration of inclusions: Homogenization and optimization

This work is devoted to strain analysis and optimal design of a Functionally Graded (FG) rods and beams with small inclusions. The homogenization procedure plays a key role in our investigations. The method is illustrated using an example of the rod longitudinal deformation and bending of a beam. We consider the cases of FG inclusion sizes and FG steps between inclusions separately. Particular problems of optimal design are discussed in some details. The mathematical model of the bending beam, which adapts to the external load action, is proposed and an illustrative example of the adaptation process is given. •Strain analysis of functionally graded rods/beams is given.•The modified homogenization/asymptotic procedures are employed.•The novel optimization method devoted to functionally graded structure is proposed.•Examples illustrating the introduced theory are added.