A New Mathematical Model of Functionally Graded Porous Euler-Bernoulli Nanoscaled Beams Taking into Account Some Types of Nonlinearities.

A new mathematical model of flexible physically (FN), geometrically (GN), and simultaneously physically and geometrically (PGN) nonlinear porous functionally graded (PFG) Euler-Bernoulli beams was developed using a modified couple stress theory. The ceramic phase of the functionally material was considered as an elastic material. The metal phase was considered as a physically non-linear material dependent on coordinates, time, and stress-strain state, which gave the opportunity to apply the deformation theory of plasticity.