Random micropolar beams: response and identification

The objective of this paper is to provide a simplified procedure for the random analysis of axially functionally graded Timoshenko–Ehrenfest beams in the field of the linearized micropolar continuum. New approximated deterministic closed form solutions are proposed, which are also useful for the study of classic 1D structural elements characterized by defects distributed along their axes, bleeding phenomena and step geometric properties. Hence, the proposed results meet several technical applications. The Maximum Entropy (MaxEnt) principle and Monte Carlo (MC) simulations are used to solve the direct and inverse stochastic problems. In order to simplify the presentation, simply-supported and clamped macro- and micro-beams are considered. It is shown that the analysis of 1D micropolar models allows us to identify one of the material parameters related to 3D micropolar models.