Linear response of a planar FGM beam with non-linear variation of the mechanical properties

Abstract

This contribution aims at proposing an effective First order Shear Deformation Theory (FSDT) capable to tackle the non-trivial effects that a continuous variation of the mechanical properties induces on stresses, displacement, and stiffness distributions within a planar beam made of Functionally Graded Material (FGM). In greater detail, the beam model assumes the Timoshenko beam kinematics and it results naturally expressed by six Ordinary Differential Equations (ODEs) considering both cross-section displacements and internal forces as unknowns. Furthermore, exploiting a recently proposed analysis tool, the paper provides also effective tools for the accurate reconstruction of cross-section stress distributions (with special emphasis on shear stresses) and the beam stiffness estimation. A simple numerical example demonstrates that the proposed beam model can catch with good accuracy the main effects induced by variations of the mechanical properties, allowing for a simple and effective modeling of a large class of structures and opening the doors to a new family of enhanced beam models.