Isogeometric analysis of size-dependent effects for functionally graded microbeams by a non-classical quasi-3D theory

A novel and effective computational approach within the context of isogeometric analysis (IGA) is developed for analyzing size-dependent mechanical behaviors of functionally graded (FG) microbeams. To capture the size effects, an extension of quasi-3D theory is established to integrate with the modified couple stress theory. The nonuniform rational B-spline (NURBS) basis functions are employed and can directly meet the first-order derivative demand of the quasi-3D theory, where four variables are involved at each node. In this new setting, both normal and shear deformations are considered, while the shear correction factor is avoided. Numerical examples are studied, in which the effects of several factors, including material gradient factor, boundary conditions, parameter of material length scale, and aspect ratio, on deflections, stresses, and fundamental frequencies of FG microbeams are explored.