I have some basic question:
What is a homogeneous beam? why do we use homogeneous beam ? what are the characteristics of homogeneous beams?
and Where do we use these beams? and what is beam homogenization ?
homogeneous implies the material (isotropic or anisotropic) are the same at all material points. Isotropic homogeneous beams are the main subject of Strength of Materials. When the material is anisotropic, the analysis is a little bit different as there are possible couplings among the six fundamental beam deformation modes (tension, bending in two directions, shear in two directions, and torsion). You usually need a general cross-sectional tool like VABS to obtain the beam constants (in the form of 6x6 stiffness matrix).
A heterogeneous beam structure usually refers to heterogeneity over the cross-section such as laminated composite beams with different layup orientation. In general a beam can also be heterogeneous both over the cross-section and along the span such as tapered composite rotorblades. VABS is developed to accurately characterize such structures within the framework of beam models.