The preprocessing of Computational Grains (CGs) is introduced in Chapter 3, and several types of CGs have been developed for the micromechanical modeling of different kinds of composites with particulates, fibers, and so on in Chapters 5–11. A multi-scale analysis framework of composite structures by using the CGs and the standard FEM is developed in this chapter, based on the homogenization of composite materials at the microlevel, and slender or shell structures at the meso- and macro-levels. The specific process of the multi-scale algorithm is illustrated with an example of a stiffened composite panel. The results show the multi-scale analysis method is an accurate and efficient tool for large composite structures, not only simulating the overall structural responses in a bottom-up fashion, but also obtaining the detailed stresses at multiple scales in the dehomogenization process.

This chapter deals with the finite element formulation for thin plate and shell structures. We will review the assumptions on the kinematics of deformation from classical plate bending theories, introduce them into the finite element formulation for plates, and then extend the formulation to curved shell structures within the isoparametric formulation. For 3D solid elements that can be used for plates and shell analysis, we will first look at solid elements with three nodes through the thickness. We will then show how solid elements with two nodes through the thickness can be constructed for analysis of plate and shell structures.