Optimization in Anisotropic Elasticity

In this chapter, Noether local method is applied for the optimizing of anisotropy of elastic bodies. The objective is the optimal tailoring of the anisotropic structural elements. The anisotropic elastic moduli in the principal anisotropy axes (in fiber coordinate system) remain equal everywhere in the structural member. In the optimization task, the distributed control functions are the Euler angles. These Euler angles are the functions of spatial coordinates and determine the alinement of the fiber coordinate system. The orientation of fibers and, consequently, the position of principal anisotropy axes are variable over the volume of structural member. The necessary conditions for optimality are obtained. Notably, that the stress and strain tensors must be coaxial and consequently the Eshelby’s energy–momentum tensor have to be symmetric for the optimal anisotropy.