On Design of Anisotropy Distributions, Applying Lamina Formulas for 2d Result Visualization

In rotational transformation of constitutive matrices, some practical quantities are often termed invariants, but the invariance relates to an unchanged reference direction. Rotating this reference direction, the practical quantities do change and this point is clarified with derived rotational transformation for these practical quantities.

The research background for optimal anisotropic constitutive matrices is shortly presented. Then design results are applied in a 2D visualization of optimized constitutive matrices, that are distributed in a finite element (FE) model where each element has a specific reference direction. The visualized distributions of physical quantities are; stiffest material direction, material stiffest longitudinal constitutive component, level of anisotropy, absolute or relative shear stiffness and orthotropy test.