Optimal orientation of the symmetry axes of orthotropic 3-D materials

Assuming the elastic energy as a meaningful measure of the global stiffness (or flexibility) of an elastic body, in this paper the interest is paid to the determination of those local orientations of the material symmetry axes in an orthotropic solid which correspond to extreme values of the energy density. In the general formulation of the problem, and assuming the strain field as given, a linear elastic orthotropic three-dimensional solid is considered and the stationarity conditions are obtained. Such a set of algebraic equations is then explicitly solved referring to the cubic case and the optimal orientations are found as well. It is also pointed out how such orientations depend both on a material parameter and on the strain field.