Optimal Orientation of Orthotropic Properties for Continuum Bodies and Structural Elements

In this paper some notes on recent results obtained in the field of optimal design of orthotropic bodies and components are given. After a brief recall of the mechanical behaviour of orthotropic bodies and structural elements, a general formulation of the optimization problem is given: assuming the elastic energy as a meaningful measure of the global stiffness (or flexibility) of a three dimensional elastic body, the interest is focused on the determination of those local orientations of material symmetry axes in an orthotropic solid, which correspond to extreme values of the energy density. The stationarity conditions are computed, and a mechanical interpretation is given as well. Then, the two dimensional case is dealt with in details, both for the elastic and plastic cases, defining also a unified approach for approximate optimal solutions. Some simple examples of application are given as well.