Ottimizzazione di elementi strutturali in materiale anisotropo

Two computer codes are developed to automatically solve bidimensional or tridimensional problems in which optimal orientation for structural elements made of orthotropic material are sought. For a given finite element model with known geometry, constraints and loading conditions, the code provides the material orientation in each finite element that maximizes the overall stiffness of the structure. The determination of the optimal arrangement of the material symmetry axes is carried out by an iterative procedure in which the objective function is the total strain energy of the body, that has to be minimized. At each step the value of the design variables, characterizing the material orientation, is modified according to the results of the structural analysis in the previous iteration. The redesign criterion is based on a generic result of optimization for elastic orthotropic materials which states that the stress and the strain tensors must be collinear at the optimum. This can be achieved either in “trivial” case, in which the principal stress and strain directions are aligned with the material symmetry axes, or in “non-trivial” cases depending on the elasticity constants. The 2D code takes into account all the possible types of solution depending on the material mechanical properties and can solve optimization plane problems involving any kind of orthotropic material. On the other hand, the 3D code provides one type of solution only (the “trivial” one) because the tridimensional problem for orthotropic material is still under study; a further extension of the code shall be implemented in the future to cover all the possible optimal solutions in 3D elasticity. The effectiveness of the codes is tested on some examples whose solutions are known and available in literature. Comparing the numerical results obtained from the codes and the exact ones, a very good match in terms of material orientations is obtained together with a very low computing time.