Conventional structures are usually designed to maintain a single shape throughout their design life; however more often in the engineering practice it's useful to have some or more structural members changing their shape under operative conditions. The design of such structures is a challenging problem from the theoretical and technological point of view, demanding to face several difficulties, among the others: i) taking into account nonlinear effects in the design and modelling process to obtain a structure with a set of assigned stable equilibrium configurations; ii) conceiving efficient actuation and control techniques to drive the passage from one configuration to another. The addressed matter involves competences from nonlinear elasticity, mechanics of plates and shells, differential geometry, smart materials and multiphysics couplings, control and system dynamics, as well as skills in problems of computational mechanics. Taking advantage of modern advanced differential geometry, the ultimate goal of this research is to develop a new theoretical framework and fine tune new techniques in order to face the problem of predicting and designing structural morphing, even in the transient configurations.
In particular, we intend to consider two specific tools, namely the Ricci flow and the optimal transport theory.
The potential impact of shape morphing panels and shells is evident. Indeed by suitably managing the shape of dedicated structural elements, it would be possible to tune the daylight illumination, to control the internal/external heat fluxes, to adapt the attitude of photovoltaic elements to the sun rays inclination, to harvest energy from wind and ventilation sources. Moreover, we assume that the theoretical tools of Ricci flow and optimal transport that will be investigated can shed light also on other technological aspects, in particular, related to the signal processing for damage imaging or inner structure inspection with sonic and ultrasonic waves.
