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.
Morphing structures find interesting applications in architecture (in the field of responsive architecture, with the aim to enable buildings to adapt their form, shape, color or character according to actual environmental), aeronautical engineering (variable sweep wing, landing and take-off flaps, air-inlets, retractable landing gears), civil engineering (adaptive skins, smart ventilation and lighting management systems), electrical (bistable switches). The present proposal is intended to convey the concept of shape morphing structures into these fields.
In particular, with reference to applications in architecture, as far as it concerns the envelopes of roof and facades, generally addressed as building skins, 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.
In addition to the study of the actual realization of the considered structural elements, the present project focuses its attention also on more basic research aspects, since one of our primary aims is the scientific understanding of the fundamental principles related to morphing structures modelling, actuation and control. The theoretical and technological issues of fundamental research that we intend to face will presumably find interesting applications also in other fields. Namely, expected applications of shape morphing structures encompass a large variety of engineering products from micro-electro-mechanical systems (system relay switches, micro-pumps and micro-motors), to human-scale systems (general purpose actuators, morphing electronic devices), up to large-scale systems (morphing flight aircraft surfaces, deployable structures and antennas).
From the scientific point of view, the design of morphing structures with embedded actuation is a problem theoretically and technologically challenging, demanding that two main difficulties are faced: 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 transition from one equilibrium configuration to another. The addressed matter is therefore interdisciplinary and involves competences from nonlinear elasticity, mechanics of plates and shells, smart materials and multi-physics couplings, control and system dynamics, as well as skills in problems of computational mechanics. Expected results are the development of simplified low-dimensional models globally equivalent to the dynamics of morphing structures, of computational models for their refined modelling in a completely nonlinear setting, of large-displacements actuators, of suitable control laws able to avoid snap-through instabilities. The aforementioned problems constitute the theoretical foundations for an efficient design, modelling and control of complex morphing structures. We envisage also the realization of experimental prototypes where these aspects are actually integrated together with demonstrative tools for the possibilities offered by morphing structures, and, as a validation for the models, the numerical schemes and the control laws developed.
Besides the mentioned outcomes expected from the development of techniques for structural morphing, 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. The techniques that are currently applied to this goal include transducer arrays used as sensors and actuators launching an -approximately- monochromatic wave. The structural response is then analyzed in terms of arrival time of the reflected wave (synthetic aperture focus) or compared to an expected signal (matched field processing). The image obtained can be blurred or suffer from the arising of artifacts, against which many approaches were proposed but, to our knowledge, an approach in terms of optimal transport was never explored. This ambit might benefit from the demonstrated improved resolution of wave propagation velocity attainable from the analysis of seismic signals when the optimal transport distance is used. Being able to inspect the internal structure of an object with a process similar to the medical ecogram has applications in several fields, ranging from the detection of holes or other defects of construction (the typical case is the train wheel, where this defects are particularly detrimental) to the reconstruction of unknown profiles of retaining walls, even in tunnels.