Francesco Dal Corso

The planar mechanics of an elastic rod constrained by a frictionless, flexible sliding sleeve is analyzed. A variational approach is first applied to the equilibrium of an equivalent compound rod system with variable length, leading to a nonlinear boundary value problem. The equilibrium equations determine the deformation kinematics and, through a frictionless sliding condition governed by the Hamiltonian invariant, specify the overlapping length, but they do not reveal interaction forces between the flexible rod and the flexible sliding sleeve. To capture the interaction in detail, the system is modeled as two sub-rods, and both variational and micromechanical methods are employed independently, yielding identical closed-form expressions for the internal forces and moments within the overlapping region. This analysis reveals the presence of tangential concentrated interaction forces of repulsive nature at both ends of the overlapping region. The investigation is complemented by the numerical solution of four case studies, illustrating the broad mechanical behavior of the flexible, frictionless sleeve system. It is found that two different mechanisms may define the maximum bearing capacity, associated with the reciprocal ejection of the two sub-rods: either (i) a quasi-static disappearance of the overlap or (ii) a snap-through instability. The study also shows the possible vanishing of the distributed interaction force, even in non-symmetric configurations. This research establishes a novel theoretical framework for the mechanics of deployable systems and offers insights to advance the design and analysis of structures in fields such as aerospace, robotics, and civil and mechanical engineering.

With recent advances in variable-length structures for use in soft actuation, energy harvesting, energy dissipation and metamaterials, the mathematical modelling and numerical simulation of physical systems with time-varying domains is becoming increasingly important. The planar nonlinear dynamics of one-dimensional elastic structures with variable domain is formulated from a Lagrangian approach by using a non-material reference frame. An Arbitrary Lagrangian-Eulerian (ALE) scheme is proposed where the domain is reparametrized based on a priori unknown configuration parameters. Based on this formulation, a Finite Element (FE) method is developed for theoretically predicting the evolution of a rod constrained at its ends by one or two sliding-sleeves, whose position and inclination can be varied in time, and under external loadings. Finally, case studies and instability problems are investigated to assess the reliability of the proposed formulation against others available and to demonstrate its effectiveness. With respect to previously developed methods for this type of structural problems, the present ALE-FE approach shows a strong theoretical and implementation simplicity, maintaining an efficient and fast convergence according to the cases analyzed. An open source code realized for the present ALE-FE model is made available for solving the nonlinear dynamics of planar systems constrained by one or two independent sliding sleeves. The present research paves the way for further extensions to easily implement solvers for the three-dimensional dynamics of flexible one- and two-dimensional structural systems with moving boundary conditions.

The building construction industry is the largest anthropogenic source of pollution, with massive energy consumption and substantial CO₂ emissions. Lightweight tension structures allow the simultaneous implementation of several sustainable strategies by using recyclable low-carbon structural membranes offering a greener alternative to glass and other cladding materials. Their efficient structural load-bearing mechanisms result in significant weight savings in buildings and a drastic reduction of the environmental impact associated with material production, transportation, use, and disposal. A subgroup of lightweight materials, structural fabrics, and foils has been gaining popularity among designers and architects in recent years because of their desirable features such as high stiffness, strength, ductility, durability, and functional properties. While these structural membranes open new crucial perspectives for the clean energy transition and have been recently employed worldwide, their full potential is still limited by the lack of construction codes, advanced optimization tools, and comprehensive viscous-thermo-mechanical constitutive models. This chapter aims to foster the design of membrane structures by presenting their basic principles and recent advancements in the field. It covers the design approaches, employed materials and efforts in their characterization and modeling, implications on the sustainability of the built environment, current challenges, and future pathways from both academic research and engineering design viewpoints.

The phenomenon of oscillatory instability called ‘flutter’ was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps and new perspectives for investigations are indicated.