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We deduce a one-dimensional model of elastic planar rods starting from the Föppl–von Kármán model of thin shells. Such model is enhanced by additional kinematical descriptors that keep explicit track of the compatibility condition requested in the two-dimensional parent continuum, that in the standard rods models are identically satisfied after the dimensional reduction. An inextensible model is also proposed, starting from the nonlinear Koiter model of inextensible shells. These enhanced models describe the nonlinear planar bending of rods and allow to account for some phenomena of preeminent importance even in one-dimensional bodies, such as formation of singularities and localization (d-cones), otherwise inaccessible by the classical one-dimensional models. Moreover, the effects of the compatibility translate into the possibility to obtain multiple stable equilibrium configurations. [ABSTRACT FROM AUTHOR]

The numerical and experimental validation of multistable behavior of cantilever shells is addressed. The design of the laminated composite shells is driven by a recently proposed semi-analytical shell model, whose predictions are verified and critically examined by means of finite element simulations and stability tests on two manufactured demonstrators. In addition, the influence of the main design parameters on the shells stability scenario is discussed. Despite its simplicity, the reduced model allows to depict a fairly faithful picture of the stability scenario; therefore, it proves to be a useful tool in the early design stages of morphing shell structures. [ABSTRACT FROM AUTHOR]

Multistable shells have been recently proposed as an effective solution to design morphing structures. We describe a class of shallow shells which are bistable after one of their sides, initially curved, is clamped along a flat line. Supposing the shell being assembled as a composite laminate, we show how the anisotropy of the material can influence the multistable behaviour and the robustness of stable configurations. Specifically, we focus on orthotropic laminated shells using the polar method for a complete representation of the anisotropic elastic properties. Two experimental prototypes have been produced and tested to validate our analytical and numerical results. [ABSTRACT FROM AUTHOR]

The nonlinear dynamics of cantilever bistable shells with asymmetric stable configurations is investigated. The possibility of maximizing the kinetic energy associated with snap-through motion offered by the considered cantilevered shells is pursued to enhance the sought-after energy harvesting capabilities. Through an experimental campaign under harmonic forcing the resonance scenarios around the stable configurations are analysed. The resulting nonlinear behaviour observed for high amplitude excitation is adopted to guide a reduced order model derivation. By combining the experimental response with two double-well oscillators derived from FE simulations, a double-well quintic oscillator capturing the observed softening behaviour is proposed. It involves a parameter identification phase in which a nonlinear damping model is introduced. A numerical continuation approach is adopted to discuss the local periodic solutions around each stable configuration in terms of resonance curves, bifurcation diagrams and basins of attraction. The global dynamics involving regular and chaotic dynamic regimes as well as snap-through motion is eventually described. • A novel cantilever composite shell with asymmetric double potential wells. • Experimental evidence of the exploitation of the bistable shell nonlinear dynamics. • Extracted kinetic energy maximization from the triggering of snap-through phenomena. • A nonlinear quintic Duffing–Holmes model for describing in- and cross-well dynamics. [ABSTRACT FROM AUTHOR]