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Equilibria of axial-transversely loaded homogenized duoskelion beams

Emilio Barchiesi

Vol. 12 (2024), No. 3, 283–309
Abstract

Periodic repetition of the duoskelion motif along a single dimension results in duoskelion beams. These beams have been proven to exhibit interesting mechanical properties like axial-transverse coupling and bimodularity, namely the coexistence of resistance to shortening and compliance to lengthening. The continuum description of these structures is achieved through homogenization, defining a family of discrete descriptions parametrized over the cell size. When the cell size tends to zero one retrieves a non-linear generalization of the Timoshenko beam model with an internal constraint involving the stretch and the shear angle. The limit model is reduced to a second order boundary value problem involving only the cross-section rotation angle, which is then recast into an initial value problem describing the motion of a particle subjected to a potential. The initial conditions of such an initial value problem have to be taken so as to fulfill the kinematic conditions at the beam’s boundaries. Exploiting the properties of this alternative representation of the boundary value problem governing the equilibrium of a homogenized duoskelion beam, the present contribution addresses the qualitative study and computation of large deformation equilibria of duoskelion beams subjected to simultaneous axial and transverse end load.

Keywords
chirality, asymptotic homogenization, Weierstrass's study, duoskelion beam
Mathematical Subject Classification
Primary: 74Q05, 74S99
Milestones
Received: 5 March 2024
Revised: 21 June 2024
Accepted: 23 September 2024
Published: 5 October 2024

Communicated by Francesco dell'Isola
Authors
Emilio Barchiesi
Dipartimento di Architettura, Design e Urbanistica
Università degli Studi di Sassari
07041 Alghero
Italy
Università degli Studi dell’Aquila
Centro Internazionale di Ricerca M&MoCS
L’Aquila
Italy