Unshearable and inextensible planar beams, in a static regime of finite displacements, are studied in this paper. A nonlinear mixed model is derived via a direct approach, in which displacements and reactive internal forces are taken as unknowns. The elasto-static problem is then addressed, and the role of the boundary conditions is systematically discussed. The relevant solutions for selected classes of problems are pursued via a perturbation method. It is shown that each considered class calls for a specific algorithm, accounting for a proper scaling and expansion of the variables. Finally, the asymptotic solutions are compared with benchmark numerical computations, grounded on finite-element analyses. The paper is focused on the case of longitudinal force significantly smaller than the buckling load, leaving the case of large force to future developments, where a different perturbation scheme is required.
Luongo, A., Zulli, D., D'Annibale, F., Casalotti, A. (2024). Revisiting the nonlinear elastic problem of internally constrained beams in a perturbation perspective. EUROPEAN JOURNAL OF MECHANICS. A, SOLIDS, 108 [10.1016/j.euromechsol.2024.105422].
Revisiting the nonlinear elastic problem of internally constrained beams in a perturbation perspective
Luongo, A.;Casalotti, A.
2024-01-01
Abstract
Unshearable and inextensible planar beams, in a static regime of finite displacements, are studied in this paper. A nonlinear mixed model is derived via a direct approach, in which displacements and reactive internal forces are taken as unknowns. The elasto-static problem is then addressed, and the role of the boundary conditions is systematically discussed. The relevant solutions for selected classes of problems are pursued via a perturbation method. It is shown that each considered class calls for a specific algorithm, accounting for a proper scaling and expansion of the variables. Finally, the asymptotic solutions are compared with benchmark numerical computations, grounded on finite-element analyses. The paper is focused on the case of longitudinal force significantly smaller than the buckling load, leaving the case of large force to future developments, where a different perturbation scheme is required.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.