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Thin-walled Beams: A Derivation of Vlassov Theory via Γ-Convergence |
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| Authors: | Lorenzo Freddi Antonino Morassi Roberto Paroni |
| Institution: | (1) Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze 206, 33100 Udine, Italy;(2) Dipartimento di Georisorse e Territorio, Università di Udine, via Cotonificio 114, 33100 Udine, Italy;(3) Dipartimento di Architettura e Pianificazione, Università degli Studi di Sassari, Palazzo del Pou Salit, Piazza Duomo, 07041 Alghero, Italy |
| Abstract: | This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order ε and ε 2, as ε goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the three-dimensional problem Γ-converges to the classical one-dimensional Vlassov model for thin-walled beams. |
| Keywords: | thin-walled cross-section beams linear elasticity Γ -convergence dimension reduction |
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