Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density

2009/01/26 by Maria Giovanna Mora, Mora, Maria Giovanna, Lucia Scardia +1
Computer Science · Mathematics · #49J45 #74B20 #74K20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:49J45 #msc:74B20 #msc:74K20

paper · pdf · doi:10.48550/arxiv.0901.4041

21 pages

arxiv created 2009/01/26 · openalex publication_date 2009/01/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness h of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional \mathcal E^h, whose energies (per unit thickness) are bounded by Ch⁴, converge to critical points of the Γ-limit of h^-4\mathcal E^h. This is proved under the physical assumption that the energy density W(F) blows up as det F→0.

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