Lower bounds for the energy in a crumpled elastic sheet - A minimal ridge
S. C. Venkataramani
Abstract
We study the linearized Fopl - von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle 2 α. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness σ and the bending angle. We show that the minimum energy scales as σ5/3 α7/3. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as σ.
Create a lesson
Related papers
Positive normalized solutions for a singular regularized p(x)-Laplacian Dirichlet problem
Mustafa Avci
Regularity for axisymmetric Navier-Stokes with an Euler length
Peter Constantin, Mihaela Ignatova, Vlad Vicol
Existence of strong initial traces for stochastic conservation laws
Marko Erceg, Nikola Konatar, Kenneth Karlsen et al.
Asymptotics of nonlocal nonlinear Robin energies
Serena Dipierro, Giuseppe Spadaro, Enrico Valdinoci
Discontinuity of the Vlasov--Poisson Flow in LxpLv∞
Ke Chen, In-Jee Jeong, Quoc-Hung Nguyen et al.
Dense orbits for scale-invariant rotationally symmetric solutions of the 2D Euler equations
Ibrahim Suleiman