Elastic membranes spanning deformable curves

Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) (74C05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Membranes (74K15) Optimization of shapes other than minimal surfaces (49Q10)

Cites Work

Unnamed Item
Unnamed Item
A corrected Sadowsky functional for inextensible elastic ribbons
Area minimizing discs in metric spaces
Automated solution of differential equations by the finite element method. The FEniCS book
The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
Global curvature and self-contact of nonlinearly elastic curves and rods
On the experimental and theoretic static of liquids based only on molecular forces.
Theoretical and experimental study of the stability of a soap film spanning a flexible loop
The problem of the least area and the problem of Plateau.
Theory and practice of finite elements.
The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
A direct approach to Plateau's problem
Dimensional reduction of the Kirchhoff-Plateau problem
Solution of the Kirchhoff-Plateau problem
Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure
Normal and integral currents
Quasi-convexity and the lower semicontinuity of multiple integrals
Stability of boundary conditions for the Sadowsky functional
The finite element methods for elliptic problems.
Geometric measure theory. A beginner's guide. Illustrated by James F. Bredt
A Variational Model for Anisotropic and Naturally Twisted Ribbons
Should we solve Plateau's problem again?
Minimal elastic networks
Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
The Relaxed Energy Density for Isotropic Elastic Membranes
There is More than One Way to Frame a Curve
Long time existence of solutions to an elastic flow of networks
Minimal surfaces with elastic and partially elastic boundary
Minimal surfaces bounded by elastic lines
Buckling of a soap film spanning a flexible loop resistant to bending and twisting
Soap film spanning an elastic link
The Mathematical Theory of Finite Element Methods
Solution of the problem of Plateau.
Semicontinuity problems in the calculus of variations
Minimal surfaces with an elastic boundary
Plateau's problem for singular curves