Results 1 to 10 of about 84,517 (317)
On the elastic closed plane curves [PDF]
Kodai Mathematical Journal, 1985 Hiroshi Yanamoto
openalex +4 more sources
Formulation and Solution of Curved Beams with Elastic Supports
Tehnicki vjesnik - Technical Gazette, 2018 This article presents the general system of differential equations that governs the behaviour of a curved beam, which can be solved by either numerical or analytical methods. The obtained solution represents the matricial expression of transference. The stiffness matrix is derived directly rearranging the transfer matrix.
Fernando Sarria +4 more
openalex +7 more sources
Numerical Solution of Differential Equations of Elastic Curves in 3-dimensional Anti-de Sitter Space [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we aim to extend the Darboux frame field into 3-dimensional Anti-de Sitter space and obtain two cases for this extension by considering a parameterized curve on a hypersurface; then we carry out the Euler-Lagrange equations and derive ...
Samira Latifi +2 more
doaj +1 more source
A Survey of the Elastic Flow of Curves and Networks [PDF]
Milan Journal of Mathematics, 2021 AbstractWe collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and smooth convergence to critical points of the solution of the elastic flow of closed curves in$${\mathbb {R}}^2$$
Carlo Mantegazza +2 more
openaire +4 more sources
Bifurcation of elastic curves with modulated stiffness [PDF]
European Journal of Applied Mathematics, 2022 We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the minimisation of a bending energy with respect to shape and density and can be considered as a one-dimensional ...
K Brazda +3 more
openaire +3 more sources
Geometric and topological approaches to shape variation in
Royal Society Open Science, 2021 Leaf shape is a key plant trait that varies enormously. The range of applications for data on this trait requires frequent methodological development so that researchers have an up-to-date toolkit with which to quantify leaf shape. We generated a dataset
Haibin Hang +3 more
doaj +1 more source
Rolling Geodesics, Mechanical Systems and Elastic Curves
Mathematics, 2022 This paper defines a large class of differentiable manifolds that house two distinct optimal problems called affine-quadratic and rolling problem.
Velimir Jurdjevic
doaj +1 more source
SIAM Journal on Applied Mathematics, 2011 We consider the problem of minimizing Euler's elastica energy for simple closed curves confined to the unit disk. We approximate a simple closed curve by the zero level set of a function with values +1 on the inside and -1 on the outside of the curve. The outer container now becomes just the domain of the phase field.
Dondl, Patrick +2 more
openaire +5 more sources
Approximation by planar elastic curves [PDF]
Advances in Computational Mathematics, 2016 18 pages, 10 figures. Version2: new section 5 added (conclusions and discussions)
David Brander +2 more
openaire +6 more sources
Elastic curves and phase transitions [PDF]
Mathematische Annalen, 2019 This paper is devoted to classical variational problems for planar elastic curves of clamped endpoints, so-called Euler's elastica problem. We investigate a straightening limit that means enlarging the distance of the endpoints, and obtain several new results concerning properties of least energy solutions.
Tatsuya Miura, Tatsuya Miura
openaire +4 more sources