Results 1 to 10 of about 413,318 (238)
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
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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
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On the elastic closed plane curves [PDF]
Kodai Mathematical Journal, 1985 Hiroshi Yanamoto
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A dynamic damage constitutive model considering the effect of joint inclination on the modulus of elasticity of slates [PDF]
Scientific ReportsThe dynamic damage constitutive model has limitations and needs to reflect the quantitative relationship between the elastic modulus and joint inclination angle of the slate.
Tingting Gu +5 more
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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.
Sarría Pueyo, Fernando +4 more
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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
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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
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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
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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
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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
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