scholarly journals Surfaces Modelling Using Isotropic Fractional-Rational Curves

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Igor V. Andrianov ◽  
Nataliia M. Ausheva ◽  
Yuliia B. Olevska ◽  
Viktor I. Olevskyi
Keyword(s):  
Computer Technology ◽  
Gaussian Curvature ◽  
Minimal Surfaces ◽  
Smooth Surface ◽  
Rational Curves ◽  
Zero Gaussian Curvature ◽  
Analytic Curves

The problem of building a smooth surface containing given points or curves is actual due to development of industry and computer technology. Previously used for those purposes, shells of zero Gaussian curvature and minimal surfaces based on isotropic analytic curves are restricted in their consumer properties. To expand the possibilities regarding the shaping of surfaces we propose the method of constructing surfaces based on isotropic fractional-rational curves. The surfaces are built using flat isothermal and orthogonal grids and on the basis of the Weierstrass method. In the latter case, the surfaces are minimal. Examples of surfaces that were built according to the proposed method are given.

A representation of distributions supported on smooth hypersurfaces of Rn

1995 ◽  
Vol 117 (1) ◽  
pp. 153-160
Author(s):  
Kanghui Guo
Keyword(s):  
Gaussian Curvature ◽  
Dual Space ◽  
Smooth Hypersurface ◽  
Zero Gaussian Curvature ◽  
Schwartz Class ◽  
Image Position

Let S(Rn) be the space of Schwartz class functions. The dual space of S′(Rn), S(Rn), is called the temperate distributions. In this article, we call them distributions. For 1 ≤ p ≤ ∞, let FLp(Rn) = {f:∈ Lp(Rn)}, then we know that FLp(Rn) ⊂ S′(Rn), for 1 ≤ p ≤ ∞. Let U be open and bounded in Rn−1 and let M = {(x, ψ(x));x ∈ U} be a smooth hypersurface of Rn with non-zero Gaussian curvature. It is easy to see that any bounded measure σ on Rn−1 supported in U yields a distribution T in Rn, supported in M, given by the formula

scholarly journals Gauss-Bonnet theorems in the generalized affine group and the generalized BCV spaces

2021 ◽  
Vol 6 (11) ◽  
pp. 11655-11685
Author(s):  
Tong Wu ◽  
◽  
Yong Wang
Keyword(s):  
Gaussian Curvature ◽  
Smooth Surface ◽  
Geodesic Curvature ◽  
Affine Group ◽  
Smooth Curves ◽  
Characteristic Points ◽  
Curves On Surfaces

<abstract><p>In this paper, we compute sub-Riemannian limits of Gaussian curvature for a Euclidean $ C^2 $-smooth surface in the generalized affine group and the generalized BCV spaces away from characteristic points and signed geodesic curvature for Euclidean $ C^2 $-smooth curves on surfaces. We get Gauss-Bonnet theorems in the generalized affine group and the generalized BCV spaces.</p></abstract>

Limit equilibrium of reinforced shells of zero gaussian curvature

1989 ◽  
Vol 25 (9) ◽  
pp. 913-919
Author(s):  
A. V. Nalimov ◽  
Yu. V. Nemirovskii
Keyword(s):  
Gaussian Curvature ◽  
Limit Equilibrium ◽  
Zero Gaussian Curvature

scholarly journals Multi-stability of free spontaneously curved anisotropic strips

2011 ◽  
Vol 468 (2138) ◽  
pp. 511-530 ◽  
Author(s):  
L. Giomi ◽  
L. Mahadevan
Keyword(s):  
Gaussian Curvature ◽  
Elastic Moduli ◽  
Composite Plates ◽  
Spontaneous Curvature ◽  
Bending Rigidity ◽  
Stable Conformation ◽  
Elastic Composite ◽  
Measuring Tape ◽  
Zero Gaussian Curvature ◽  
The Common

Multi-stable structures are objects with more than one stable conformation, exemplified by the simple switch. Continuum versions are often elastic composite plates or shells, such as the common measuring tape or the slap bracelet, both of which exhibit two stable configurations: rolled and unrolled. Here, we consider the energy landscape of a general class of multi-stable anisotropic strips with spontaneous Gaussian curvature. We show that while strips with non-zero Gaussian curvature can be bistable, and strips with positive spontaneous curvature are always bistable, independent of the elastic moduli, strips of spontaneous negative curvature are bistable only in the presence of spontaneous twist and when certain conditions on the relative stiffness of the strip in tension and shear are satisfied. Furthermore, anisotropic strips can become tristable when their bending rigidity is small. Our study complements and extends the theory of multi-stability in anisotropic shells and suggests new design criteria for these structures.

Steady-state creep of shells of zero Gaussian curvature with allowance for shear stresses

1982 ◽  
Vol 18 (2) ◽  
pp. 104-109
Author(s):  
P. I. Danchak ◽  
M. S. Mikhalishin ◽  
O. N. Shablii
Keyword(s):  
Steady State ◽  
Gaussian Curvature ◽  
Steady State Creep ◽  
Shear Stresses ◽  
Zero Gaussian Curvature
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