Laguerre geometry of surfaces with plane lines of curvature

1999 ◽  
Vol 69 (1) ◽  
pp. 123-138 ◽  
Author(s):  
Emilio Musso ◽  
Lorenzo Nicolodi
Keyword(s):  
Laguerre Geometry ◽  
Lines Of Curvature

Visualization of Enneper’s surface by line graphics

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 387-405 ◽  
Author(s):  
Vesna Velickovic
Keyword(s):  
Minimal Surface ◽  
Graphical Representations ◽  
Lines Of Curvature ◽  
Geodesic Lines

Here we study Enneper?s minimal surface and some of its properties. We compute and visualize the lines of self-intersection, lines of intersections with planes, lines of curvature, asymptotic and geodesic lines of Enneper?s surface. For the graphical representations of all the results we use our own software for line graphics.

scholarly journals Surfaces in Laguerre geometry

2019 ◽  
Vol 117 ◽  
pp. 223-255 ◽  
Author(s):  
Emilio Musso ◽  
Lorenzo Nicolodi
Keyword(s):  
Laguerre Geometry

Lines of curvature and umbilical points for implicit surfaces

2007 ◽  
Vol 24 (7) ◽  
pp. 395-409 ◽  
Author(s):  
Wujun Che ◽  
Jean-Claude Paul ◽  
Xiaopeng Zhang
Keyword(s):  
Implicit Surfaces ◽  
Lines Of Curvature ◽  
Umbilical Points

Nonlinear Theory for Composite Laminated Shells With Interfacial Damage

1998 ◽  
Vol 65 (3) ◽  
pp. 711-718 ◽  
Author(s):  
Zhen-qiang Cheng ◽  
S. Kitipornchai
Keyword(s):  
Nonlinear Theory ◽  
Virtual Work ◽  
Shear Stresses ◽  
Interfacial Damage ◽  
Laminated Shells ◽  
Lines Of Curvature ◽  
Perfect Bonding ◽  
Transverse Shear Stresses ◽  
Bounding Surfaces ◽  
Special Case

Interfacial damage is incorporated in the proposed nonlinear theory. for composite laminated shells. A spring-layer model is employed to characterize damaged interfaces spanning from perfect bonding to different degrees of imperfect bonding in shear. By enforcing compatibility conditions for transverse shear stresses both at interfaces and on two bounding surfaces of a laminated shell, only five unknowns are needed for modeling its behavior. The principle of virtual work is used to derive the governing equations, which are of 14th order in lines of curvature coordinates, variationally self-consistent with seven prescribed boundary conditions. This theory includes the conventional higher-order zigzag model for a perfectly bonded shell as a special case. Numerical results provide a physical understanding of the effect of interracial damage on bending and buckling responses of composite laminated shells.

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