Algorithm for calculating geometric parameter of axial symmetry conic surface

2015 ◽  
Vol 36 (6) ◽  
pp. 890-904
Author(s):  
Du Jian-xiang ◽  
Zong Xiao-ying
2020 ◽  
Vol 51 (1) ◽  
pp. 57-82
Author(s):  
Chen Wang ◽  
Jing-Zhou Zhang ◽  
Chun-hua Wang ◽  
Jun Ji ◽  
Xiao-Ming Tan
Keyword(s):  

2021 ◽  
Vol 11 (7) ◽  
pp. 592
Author(s):  
Sonja A. G. A. Grothues ◽  
Klaus Radermacher

The native femoral J-Curve is known to be a relevant determinant of knee biomechanics. Similarly, after total knee arthroplasty, the J-Curve of the femoral implant component is reported to have a high impact on knee kinematics. The shape of the native femoral J-Curve has previously been analyzed in 2D, however, the knee motion is not planar. In this study, we investigated the J-Curve in 3D by principal component analysis (PCA) and the resulting mean shapes and modes by geometric parameter analysis. Surface models of 90 cadaveric femora were available, 56 male, 32 female and two without respective information. After the translation to a bone-specific coordinate system, relevant contours of the femoral condyles were derived using virtual rotating cutting planes. For each derived contour, an extremum search was performed. The extremum points were used to define the 3D J-Curve of each condyle. Afterwards a PCA and a geometric parameter analysis were performed on the medial and lateral 3D J-Curves. The normalized measures of the mean shapes and the aspects of shape variation of the male and female 3D J-Curves were found to be similar. When considering both female and male J-Curves in a combined analysis, the first mode of the PCA primarily consisted of changes in size, highlighting size differences between female and male femora. Apart from changes in size, variation regarding aspect ratio, arc lengths, orientation, circularity, as well as regarding relative location of the 3D J-Curves was found. The results of this study are in agreement with those of previous 2D analyses on shape and shape variation of the femoral J-Curves. The presented 3D analysis highlights new aspects of shape variability, e.g., regarding curvature and relative location in the transversal plane. Finally, the analysis presented may support the design of (patient-specific) femoral implant components for TKA.


1991 ◽  
Vol 44 (18) ◽  
pp. 10385-10388 ◽  
Author(s):  
Tiôru Sakai ◽  
Minoru Takahashi

2015 ◽  
Vol 29 (03) ◽  
pp. 1550009 ◽  
Author(s):  
Shan-Shan Wang ◽  
Guo-Qiao Zha

Based on the time-dependent Ginzburg–Landau equations, we study numerically the vortex configuration and motion in mesoscopic superconducting cylinders. We find that the effects of the geometric symmetry of the system and the noncircular multiply-connected boundaries can significantly influence the steady vortex states and the vortex matter moving. For the square cylindrical loops, the vortices can enter the superconducting region in multiples of 2 and the vortex configuration exhibits the axial symmetry along the square diagonal. Moreover, the vortex dynamics behavior exhibits more complications due to the existed centered hole, which can lead to the vortex entering from different edges and exiting into the hole at the phase transitions.


2000 ◽  
Vol 123 (3) ◽  
pp. 288-292 ◽  
Author(s):  
Arturs Kalnins ◽  
Dean P. Updike

Tresca limit pressures for long cylindrical shells and complete spherical shells subjected to arbitrary pressure, and several approximations to the exact limit pressures for limited pressure ranges, are derived. The results are compared with those in Section III-Subsection NB and in Section VIII-Division 2 of the ASME B&PV Code. It is found that in Section VIII-Division 2 the formulas agree with the derived limit pressures and their approximations, but that in Section III-Subsection NB the formula for spherical shells is different from the derived approximation to the limit pressure. The length effect on the limit pressure is investigated for cylindrical shells with simply supported ends. A geometric parameter that expresses the length effect is determined. A formula and its limit of validity are derived for an assessment of the length effect on the limit pressures.


1985 ◽  
Vol 63 (8) ◽  
pp. 1098-1104
Author(s):  
Giulio Bosi ◽  
Alain Durand

The present paper is devoted to analyzing the magnetic fringe-field and space-charge effects on a beam of nonrelativistic electrons crossing a sequence of cylindrical and toroidal solenoids, as may be found in an electron cooler. The investigation is mainly aimed at searching for suitable conditions that ensure conservation of the axial symmetry of a given beam throughout the whole system. The need for a vertical steering field, in addition to the longitudinal one provided by each toroidal coil, is emphasized and its form determined. A suitable choice of the angular extent of a torus is shown to suppress axis vibrations at the entrance of the following sector. Finally, the transverse temperature of a cylindrical beam is calculated after specifying the appropriate distribution function.


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