Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing

2010 ◽  
Vol 14 (10) ◽  
pp. 893-904 ◽  
Author(s):  
Austin J. Ramme ◽  
Kiran H. Shivanna ◽  
Vincent A. Magnotta ◽  
Nicole M. Grosland
Keyword(s):  
Gaussian Curvature ◽  
Curvature Analysis ◽  
Hexahedral Meshing ◽  
Block Placement

Growing multiblock structures: a semi-automated approach to block placement for multiblock hexahedral meshing

2012 ◽  
Vol 15 (10) ◽  
pp. 1043-1052 ◽  
Author(s):  
Austin J. Ramme ◽  
Kiran H. Shivanna ◽  
Amy J. Criswell ◽  
Nicole A. Kallemeyn ◽  
Vincent A. Magnotta ◽  
...  
Keyword(s):  
Hexahedral Meshing ◽  
Block Placement

scholarly journals Initial Clinical Experience With a New Conformable Abdominal Aortic Endograft: Aortic Neck Coverage and Curvature Analysis in Challenging Aortic Necks

2021 ◽  
pp. 152660282199672
Author(s):  
Alice Finotello ◽  
Richte Schuurmann ◽  
Sara Di Gregorio ◽  
Gian Antonio Boschetti ◽  
Nabil Chakfé ◽  
...  
Keyword(s):  
Aortic Wall ◽  
Surface Coverage ◽  
Infrarenal Aorta ◽  
Technical Success ◽  
Curvature Analysis ◽  
Average Curvature ◽  
Aortic Neck ◽  
Abdominal Aortic ◽  
Shortest Distance ◽  
New Generation

Objectives: Aim of this work was to investigate precision of deployment and conformability of a new generation GORE EXCLUDER Conformable Endoprosthesis with active control system (CEXC Device, W.L. Gore and Associates, Flagstaff, AZ, USA) by analyzing aortic neck coverage and curvature. Methods: All consecutive elective patients affected by abdominal aortic aneurysm or aortoiliac aneurysm treated at our institution between November 2018 and June 2019 with the new CEXC Device were enrolled. Validated software was adopted to determine the available apposition surface area into the aortic neck, apposition of the endograft to the aortic wall, shortest apposition length (SAL), shortest distance between the endograft fabric and the lowest renal arteries (SFD) and between the endograft fabric and the contralateral renal artery (CFD). Pointwise centerline curvature was also computed. Results: Twelve patients (10 men, median age 78 years (71.75, 81.0)) with available pre- and postoperative computed tomography angiography (CTA) were included. Technical success was obtained in all the cases. Preoperative median length of the proximal aortic neck was 16.1 mm (10.7, 21.7) and suprarenal (α) and infrarenal (β) neck angulation were, respectively, 28.9° (15.7°, 47.5°) and 75.0° (66.9°, 81.4°). Postoperative median apposition surface coverage was 79% (69.25%, 90.75%) of the available apposition surface. SFD and CFD were 1.5 mm (0.75, 5.25) and 7 mm (4.5, 21.5), respectively. Average curvature over the infrarenal aorta decreased from 25 m−1 (21.75, 29.0) to 22.5 m−1 (18.75, 24.5) postoperatively (p=0.02). Maximum curvature did not decrease significantly from 64.5 m−1 (54.25, 92.0) to 62 m−1 (41.75, 71.5) (p=0.1). Conclusions: Our early experience showed that deployment of the CEXC Device is safe and effective for patients with challenging proximal aortic necks. Absence of significant changes between pre- and postoperative proximal aortic neck angulations and curvature confirms the high conformability of this endograft.

scholarly journals Universally bistable shells with nonzero Gaussian curvature for two-way transition waves

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Nikolaos Vasios ◽  
Bolei Deng ◽  
Benjamin Gorissen ◽  
Katia Bertoldi
Keyword(s):  
Gaussian Curvature ◽  
Energy Landscape ◽  
Propagation Distance ◽  
Energy Landscapes ◽  
Bending Energy ◽  
Nonlinear Dynamic Response ◽  
One Dimensional ◽  
Doubly Curved Shells ◽  
Doubly Curved ◽  
The Waves

AbstractMulti-welled energy landscapes arising in shells with nonzero Gaussian curvature typically fade away as their thickness becomes larger because of the increased bending energy required for inversion. Motivated by this limitation, we propose a strategy to realize doubly curved shells that are bistable for any thickness. We then study the nonlinear dynamic response of one-dimensional (1D) arrays of our universally bistable shells when coupled by compressible fluid cavities. We find that the system supports the propagation of bidirectional transition waves whose characteristics can be tuned by varying both geometric parameters as well as the amount of energy supplied to initiate the waves. However, since our bistable shells have equal energy minima, the distance traveled by such waves is limited by dissipation. To overcome this limitation, we identify a strategy to realize thick bistable shells with tunable energy landscape and show that their strategic placement within the 1D array can extend the propagation distance of the supported bidirectional transition waves.

scholarly journals Comment on ,,On the integrability of 2D Hamiltonian systems with variable Gaussian curvature” by A. A. Elmandouh

2021 ◽  
Author(s):  
Wojciech Szumiński ◽  
Andrzej J. Maciejewski
Keyword(s):  
Hamiltonian Systems ◽  
Gaussian Curvature ◽  
Necessary Conditions ◽  
Constant Gaussian Curvature ◽  
Local Coordinates ◽  
Hamiltonian Functions

AbstractIn the paper [1], the author formulates in Theorem 2 necessary conditions for integrability of a certain class of Hamiltonian systems with non-constant Gaussian curvature, which depends on local coordinates. We give a counterexample to show that this theorem is not correct in general. This contradiction is explained in some extent. However, the main result of this note is our theorem that gives new simple and easy to check necessary conditions to integrability of the system considered in [1]. We present several examples, which show that the obtained conditions are effective. Moreover, we justify that our criterion can be extended to wider class of systems, which are given by non-meromorphic Hamiltonian functions.

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