Parallel Multilevel Preconditioners for Thin Shell Problems

2009 ◽  
Author(s):  
M. Theß
Keyword(s):  
Thin Shell ◽  
Multilevel Preconditioners

Preparation and Electrocatalytic Performance of Thin-shell Ni/Pt Core-shell Nanoparticles

2012 ◽  
Vol 27 (1) ◽  
pp. 95-101
Author(s):  
Shi-Bin LIU ◽  
Chun-Ying YANG ◽  
Zhong-Lin ZHANG ◽  
Dong-Hong DUAN ◽  
Xiao-Gang HAO ◽  
...  
Keyword(s):  
Thin Shell ◽  
Core Shell ◽  
Shell Nanoparticles ◽  
Electrocatalytic Performance ◽  
Core Shell Nanoparticles

scholarly journals Thin shell aerogel fabrication for FIREX-I targets using high viscosity (phloroglucinol carboxylic acid)/formaldehyde solution

2008 ◽  
Vol 26 (3) ◽  
pp. 449-453 ◽  
Author(s):  
H. Yang ◽  
K. Nagai ◽  
M. Nakai ◽  
T. Norimatsu
Keyword(s):  
Carboxylic Acid ◽  
Thin Shell ◽  
Shell Thickness ◽  
High Viscosity ◽  
Formaldehyde Solution ◽  
Resorcinol Formaldehyde ◽  
Foam Structure ◽  
Final Density ◽  
Emulsion Process ◽  
High Level

AbstractCapsules with a thin aerogel shell were prepared by the OO/W/OIemulsion process. (Phloroglucinol carboxylic acid)/formaldehyde (PF) was used as the water phase (W) solution to form the shell of the capsule. PF is a linear polymer prepared from phloroglucinol carboxylic acid. The viscosity of the PF solution can reach a high level of 9×10−5m2/s without gelation while resorcinol/formaldehyde (RF) gelates at ~3–4×10−5m2/s. Using the viscous PF solution, capsule with a 17 µm gel shell was fabricated. This thickness satisfies the specification of the first phase of Fast Ignition Realization Experiment (FIREX-I) at Osaka University. When PF gel was extracted to remove the organic solvent, shrinkage of 9% occurred. The final density of the PF aerogel was 145 mg/cm3. Both the shell thickness and density can satisfy the specification of FIREX-I. The pore size of the PF aerogel was less than 100 nm while that of RF was 200–500 nm. The SEM showed that PF had particle-like foam structure while RF had fibrous-like foam structure.

scholarly journals Volume decay and concentration of high-dimensional Euclidean balls – a PDE and variational perspective

Analysis ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Siran Li
Keyword(s):  
Banach Space ◽  
Discrete Geometry ◽  
Thin Shell ◽  
Euclidean Geometry ◽  
Convex Geometry ◽  
Regularity Theory ◽  
Elliptic Partial Differential Equations ◽  
High Dimensional ◽  
Space Theory ◽  
Elementary Calculus

AbstractIt is a well-known fact – which can be shown by elementary calculus – that the volume of the unit ball in \mathbb{R}^{n} decays to zero and simultaneously gets concentrated on the thin shell near the boundary sphere as n\nearrow\infty. Many rigorous proofs and heuristic arguments are provided for this fact from different viewpoints, including Euclidean geometry, convex geometry, Banach space theory, combinatorics, probability, discrete geometry, etc. In this note, we give yet another two proofs via the regularity theory of elliptic partial differential equations and calculus of variations.

Hybrid mesh generation for the thin shell of thin-shell plastic parts for mold flow analysis

2021 ◽  
Author(s):  
Jiing-Yih Lai ◽  
Jia-Wei Wu ◽  
Pei-Pu Song ◽  
Tzu-Yao Chou ◽  
Yao-Chen Tsai ◽  
...  
Keyword(s):  
Mesh Generation ◽  
Thin Shell ◽  
Flow Analysis ◽  
Hybrid Mesh ◽  
Mold Flow Analysis ◽  
Plastic Parts ◽  
Mold Flow

scholarly journals Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1450
Author(s):  
Yuri Vassilevski ◽  
Alexey Liogky ◽  
Victoria Salamatova
Keyword(s):  
Aortic Valve ◽  
Finite Elements ◽  
Shell Model ◽  
Thin Shell ◽  
Aortic Valves ◽  
Shear Moduli ◽  
Force Method ◽  
Elastic Potentials ◽  
Shell Analysis ◽  
First Time

Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first time. Our numerical thin shell model is based on a combination of the hyperelastic nodal forces method and the rotation-free finite elements. The shell model is verified on several popular benchmarks for thin-shell analysis. The relative error with respect to reference solutions does not exceed 1–2%. We apply our numerical shell and membrane formulations to model the closure of an idealized aortic valve varying hyperelasticity models and their shear moduli. The coaptation characteristics become almost insensitive to elastic potentials and sensitive to bending stiffness, which reduces the coaptation zone.

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