A weak form quadrature element formulation for geometrically exact thin shell analysis

2018 ◽  
Vol 202 ◽  
pp. 44-59 ◽  
Author(s):  
Run Zhang ◽  
Hongzhi Zhong
Keyword(s):  
Thin Shell ◽  
Weak Form ◽  
Element Formulation ◽  
Shell Analysis

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.

scholarly journals The fragmentation of expanding shells – limitations of the thin-shell model

2009 ◽  
Vol 5 (S266) ◽  
pp. 375-375
Author(s):  
Jim Dale ◽  
Richard Wünsch ◽  
Jan Palouš ◽  
Ant Whitworth
Keyword(s):  
Shell Model ◽  
Thin Shell ◽  
Shell Analysis ◽  
Expanding Shells

AbstractWe study the fragmentation of expanding shells in the context of the linear thin-shell analysis. We simulate shell fragmentation using the flash AMR code and a variant of the Benz SPH code.

FINITE ELEMENT ANALYSIS OF PIEZOELECTRIC ELASTICITY WITH SINGULAR INPLANE ELECTROELASTIC FIELDS

2006 ◽  
Vol 03 (01) ◽  
pp. 115-135 ◽  
Author(s):  
MENG-CHENG CHEN ◽  
JIAN-JUN ZHU ◽  
K. Y. SZE
Keyword(s):  
Finite Element ◽  
Ad Hoc ◽  
Wedge Angle ◽  
Electric Displacement ◽  
Weak Form ◽  
Efficient Solutions ◽  
Element Formulation ◽  
Displacement Fields ◽  
Element Analysis ◽  
Electroelastic Fields

An ad hoc one-dimensional finite element formulation is developed for the eigenanalysis of inplane singular electroelastic fields at material and geometric discontinuities in piezoelectric elastic materials by using the eigenfunction expansion procedure and the weak form of the governing equations for prismatic sectorial domains composed of piezoelectrics, composites or air. The order of the electroelastic singularities and the angular variation of the stress and electric displacement fields are obtained with the formulation. The influence of wedge angle, polarization orientation, material types, and boundary and interface conditions on the singular electroelastic fields and the order of their singularity are also examined. The simplicity and accuracy of the formulation are demonstrated by comparison to several analytical solutions for piezoelectric and composite multi-material wedges. The nature and speed of convergence suggests that the present eigensolution could be used in developing hybrid elements for use along with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries leading to singular electroelastic states.

Weak Form Finite Element Formulation for the Helmholtz Equation

2004 ◽  
Vol 41 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Lian Yuh Tio ◽  
Andrew A. P. Gibson ◽  
Bernice M. Dillon ◽  
Lionel E. Davis
Keyword(s):  
Finite Element ◽  
Helmholtz Equation ◽  
Weak Form ◽  
Finite Element Formulation ◽  
Element Formulation
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