On Non-Linear Static and Dynamic Thin Shell Analysis

1999 ◽  
pp. 131-138
Author(s):  
Frano B. Damjanić
Keyword(s):  
Thin Shell ◽  
Shell Analysis ◽  
Non Linear

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.

ANALYSIS OF ELASTIC IMPACT ON THIN SHELL STRUCTURES

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1349-1354 ◽  
Author(s):  
SHIUH-CHUAN HER ◽  
CHING-CHUAN LIAO
Keyword(s):  
Differential Equation ◽  
Contact Force ◽  
Thin Shell ◽  
Time History ◽  
Dynamic Responses ◽  
Low Velocity Impact ◽  
Integro Differential Equation ◽  
Impact Process ◽  
Non Linear ◽  
The Impact

In this paper, a solution method for the response of a thin shell structure subjected to low velocity impact by a sphere is presented. The governing equation of the impact process is obtained by simultaneously solving the equations of motions for the sphere and shell. The derivation is based on the explicit expression of the displacement of the mid-surface of the shell under a single impulse load acting normal to apex of the shell. Incorporating the theory of convolution and Hertz contact law, a non-linear integro-differential equation in terms of the indentation of the contact, for the impact process is derived. The non-linear integro-differential equation is solved by the numerical scheme of Runge-Kutta method to obtain the time history of the contact force at the impact point of the shell. The contact force is then applied on the apex of the shell, the dynamic responses of the shell including the displacement and stress are obtained by the finite element method. The results are validated with the experimental test and numerical calculation published in the literatures. The effects of the radius and velocity of the impactor on the impact response is investigated through parametric study.

scholarly journals Simulations of the non-linear thin shell instability

2013 ◽  
Vol 431 (1) ◽  
pp. 710-721 ◽  
Author(s):  
A. D. McLeod ◽  
A. P. Whitworth
Keyword(s):  
Thin Shell ◽  
Non Linear
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