scholarly journals Using a Combination of FEM and Perturbation Method in Frequency Split Calculation of a Nearly Axisymmetric Shell with Middle Surface Shape Defect

2016 ◽  
Vol 16 (05) ◽  
Author(s):  
D Vakhlyarskiy ◽  
A Guskov ◽  
M Basarab ◽  
V Matveev
Keyword(s):  
Perturbation Method ◽  
Middle Surface ◽  
Surface Shape ◽  
Axisymmetric Shell ◽  
Frequency Split

A Weak Form Implementation of Nonlinear Axisymmetric Shell Equations With Examples

2019 ◽  
Vol 86 (12) ◽  
Author(s):  
Matteo Pezzulla ◽  
Pedro M. Reis
Keyword(s):  
Weak Form ◽  
Surface Shape ◽  
Energy Potential ◽  
Spherical Shells ◽  
Axisymmetric Shell ◽  
Axisymmetric Shells ◽  
Shell Equations ◽  
Thickness Variations ◽  
Nonlinear Deformations ◽  
Dynamic Community

Abstract We present a weak form implementation of the nonlinear axisymmetric shell equations. This implementation is suitable to study the nonlinear deformations of axisymmetric shells, with the capability of considering a general mid-surface shape, non-homogeneous (axisymmetric) mechanical properties and thickness variations. Moreover, given that the weak balance equations are arrived to naturally, any external load that can be expressed in terms of an energy potential can, therefore, be easily included and modeled. We validate our approach with existing results from the literature, in a variety of settings, including buckling of imperfect spherical shells, indentation of spherical and ellipsoidal shells, and geometry-induced rigidity (GIR) of pressurized ellipsoidal shells. Whereas the fundamental basis of our approach is classic and well established, from a methodological view point, we hope that this brief note will be of both technical and pedagogical value to the growing and dynamic community that is revisiting these canonical but still challenging class of problems in shell mechanics.

scholarly journals Frequency Split Elimination Method for a Solid-State Vibratory Angular Rate Gyro with an Imperfect Axisymmetric-Shell Resonator

Sensors ◽  
2015 ◽  
Vol 15 (2) ◽  
pp. 3204-3223 ◽  
Author(s):  
Zhen Lin ◽  
Mengyin Fu ◽  
Zhihong Deng ◽  
Ning Liu ◽  
Hong Liu
Keyword(s):  
Solid State ◽  
Angular Rate ◽  
Elimination Method ◽  
Axisymmetric Shell ◽  
Rate Gyro ◽  
Frequency Split

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

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