Numerical analysis of the branching of solutions to nonlinear equations for cylindrical shells

2006 ◽  
Vol 42 (1) ◽  
pp. 90-97 ◽  
Author(s):  
N. I. Obodan ◽  
V. A. Gromov
Keyword(s):  
Numerical Analysis ◽  
Nonlinear Equations ◽  
Cylindrical Shells ◽  
Branching Of Solutions

scholarly journals Numerical Analysis of Natural Vibrations of Cylindrical Shells Made of Aluminum Alloy

2020 ◽  
Vol 55 (4) ◽  
pp. 502-508
Author(s):  
P. V. Yasniy ◽  
M. S. Mykhailyshyn ◽  
Yu. I. Pyndus ◽  
M. I. Hud
Keyword(s):  
Aluminum Alloy ◽  
Numerical Analysis ◽  
Cylindrical Shells ◽  
Natural Vibrations

Large-Strain Axisymmetric Deformation of Cylindrical Shells

1987 ◽  
Vol 54 (2) ◽  
pp. 287-291 ◽  
Author(s):  
G. W. Brodland ◽  
H. Cohen
Keyword(s):  
Nonlinear Equations ◽  
Energy Minimization ◽  
Parametric Analysis ◽  
Large Strain ◽  
Cylindrical Shells ◽  
Radial Force ◽  
Axisymmetric Deformation ◽  
The Other ◽  
Large Strains ◽  
Minimization Technique

Nonlinear equations are derived for the axisymmetric deformation of thin, cylindrical shells made of Mooney-Rivlin materials and subject to arbitrarily large strains and rotations. These equations are then implemented numerically using an energy minimization technique. Finally, an extensive parametric analysis is done of cylindrical shells which are clamped at one end and loaded with either a radial force or an edge moment uniformly distributed along the circumference of the other end.

Branching of Solutions of Nonlinear Equations

SIAM Review ◽  
1971 ◽  
Vol 13 (3) ◽  
pp. 289-332 ◽  
Author(s):  
Ivar Stakgold
Keyword(s):  
Nonlinear Equations ◽  
Branching Of Solutions

scholarly journals A New Iterative Numerical Continuation Technique for Approximating the Solutions of Scalar Nonlinear Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-21 ◽  
Author(s):  
Grégory Antoni
Keyword(s):  
Numerical Analysis ◽  
Iterative Method ◽  
Iterative Algorithm ◽  
Nonlinear Equations ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Numerical Continuation ◽  
Stationary Type ◽  
Continuation Technique ◽  
New Iterative Method

The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.

Numerical Analysis of the Kinematic Working Capability of Mechanisms

1991 ◽  
Author(s):  
Feng-Cheng Yang ◽  
Edward J. Haug
Keyword(s):  
Numerical Analysis ◽  
Computer Graphics ◽  
Nonlinear Equations ◽  
Numerical Algorithm ◽  
Systems Of Nonlinear Equations ◽  
Computer Implementation ◽  
Numerical Techniques ◽  
Workspace Analysis ◽  
Working Capability ◽  
Numerical Formulation

Abstract An approach to numerical analysis of the kinematic dexterity of mechanisms is presented. Dextrous workspace problems are defined and illustrated. Composite workspaces are introduced to characterize both positioning and orienting capabilities of mechanisms. Using the composite workspace, numerical techniques for dextrous workspace analysis are presented. A numerical formulation and computer implementation that incorporates computer graphics and a numerical algorithm for solving systems of nonlinear equations are presented. Examples are given to illustrate the techniques developed.

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