Relations Between Several Path Following Algorithms and Local and Global Newton Methods

SIAM Review ◽  
1980 ◽  
Vol 22 (3) ◽  
pp. 263-274 ◽  
Author(s):  
C. B. Garcia ◽  
F. J. Gould
Keyword(s):  
Path Following ◽  
Newton Methods ◽  
Path Following Algorithms

On Numerical Results of Reticulated Shell Buckling

1992 ◽  
Vol 7 (4) ◽  
pp. 299-319 ◽  
Author(s):  
Heinrich Rothert ◽  
Norbert Gebbeken
Keyword(s):  
Path Following ◽  
Shell Structures ◽  
Element Analysis ◽  
Economical Analysis ◽  
Shell Buckling ◽  
Stiffness Matrices ◽  
Load Carrying ◽  
The Stability ◽  
Stability Of Structures ◽  
Path Following Algorithms

This paper is mainly focused on the numerical methods which are used to calculate realistically the load-carrying behaviour of reticulated shell structures. It is generally assumed that for an economical analysis, aimed at the saving of material, the material non-linearity has to be taken into consideration if dead loads prevail. For this in the context of finite element analysis the stiffness matrices of elastic and elastic-plastic rod elements are presented. In order to ensure the stability of structures it is indispensable to detect limit loads such as snap-through loads and bifurcation loads. Assuming that snap-through phenomena are quasi static, path-following algorithms can be implemented to trace the load-deflection curves in the postbuckling domain. The testing of the reliability and stability of the algorithms requires a sufficient number of numerical examples. Few will be presented.

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