Energy and momentum conserving elastodynamics of a non-linear brick-type mixed finite shell element

2001 ◽  
Vol 50 (8) ◽  
pp. 1801-1823 ◽  
Author(s):  
Christian Miehe ◽  
Jörg Schröder
Keyword(s):  
Shell Element ◽  
Non Linear ◽  
Energy And Momentum ◽  
Finite Shell

AC0 three-node shell element for non-linear structural analysis

1994 ◽  
Vol 37 (14) ◽  
pp. 2339-2364 ◽  
Author(s):  
P. Boisse ◽  
J. L. Daniel ◽  
J. C. Gelin
Keyword(s):  
Structural Analysis ◽  
Shell Element ◽  
Non Linear

A non-linear investigation of critical levels for internal atmospheric gravity waves

1971 ◽  
Vol 50 (3) ◽  
pp. 545-563 ◽  
Author(s):  
R. J. Breeding
Keyword(s):  
Steady State ◽  
Linear Theory ◽  
Gravity Waves ◽  
Incident Wave ◽  
Critical Level ◽  
Internal Gravity Waves ◽  
Mean Flow ◽  
Non Linear ◽  
Energy And Momentum ◽  
Almost All

The behaviour of internal gravity waves near a critical level is investigated by means of a transient two dimensional finite difference model. All the important non-linear, viscosity and thermal conduction terms are included, but the rotational terms are omitted and the perturbations are assumed to be incompressible. For Richardson numbers greater than 2·0 the interaction of the incident wave and the mean flow is largely as predicted by the linear theory–very little of the incident wave penetrates through the critical level and almost all of the wave's energy and momentum are absorbed by changes in the original wind. However, these changes in the wind are centred above the critical level, so that the change in the wind has only a small effect on the height of the critical level. For Richardson numbers less than 2·0 and greater than 0·25 a significant fraction of the incident wave is reflected, part of which could have been predicted by the linear theory. For these stable Richardson numbers a steady state is apparently reached where the maximum wind change continues to grow slowly, but the minimum Richardson number and wave magnitudes remain constant. This condition represents a balance between the diffusion outward of the added momentum and the rate at which it is absorbed. For Richardson numbers less than 0·25, over-reflexion, predicted from the linear theory, is observed, but because the system is dynamically unstable no over-reflecting steady state is ever reached.

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