Counterintuitive Behavior in a Problem of Elastic-Plastic Beam Dynamics

1985 ◽  
Vol 52 (3) ◽  
pp. 517-522 ◽  
Author(s):  
P. S. Symonds ◽  
T. X. Yu
Keyword(s):  
Numerical Solution ◽  
Structural Dynamics ◽  
Geometric Nonlinearity ◽  
Short Pulse ◽  
Beam Dynamics ◽  
Pulse Loading ◽  
Type Model ◽  
Wide Spread ◽  
Load Analysis ◽  
Direction Opposite

In a particular example of short pulse loading on a pin-ended beam, the permanent deflection is predicted by a numerical solution to be in the direction opposite that of the load. Analysis of a Shanley-type model shows that this surprising behavior may occur as a consequence of plastic irreversibility combined with geometric nonlinearity, when the peak deflection produced by the pulse lies in a certain range of small magnitudes. Results from a number of well-known structural dynamics codes are shown. These exhibit a wide spread in the predicted final deflections, indicating strong sensitivities of both physical and computational nature.

scholarly journals Beam dynamics issues for the two-frequency crab cavity short pulse scheme

2019 ◽  
Vol 22 (9) ◽  
Author(s):  
Xiaobiao Huang ◽  
Bob Hettel ◽  
Tom Rabedeau ◽  
James Safranek ◽  
Jim Sebek ◽  
...  
Keyword(s):  
Short Pulse ◽  
Beam Dynamics

scholarly journals CLEAVAGE FRACTURE UNDER SHORT PULSE LOADING

1991 ◽  
Vol 01 (C3) ◽  
pp. C3-589-C3-596 ◽  
Author(s):  
H. HOMMA ◽  
Y. KANTO ◽  
K. TANAKA
Keyword(s):  
Cleavage Fracture ◽  
Short Pulse ◽  
Pulse Loading

Evaluation of maximum stresses in thick-walled spherical shell designs subjected to a short pulse loading

1985 ◽  
Vol 17 (12) ◽  
pp. 1765-1771
Author(s):  
V. A. Mal'tsev ◽  
G. V. Stepanov ◽  
Yu. A. Konon ◽  
L. B. Pervukhin
Keyword(s):  
Spherical Shell ◽  
Short Pulse ◽  
Pulse Loading ◽  
Maximum Stresses

On the numerical solution of a BGK-type model for chemical reactions

2007 ◽  
Vol 26 (4) ◽  
pp. 455-472 ◽  
Author(s):  
A. Aimi ◽  
M. Diligenti ◽  
M. Groppi ◽  
C. Guardasoni
Keyword(s):  
Numerical Solution ◽  
Chemical Reactions ◽  
Type Model

Fractal Dimensions in Elastic-Plastic Beam Dynamics

1995 ◽  
Vol 62 (2) ◽  
pp. 523-526 ◽  
Author(s):  
P. S. Symonds ◽  
J.-Y. Lee
Keyword(s):  
Short Pulse ◽  
Fractal Dimensions ◽  
Pulse Loading ◽  
Load Parameter ◽  
Beam Model ◽  
Self Similarity ◽  
Elastic Plastic ◽  
Intersection Points ◽  
Two Degree Of Freedom ◽  
Fractal Number

Calculations of two types of fractal dimension are reported, regarding the elastic-plastic response of a two-degree-of-freedom beam model to short pulse loading. The first is Mandelbrot’s (1982) self-similarity dimension, expressing independence of scale of a figure showing the final displacement as function of the force in the pulse loading; these calculations were made with light damping. These results are equivalent to a microscopic examination in which the magnification is increased by factors of 102; 104; and 106. It is found that the proportion and distribution of negative final displacements remain nearly constant, independent of magnification. This illustrates the essentially unlimited sensitivity to the load parameter, and implies that the final displacement in this range of parameters is unpredictable. The second fractal number is the correlation dimension of Grassberger and Procaccia (1983), derived from plots of Poincare intersection points of solution trajectories computed for the undamped model. This fractional number for strongly chaotic cases underlies the random and discontinuous selection by the solution trajectory of the potential well leading to the final rest state, in the case of the lightly damped model.

scholarly journals Nonlinear deformation of circular discrete ribbed plate under influence of pulse loading

2021 ◽  
Vol 264 ◽  
pp. 02018
Author(s):  
Rustam Khalmuradov ◽  
Utkir Nishonov
Keyword(s):  
Numerical Method ◽  
Geometric Nonlinearity ◽  
Nonlinear Deformation ◽  
Strain State ◽  
Circular Disc ◽  
Pulse Loading ◽  
Stress Strain ◽  
Pulsed Loading ◽  
Stress Strain State ◽  
Unit Function

The stress-strain state of a circular disc, discretely finned in a circle, under the influence of the pulse loading, is numerically investigated. Thus the geometric nonlinearity between displacement and deformation is taken into account. The structure consists of boarding and reinforced ribs, the materials of which are the same and obey Hooke's law. The sections of the ribs are constant. The height of the ribs and their locations are specified using a unit function. It is considered that the plate is deformed under the influence of the pulsed loading. A numerical method is used to solve the problem.

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