Mathematical modelling of enzyme kinetics reaction mechanisms and analytical solutions of non-linear reaction equations

2010 ◽  
Vol 48 (2) ◽  
pp. 179-186 ◽  
Author(s):  
A. Meena ◽  
A. Eswari ◽  
L. Rajendran
Keyword(s):  
Mathematical Modelling ◽  
Enzyme Kinetics ◽  
Analytical Solutions ◽  
Reaction Mechanisms ◽  
Linear Reaction ◽  
Non Linear ◽  
Reaction Equations

On the classification and coding of linear reaction mechanisms

1980 ◽  
Vol 15 (1) ◽  
pp. 113-117 ◽  
Author(s):  
D. Bonchev ◽  
O. N. Temkin ◽  
D. Kamenski
Keyword(s):  
Reaction Mechanisms ◽  
Linear Reaction

Erratum to “Approximate analytical solutions for primary chatter in the non-linear metal cutting model”

2004 ◽  
Vol 272 (1-2) ◽  
pp. 469-470
Author(s):  
J. Warmiński ◽  
G. Litak ◽  
M.P. Cartmell ◽  
R. Khanin ◽  
M. Wiercigroch
Keyword(s):  
Analytical Solutions ◽  
Metal Cutting ◽  
Approximate Analytical Solutions ◽  
Non Linear ◽  
Cutting Model

scholarly journals The elastic-plastic delamination analysis of layered beam configurations

2019 ◽  
Vol 39 (2) ◽  
pp. 165-173
Author(s):  
Victor Rizov
Keyword(s):  
Analytical Solutions ◽  
Strain Energy Release ◽  
Integral Approach ◽  
J Integral ◽  
Elastic Plastic ◽  
Crack Location ◽  
Layered Beams ◽  
Delamination Fracture ◽  
Non Linear ◽  
Point Bend

The elastic-plastic delamination fracture in layered beams was studied theoretically. Two Four Point Bend (FPB) beam configurations (the Double Leg Four Point Bend (DLFPB) and the Single Leg Four Point Bend (SLFPB)) were analyzed. An elastic-plastic constitutive model with power law hardening was used in the analysis. Fracture behavior was studied by applying the J-integral approach. The analytical solutions of the J-integral were obtained at characteristic levels of the external load. The solutions obtained were verified by analyzing the strain energy release rate with taking into account the material non-linearity. The variation of J-integral value in a function of crack location along the beam dept was investigated. The effect of material non-linearity on the fracture was evaluated. The analysis revealed that the J-integral value decreased with increasing the lower crack arm thickness. It was also found that the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members and components made of layered materials. The analytical solutions obtained are very useful for non-linear investigations, since the simple formulae derived capture the essentials of non-linear fracture in the layered beams under consideration.

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