Solvability of Pseudoparabolic Equations with Non-Linear Boundary Condition

2020 ◽  
Vol 41 (9) ◽  
pp. 1772-1783
Author(s):  
A. S. Berdyshev ◽  
S. E. Aitzhanov ◽  
G. O. Zhumagul
Keyword(s):  
Boundary Condition ◽  
Linear Boundary ◽  
Linear Boundary Condition ◽  
Non Linear ◽  
Pseudoparabolic Equations

A Three-Dimensional Finite Element Method for Nonsteady State Temperature Distribution in the Rolling Process

2011 ◽  
Vol 101-102 ◽  
pp. 521-524
Author(s):  
Shu Ni Song ◽  
Jing Yi Liu
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Temperature Distribution ◽  
Three Dimensional ◽  
Rolling Process ◽  
Linear Boundary ◽  
Linear Boundary Condition ◽  
Non Linear ◽  
Metal Deformation

The temperature is a key factor that affects the metal deformation and the material property in the rolling process. The metal deformation is often carried along with the variety of temperature. Moreover, the plastic work is converted into the thermal energy during the process of the metal deformation. Therefore, the numerical simulation of the rolling process should take the temperature factors into consideration to improve the prediction accuracy. In this paper, we use the full three-dimensional Rigid-plastic finite element method to predict the temperature distribution which relate to linear or non-linear boundary condition of the free surface. Based on the simulation, the impact of radiant heat-transfer coefficient on the temperature prediction can be obtained. The comparison of the calculated results between the linear and non-linear boundary conditions demonstrates that the temperature obtained on the linear boundary condition has higher accurateness than that obtained on the non-linear boundary condition.

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