Combined Torsion, Circular and Axial Shearing of a Compressible Hyperelastic and Prestressed Tube

1999 ◽  
Vol 67 (1) ◽  
pp. 33-40 ◽  
Author(s):  
M. Zidi
Keyword(s):  
Nonlinear Equations ◽  
Elastic Material ◽  
Volume Change ◽  
Stretch Ratio ◽  
Kutta Method ◽  
Local Volume ◽  
Runge Kutta Method ◽  
Dependent Behavior ◽  
Runge Kutta ◽  
Circumferential Stretch

In this paper, we study the combined torsion, circular and axial shearing of a compressible hyperelastic and prestressed tube. The analysis is carried out for a class of Ogden elastic material and the governing nonlinear equations are solved numerically using the Runge-Kutta method. The results reported present the effects of the torsion for different shearing loads on the local volume change and the circumferential stretch ratio. The effect of the second invariant-dependent behavior of polynomial materials is also investigated. [S0021-8936(00)01301-5]

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

scholarly journals Randomized Runge–Kutta method — Stability and convergence under inexact information

2021 ◽  
pp. 101554
Author(s):  
Tomasz Bochacik ◽  
Maciej Goćwin ◽  
Paweł M. Morkisz ◽  
Paweł Przybyłowicz
Keyword(s):  
Stability And Convergence ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Inexact Information ◽  
Runge Kutta
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