Extended precise integration method for axisymmetric thermo-elastic problem in transversely isotropic material

2015 ◽  
Vol 40 (2) ◽  
pp. 297-312 ◽  
Author(s):  
Zhi Yong Ai ◽  
Quan Long Wu ◽  
Lu Jun Wang
Keyword(s):  
Isotropic Material ◽  
Integration Method ◽  
Transversely Isotropic ◽  
Elastic Problem ◽  
Transversely Isotropic Material ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Extended Precise Integration Method

Instability Analysis of Parametrically Excited Marine Risers by Extended Precise Integration Method

2017 ◽  
Vol 17 (08) ◽  
pp. 1750096 ◽  
Author(s):  
Song Lei ◽  
Xiang Yuan Zheng ◽  
Daoyi Chen ◽  
Yi Li
Keyword(s):  
Integration Method ◽  
Dynamic Instability ◽  
Lateral Displacement ◽  
Dynamic Buckling ◽  
Structural Safety ◽  
Local Dynamic ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Hydrodynamic Damping ◽  
Extended Precise Integration Method

The objective of this paper is to investigate the dynamic instability of deepwater top-tensioned risers (TTRs), when subjected to the fluctuating axial tension originated from the heave motion of a surface floating platform as the instability source. Based on a rigorous derivation on the governing equation, a reduced model of the lateral displacement of a TTR is achieved by an ordinary differential equation with periodic coefficients. To identify the instability range of practical amplitudes and frequencies of the excitation, a newly proposed extended precise integration method (EPIM) is employed to generate the Floquet transition matrix (FTM). EPIM possesses high precision and efficiency due to the doubling algorithm and the increment-storing technique. The instability charts of TTRs in several typical depths are numerically obtained using EPIM. The effects of factors such as the top tension ratio, the stiffness of the heave compensators, damping constant, and internal flow velocity on the instability region are analyzed. In addition, because the nonlinear hydrodynamic damping will lead the TTR’s lateral vibration to reach a steady state, the instability response is thereby simulated by EPIM. Three response scenarios are discussed with examples. As the heave amplitude increases, the parametric resonance of the TTR is first triggered, then the transition stage appears, and ultimately the local dynamic buckling occurs. The bending stress analysis shows that the local dynamic buckling is the worst scenario for structural safety.

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

THE ANALYSIS OF DYNAMICAL RESPONSE OF TRANSVERSELY ISOTROPIC MATERIAL UNDER BLASTING LOAD

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1443-1448
Author(s):  
YUE-XIU WU ◽  
QUAN-SHENG LIU
Keyword(s):  
Isotropic Material ◽  
Peak Velocity ◽  
Transversely Isotropic ◽  
Normal Direction ◽  
Dynamical Response ◽  
Transversely Isotropic Material ◽  
Peak Acceleration ◽  
Loading Direction ◽  
Blasting Load ◽  
Explosion Load

To understand the dynamic response of transversely isotropic material under explosion load, the analysis is done with the help of ABAQUS software and the constitutive equations of transversely isotropic material with different angle of isotropic section. The result is given: when the angle of isotropic section is settled, the velocity and acceleration of measure points decrease with the increasing distance from the explosion borehole. The velocity and acceleration in the loading direction are larger than those in the normal direction of the loading direction and their attenuation are much faster. When the angle of isotropic section is variable, the evolution curves of peak velocity and peak acceleration in the loading direction with the increasing angles are notching parabolic curves. They get their minimum values when the angle is equal to 45 degree. But the evolution curves of peak velocity and peak acceleration in the normal direction of the loading direction with the increasing angles are overhead parabolic curves. They get their maximum values when the angle is equal to 45 degree.

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