Simulation of Transient Heat Transfer Based on Element-Free Galerkin Method and Increment-Dimensional Precise Integration Method

2012 ◽  
Vol 204-208 ◽  
pp. 4254-4259
Author(s):  
Fu Liang Mei ◽  
Gui Ling Li
Keyword(s):  
Heat Transfer ◽  
Integration Method ◽  
Step Length ◽  
Grid Size ◽  
Inverse Matrix ◽  
Coupling Method ◽  
Time Step ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Element Free

There were many issues in numerical methods of heat transfer problems such as instability at a big time step length or grid size and no-existence of inverse matrix by time-precise integration method. For sake of avoiding instability and calculating an inverse matrix, a coupling method was put forward based on EFGM and IDPIM. Formulae were deduced according to EFGM and IDPIM. Results show that the coupling method has a higher accuracy and its stability is small subjected to the time step length or grid size, and is to deserve to be popularized.

Precise Integration Method of Pseudo-Dynamic Testing of Structures

2014 ◽  
Vol 580-583 ◽  
pp. 1574-1580
Author(s):  
Hai Bo Wang ◽  
Rong Liu
Keyword(s):  
Integration Method ◽  
Dynamic Test ◽  
Multistep Method ◽  
The State ◽  
State Matrix ◽  
Time Step ◽  
Order Accuracy ◽  
Central Difference ◽  
Precise Integration ◽  
Precise Integration Method

Based on nonlinear precise integration method, two new numerical integration methods of pseudo-dynamic test of structures are presented. One is explicit predict-correct, four order accuracy and multistep method avoiding calculating the inversion of the state matrix. The other is implicit predict-correct, four order accuracy and multistep method that need calculate the inversion of the state matrix. Since their accuracies are superior to the central difference method by enlarging time step and their stabilities are better, the structural systems of multi-degree of freedom could be well tested and the testing work would be largely reduced. Finally, a pseudo-dynamic test of combined tube structure has been executed with the explicit multi-step method.

scholarly journals A Modified Precise Integration Method for Long-Time Duration Dynamic Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Ce Huang ◽  
Minghui Fu
Keyword(s):  
Dynamic Analysis ◽  
Integration Method ◽  
Original Method ◽  
Numerical Dissipation ◽  
Time Duration ◽  
Time Step ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Long Time ◽  
First Time

This paper presents a modified Precise Integration Method (PIM) for long-time duration dynamic analysis. The fundamental solution and loading operator matrices in the first time substep are numerically computed employing a known unconditionally stable method (referred to as original method in this paper). By using efficient recursive algorithms to evaluate these matrices in the first time-step, the same numerical results as those using the original method with small time-step are obtained. The proposed method avoids the need of matrix inversion and numerical quadrature formulae, while the particular solution obtained has the same accuracy as that of the homogeneous solution. Through setting a proper value of the time substep, satisfactory accuracy and numerical dissipation can be achieved.

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”.

Extension of the Wittrick-Williams Algorithm to Mixed Variable Systems

1997 ◽  
Vol 119 (3) ◽  
pp. 334-340 ◽  
Author(s):  
Zhong Wanxie ◽  
F. W. Williams ◽  
P. N. Bennett
Keyword(s):  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Integration Method ◽  
Dynamic Stiffness ◽  
Integration Algorithm ◽  
Precise Integration ◽  
Matrix Computations ◽  
Precise Integration Method ◽  
Count Method ◽  
Mixed Variable

A precise integration algorithm has recently been proposed by Zhong (1994) for dynamic stiffness matrix computations, but he did not give a corresponding eigenvalue count method. The Wittrick-Williams algorithm gives an eigenvalue count method for pure displacement formulations, but the precise integration method uses a mixed variable formulation. Therefore the Wittrick-Williams method is extended in this paper to give the eigenvalue count needed by the precise integration method and by other methods involving mixed variable formulations. A simple Timoshenko beam example is included.

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