A simple explicit single step time integration algorithm for structural dynamics

2019 ◽  
Vol 119 (5) ◽  
pp. 383-403 ◽  
Author(s):  
Wooram Kim
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Single Step ◽  
Integration Algorithm ◽  
Time Integration Algorithm

An explicit time integration algorithm for linear and non-linear finite element analyses of dynamic and wave problems

2018 ◽  
Vol 36 (1) ◽  
pp. 161-177 ◽  
Author(s):  
Mi Zhao ◽  
Huifang Li ◽  
Shengtao Cao ◽  
Xiuli Du
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Single Step ◽  
Degree Of Freedom ◽  
Integration Algorithm ◽  
Explicit Time Integration ◽  
Content Type ◽  
Time Integration Algorithm ◽  
Non Linear ◽  
Explicit Time Integration Algorithm

Purpose The purpose of this paper is to propose a new explicit time integration algorithm for solution to the linear and non-linear finite element equations of structural dynamic and wave propagation problems. Design/methodology/approach The algorithm is completely explicit so that no linear equation system requires solving, if the mass matrix of the finite element equation is diagonal and whether the damping matrix does or not. The algorithm is a single-step method that has the simple starting and is applicable to the analysis with the variable time step size. The algorithm is second-order accurate and conditionally stable. Its numerical stability, dissipation and dispersion are analyzed for the dynamic single-degree-of-freedom equation. The stability of the multi-degrees-of-freedom non-proportional damping system can be evaluated directly by the stability theory on ordinary differential equation. Findings The performance of the proposed algorithm is demonstrated by several numerical examples including the linear single-degree-of-freedom problem, non-linear two-degree-of-freedom problem, wave propagation problem in two-dimensional layer and seismic elastoplastic analysis of high-rise structure. Originality/value A new single-step second-order accurate explicit time integration algorithm is proposed to solve the linear and non-linear dynamic finite element equations. The algorithm has advantages on the numerical stability and accuracy over the existing modified central difference method and Chung-Lee method though the theory and numerical analyses.

Impact Dynamic Analysis of Horizontally Vibrated Conveyor with Coulomb Friction Modeling

2012 ◽  
Vol 619 ◽  
pp. 26-29
Author(s):  
Chao Sheng Song ◽  
Qi Ming Huang ◽  
Zhan Gao ◽  
Jie Xu
Keyword(s):  
Coulomb Friction ◽  
Impact Analysis ◽  
Time Integration ◽  
Impact Excitation ◽  
Friction Modeling ◽  
Integration Algorithm ◽  
Conveyor System ◽  
Time Integration Algorithm ◽  
And Control ◽  
The Impact

This paper introduces dynamic impact analysis as an effective technique for studying the response of horizontal vibrated conveyor with time-varying impact excitation by the falling of the scrap. A two degree-of-freedoms impact dynamic model is formulated considering the static and dynamic coulomb friction between the scrap and chute. Then the time integration algorithm was applied in the program to solve the dynamic equations. Using the proposed method, the impact effects of ideal single scrap and multiple scraps on the dynamic response of the conveyor were analyzed. Computational results reveal numerous interesting dynamic characteristics which can be used to forecast and control the vibration of the scrap and conveyor system.

A Precise and Stiffly Stable Time Integration Method for Vibration Equations

2001 ◽  
Author(s):  
Takeshi Fujikawa ◽  
Etsujiro Imanishi
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Low Frequency ◽  
Quadratic Function ◽  
Time Step ◽  
Integration Algorithm ◽  
Time Integration Method ◽  
Time Integration Algorithm ◽  
Time Integration Methods ◽  
Motion Problems

Abstract A method of time integration algorithm is presented for solving stiff vibration and motion problems. It is absolutely stable, numerically dissipative, and much accurate than other dissipative time integration methods. It achieves high-frequency dissipation, while minimizing unwanted low-frequency dissipation. In this method change of acceleration during time step is expressed as quadratic function including some parameters, whose appropriate values are determined through numerical investigation. Two calculation examples are demonstrated to show the usefulness of this method.

Sign in / Sign up

Export Citation Format

Share Document