Dispersion and Time Integration Schemes in Finite-Element Analysis — A Practical Pictorial Manual

2013 ◽  
Vol 41 (1) ◽  
pp. 44-71
Author(s):  
Miloslav Okrouhlik
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Time Integration ◽  
Element Analysis ◽  
Integration Schemes ◽  
Time Integration Schemes

A Finite Element Analysis for Unbonded Flexible Risers Under Torsion

2007 ◽  
Author(s):  
A. Bahtui ◽  
H. Bahai ◽  
G. Alfano
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Model ◽  
Finite Element Model ◽  
Time Integration ◽  
Element Model ◽  
Integration Scheme ◽  
Element Analysis ◽  
Benchmark Solutions ◽  
The Finite Element Model

This paper presents a detailed finite element analysis of a five-layer unbonded flexible riser. The numerical results are compared analytical solutions for various load cases. In the finite element model all layers are modelled separately with contact interfaces placed between each layer. The finite element model includes the main features of the riser geometry with very little simplifying assumptions made. The numerical model was solved using a fully explicit time-integration scheme implemented in a parallel environment on a 16-processor cluster. The very good agreement found from numerical and analytical comparisons validates the use of our numerical model to provide benchmark solutions against which further detailed investigation will be made.

An Improved Time Integration Algorithm: A Collocation Time Finite Element Approach

2017 ◽  
Vol 17 (02) ◽  
pp. 1750024 ◽  
Author(s):  
Wooram Kim ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Integration Algorithm ◽  
Finite Element Approach ◽  
New Family ◽  
Integration Schemes ◽  
Time Integration Algorithm ◽  
Time Integration Schemes ◽  
Element Approach ◽  
Integration Algorithms

A time collocation finite element approach is employed to develop one- and two-step time integration schemes with algorithmic dissipation control capability. The newly developed time integration schemes are combined to obtain a new family of time integration algorithms using the concept employed by Baig and Bathe. The newly developed algorithm can effectively control the algorithmic dissipation by relating the collocation parameters with the spectral radius in the high frequency limit. The new algorithm provides better accuracy compared with the generalized-[Formula: see text] method for highly dissipative cases and includes the Baig and Bathe method within its family as a special case.

Finite Element Simulation of Diffusion and Precipitation with Application to Internal Oxidation of Ni-Xwt%Cr Alloys at 950°C

2014 ◽  
Vol 783-786 ◽  
pp. 126-135
Author(s):  
Eric Feulvarch
Keyword(s):  
Finite Element ◽  
Internal Oxidation ◽  
Finite Differences ◽  
Time Integration ◽  
Small Time ◽  
Implicit Time ◽  
Integration Algorithm ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes

For the simulation of internal oxidation phenomena, different numerical approaches are proposed in the literature based on 1D finite differences or on explicit time integration schemes which need small time-steps leading to very long computation times. The aim of this paper is to detail a multi-dimentional finite element approach which is coupled with an efficient implicit time integration algorithm. The thermodynamic activities and the total mass fractions are both used as principal nodal variables. The use of finite elements rather than finite differences greatly facilitates the meshing of 2D and 3D bodies. Its implicit time-integration allows using much larger time-steps without any degradation of the results. An application is proposed for the modeling of internal oxidation of chromia for Ni-Xwt%Cr alloys at 950°C by considering the barrier effect of precipitates.

Vibration of a Simple Beam Subjected to a Moving Sprung Mass with Initial Velocity and Constant Acceleration

2016 ◽  
Vol 16 (03) ◽  
pp. 1450109 ◽  
Author(s):  
Shih-Hsun Yin
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Initial Velocity ◽  
Time Integration ◽  
Dynamic Responses ◽  
Constant Acceleration ◽  
Element Discretization ◽  
Integration Schemes ◽  
Average Acceleration ◽  
Time Integration Schemes

In this paper, a semi-analytical solution to the problem of a simply supported beam subjected to a moving sprung mass with initial velocity and constant acceleration or deceleration was presented, which serves as a benchmark for checking the performance of other numerical methods. Herein, a finite element modeling procedure was adopted to tackle the vehicle–bridge interaction, and the responses of the vehicle and bridge were computed by time integration schemes such as the Newmark average acceleration, HHT-[Formula: see text], and Wilson-[Formula: see text] methods. In comparison with the semi-analytical solution, the acceleration response of the beam solved by the Newmark average acceleration method shows spurious high-frequency oscillations caused by the finite element discretization. In contrast, the HHT-[Formula: see text] and Wilson-[Formula: see text] methods can dissipate these oscillations and show more accurate results. Moreover, we found that the dynamic responses of the beam and sprung mass were mainly determined by the initial velocity of the sprung mass, but not by the acceleration or deceleration.

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