Subcycled Hourglass Control for Explicit Time Integration of Dynamic Relaxation Equations

2002 ◽  
Author(s):  
D. R. Metzger ◽  
S. Gao
Keyword(s):  
Temporal Integration ◽  
Time Integration ◽  
Three Dimensional ◽  
Internal Force ◽  
Time Interval ◽  
Time Step ◽  
Central Difference ◽  
Finite Element Program ◽  
Explicit Finite Element ◽  
Hourglass Control

Explicit methods, such as the central difference operator, rely on the economical evaluation of internal forces at each time step of a transient dynamic problem. One-point quadrature applied to the spatial discretization provides the greatest efficiency, but hourglass control is required to eliminate spurious zero energy modes. Computationally practical hourglass control methods involve considerable approximation in evaluating the internal force. Thus, a small additional approximation due to an alternative temporal integration of the hourglass force may not seriously affect the accuracy of the analysis. In particular, the possibility of evaluating the hourglass terms on a larger time interval than the usual stable time step could provide significant efficiencies. The proposed approach of subcycling the hourglass terms is examined in detail with respect to stability and accuracy. Implementation into an explicit finite element program is demonstrated on a three-dimensional example that involves several hourglass modes, and the new method proves to be beneficial for noninertial problems where artificial damping is used.

Comparison of Two Time-Integration Algorithms for an Anisotropic Damage Model Coupled with Plasticity

2015 ◽  
Vol 784 ◽  
pp. 292-299 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Marek Fassin ◽  
Stefanie Reese
Keyword(s):  
Evolution Equations ◽  
Damage Model ◽  
Time Integration ◽  
Three Dimensional ◽  
Anisotropic Damage ◽  
Euler Scheme ◽  
The Finite Element Method ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Integration Algorithms

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. (2000) are compared. Specifically, the standard implicit Euler scheme is compared to an algorithm which implicitly solves the elasto-plastic evolution equations and explicitly computes the damage update. To this end, a three dimensional bending example is solved using the finite element method and the results of the two algorithms are compared for different time step sizes.

Direct Numerical Simulation of the Interaction of an Ultra Short-Pulsed Intense Laser With a H2+ Molecule

2008 ◽  
Author(s):  
Y.-M. Lee ◽  
J.-S. Wu ◽  
T.-F. Jiang ◽  
Y.-S. Chen
Keyword(s):  
Domain Decomposition Method ◽  
Time Integration ◽  
Three Dimensional ◽  
Time Algorithm ◽  
Intense Laser ◽  
Angle Of Incidence ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
H2 Molecule

In this paper, interactions of a linearly polarized ultra short-pulsed intense laser with a single H2+ molecule at various angles of incidence are studied by directly solving the time-dependent three-dimensional Schrodinger equation (TDSE), assuming Born-Oppenheimer approximation. An explicit stagger-time algorithm is employed for time integration of the TDSE, in which the real and imaginary parts of the wave function are defined at alternative times, while a cell-centered finite-volume method is utilized for spatial discretization of the TDSE on Cartesian grids. The TDSE solver is then parallelized using domain decomposition method on distributed memory machines by applying a multi-level graph-partitioning technique. The solver is applied to simulate laser-molecular interaction with test conditions including: laser intensity of 0.5*1014 W/cm2, wavelength of 800 nm, three pulses in time, angle of incidence of 0–90° and inter-nuclear distance of 2 a.u.. Simulation conditions include 4 million hexahedral cells, 90 a.u. long in z direction, and time-step size of 0.005 a.u.. Ionization rates, harmonic spectra and instantaneous distribution of electron densities are then obtained from the solution of the TDSE. Future possible extension of the present method is also outlined at the end of this paper.

Studies on the Accuracy Stability and Efficiency of a New Time Integration Scheme for Ballast Modeling Using the Discrete Element Method

2014 ◽  
Author(s):  
G. F. Mathews ◽  
R. L. Mullen ◽  
D. C. Rizos
Keyword(s):  
Particle Interaction ◽  
Time Integration ◽  
Discrete Element ◽  
Critical Discussion ◽  
Implicit Time ◽  
Integration Scheme ◽  
Computationally Efficient ◽  
Time Step ◽  
Central Difference ◽  
Time Integration Scheme

This paper presents the development of a semi-implicit time integration scheme, originally developed for structural dynamics in the 1970’s, and its implementation for use in Discrete Element Methods (DEM) for rigid particle interaction, and interaction of elastic bodies that are modeled as a cluster of rigid interconnected particles. The method is developed in view of ballast modeling that accounts for the flexibility of aggregates and the arbitrary shape and size of granules. The proposed scheme does not require any matrix inversions and is expressed in an incremental form making it appropriate for non-linear problems. The proposed method focuses on improving the efficiency, stability and accuracy of the solutions, as compared to current practice. A critical discussion of the findings of the studies is presented. Extended verification and assessment studies demonstrate that the proposed algorithm is unconditionally stable and accurate even for large time step sizes. It is demonstrated that the proposed method is at least as computationally efficient as the Central Difference Method. Guidelines for the implementation of the method to ballast modeling are discussed.

Bulk Forming Simulation on High Performance Computers

1994 ◽  
Author(s):  
Wing L. Cheng
Keyword(s):  
Geometric Modeling ◽  
Three Dimensional ◽  
Work Piece ◽  
Communication Line ◽  
Finite Element Program ◽  
Valve Body ◽  
Explicit Finite Element ◽  
Forging Process ◽  
Fine Mesh ◽  
Bulk Forming

Abstract Modeling of complicated three-dimensional bulk forming processes remains a challenge to scientists and engineers. Not only does it require a good mathematical model which gives an accurate geometric representation of the dies and the work-piece to capture the physics of the forming processes, it also needs the appropriate computers to carry out different parts of the modeling effort including the numerical simulation. This paper describes our experience on a computer analysis of a three-dimensional multi-stage forging process using an explicit finite element program and a combination of graphic workstations and supercomputers. A three-stage forging of a valve body was used to illustrate the simulation process. A Scalar Graphic Workstation was used in geometric modeling, numerical calculations for the first two stages of the forging process when a coarse model was adequate, and post-processing of the results. A CRAY Y-MP Supercomputer was required to simulate the third stage of the forging process when a fine mesh was needed to capture the details of the material flows. Data transfer was accommodated by a full T-1 communication line between the supercomputer and the workstation. The availability of the advanced software tools and these computer resources provides us the ability to model an entire range of bulk forming problems.

AN EXPLICIT SMOOTHED FINITE ELEMENT METHOD (SFEM) FOR ELASTIC DYNAMIC PROBLEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 1340002 ◽  
Author(s):  
X. Y. CUI ◽  
G. Y. LI ◽  
G. R. LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Time Integration ◽  
Internal Force ◽  
Dynamic Problems ◽  
Central Difference ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Central Difference Method ◽  
Element Method

This paper presents an explicit smoothed finite element method (SFEM) for elastic dynamic problems. The central difference method for time integration will be used in presented formulations. A simple but general contact searching algorithm is used to treat the contact interface and an algorithm for the contact force is presented. In present method, the problem domain is first divided into elements as in the finite element method (FEM), and the elements are further subdivided into several smoothing cells. Cell-wise strain smoothing operations are used to obtain the stresses, which are constants in each smoothing cells. Area integration over the smoothing cell becomes line integration along its edges, and no gradient of shape functions is involved in computing the field gradients nor in forming the internal force. No mapping or coordinate transformation is necessary so that the element can be used effectively for large deformation problems. Through several examples, the simplicity, efficiency and reliability of the smoothed finite element method are demonstrated.

Time-Varying Behavior of a Statically Indeterminate Shafting System in a Hydrodynamic Journal Bearing

1987 ◽  
Vol 109 (1) ◽  
pp. 115-123 ◽  
Author(s):  
Z. H. Karni ◽  
M. G. Parsons ◽  
Z. P. Mourelatos
Keyword(s):  
Control Method ◽  
Optimization Technique ◽  
Three Dimensional ◽  
Integration Time ◽  
Time Varying ◽  
The Finite Element Method ◽  
Time Step ◽  
Hydrodynamic Analysis ◽  
Oil Film ◽  
Hourglass Control

A new direct iterative method for obtaining the time-varying behavior of a statically indeterminate shafting system within one of its hydrodynamic journal bearings is described. A modified Newmark’s method is used to step in time. At each integration time step an optimization technique iterates between the shafting system and the oil film analyses until an equilibrium is achieved. The three-dimensional shafting system structural analysis and the two-dimensional oil film hydrodynamic analysis utilize the finite element method. The “hourglass control” method is employed for the construction of the oil film fluidity matrix. A numerical example illustrates the method.

Study on the Vertical Rational Structure of Tunnel Lining in the Fault-Rupture Zone

2011 ◽  
Vol 368-373 ◽  
pp. 2870-2874
Author(s):  
De Wu Li
Keyword(s):  
Three Dimensional ◽  
Internal Force ◽  
Surrounding Rock ◽  
Tunnel Lining ◽  
Rupture Zone ◽  
Fault Rupture ◽  
Finite Element Program ◽  
Element Program ◽  
Initial Support ◽  
In The Beginning

Related to the actual project in the new Qi Daoliang tunnel between Lanzhou and Lintao highway, select 300-meter calculation range along the tunnel vertically including fault-rupture zone and effect fault-rupture zone, utilize 8 -node, 6-plane block element to scatter the calculating range, at the same time, use the deduced 8 -node, three dimensional jointed element to imitate the transformation gap of the tunnel lining, employ three-dimensional elasto-plastic static finite element program to analyze stress and transformation state of surrounding rock and lining in different construction stages of the new Qi Daoliang tunnel. Through the analysis and comparison of the calculation result of the three conditions: not placing transformation gap through, placing one transformation gap in the middle of the fault-rupture zone, placing two transformation gaps in the beginning and the end of the fault-rupture zone etc, we can get the following points: ①The gallery transformation in the fault-rupture zone and the plastic area in the surrounding rock are obviously bigger than the non-fault-rupture zone. ②Owing to the effect of fault-rupture zone, the increasing range of internal force of the initial support and twice lining is about 10% to 30%. ③Placing the transformation gap in the fault-rupture zone can obviously play a role in releasing lining internal force and transformation energy in the surrounding rock. ④In the start and end changing point of fault-rupture zone, the transformation gap should be placed in the tunnel lining.

Unconditional Stability in Numerical Time Integration Methods

1973 ◽  
Vol 40 (2) ◽  
pp. 417-421 ◽  
Author(s):  
R. D. Krieg
Keyword(s):  
Time Integration ◽  
Step Size ◽  
Time Step ◽  
Central Difference ◽  
Integration Methods ◽  
Time Step Size ◽  
Time Integration Method ◽  
Time Integration Methods ◽  
Numerical Time Integration ◽  
Difference Time

Methods of numerical time integration of the equation M¯q¨ + K¯q = f are examined in this paper. A particular class of explicit time integration methods is defined and this class is searched for an unconditionally stable method. The class is found to contain no such method and, furthermore, is found to contain no method with a larger stable time step size than that characterized by the simple central difference time integration method.

Dynamic, Modal and Wave Propagation Analyses of 3D Functionally Graded Continua

2009 ◽  
Vol 631-632 ◽  
pp. 17-22
Author(s):  
Ganesh Anandakumar ◽  
Jeong Ho Kim
Keyword(s):  
Wave Propagation ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Axial Stress ◽  
Time Integration ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Central Difference ◽  
Base Function ◽  
Fixed End

Transient dynamic behavior of a three-dimensional (3D) homogeneous cantilever beam under sinusoidal loading at the free end is verified using the finite element method (FEM). Explicit central difference technique is used for the time integration of finite elements. The tip displacement and maximum stress at the fixed end obtained using the FEM agree well with exact solutions. Modal analysis of a functionally graded (FG) 3D cantilever beam is investigated using Rayleigh-Ritz (RR) method and the FEM. The natural frequencies obtained using the RR method converges as the number of terms in the assumed base function increases. The natural frequencies vary considerably with the gradation of the beam, more for lower modes than for higher modes. Wave propagation in a fixed-free 3D bar is studied using the FEM. Axial stress results for the homogeneous bar with zero Poisson’s ratio agree closely with 1D exact solution. For the FG bar, we see that gradation affects stresses considerably more so at the fixed end than at other locations.

Sign in / Sign up

Export Citation Format

Share Document