scholarly journals High-Order Time-Integration Schemes with Explicit Time-Splitting Methods

2009 ◽  
Vol 137 (11) ◽  
pp. 4047-4060 ◽  
Author(s):  
Sang-Hun Park ◽  
Tae-Young Lee
Keyword(s):  
Numerical Models ◽  
Time Integration ◽  
High Order ◽  
Integration Scheme ◽  
High Order Schemes ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Time Integration Scheme ◽  
High Order Time ◽  
Fast Waves

Abstract New high-order time-integration schemes for fully elastic models are presented. The new schemes, formulated using the Richardson extrapolation that employs leapfrog-type schemes, can give a good performance for linear model problems and ensure overall stability when they are combined with a forward–backward scheme for fast waves. The new and existing schemes show differences in the order of accuracy. Thus, they can be useful for investigating the impacts of time-integration scheme accuracy on the performance of numerical models. The high-order schemes are found to play an important role in the improvement of high-resolution simulations, according to idealized tests. The new schemes are less efficient than other well-known schemes at moderate spatial resolutions. However, the new schemes can be more efficient than the existing schemes when the resolution becomes very high.

A COMPOSITE TIME INTEGRATION SCHEME FOR DYNAMIC ADHESION AND ITS APPLICATION TO GECKO SPATULA PEELING

2014 ◽  
Vol 11 (05) ◽  
pp. 1350104 ◽  
Author(s):  
SACHIN S. GAUTAM ◽  
ROGER A. SAUER
Keyword(s):  
Nonlinear Response ◽  
Time Integration ◽  
Computational Cost ◽  
Integration Scheme ◽  
Time Step ◽  
Integration Schemes ◽  
Newmark Scheme ◽  
Highly Nonlinear ◽  
Time Integration Schemes ◽  
Time Integration Scheme

Simulation of dynamic adhesive peeling problems at small scales has attracted little attention so far. These problems are characterized by a highly nonlinear response. Accurate and stable time integration schemes are required for simulation of dynamic peeling problems. In the present work, a composite time integration scheme is proposed for the simulation of dynamic adhesive peeling problems. It is shown through numerical examples that the proposed scheme remains stable and also has some gain in accuracy. The performance of the scheme is compared with two collocation-based schemes, i.e., Newmark scheme and Bathe composite scheme. It is shown that the proposed scheme and Bathe composite scheme perform equally. However, the proposed scheme adds very little to the computational cost of Newmark scheme. Through a numerical simulation of the peeling of a gecko spatula from a rigid substrate it is shown that the proposed scheme and the Bathe composite scheme are able to simulate the complete peeling process for given time step whereas the Newmark scheme diverges. It is also shown that the maximum pull-off force is within the range reported in the literature.

A Cross Weighted-Residual Time Integration Scheme for Structural Dynamics

2014 ◽  
Vol 14 (06) ◽  
pp. 1450023 ◽  
Author(s):  
Wooram Kim ◽  
Sang-Shin Park ◽  
J. N. Reddy
Keyword(s):  
Structural Dynamics ◽  
Linear Time ◽  
Time Integration ◽  
Velocity Fields ◽  
Inner Product ◽  
Integration Scheme ◽  
Time Interval ◽  
Element Discretization ◽  
Integration Schemes ◽  
Time Integration Scheme

In this article, we develop a novel stable time integration scheme for the transient analysis of structural dynamics problems. A second-order (in time) differential operator equation (e.g. obtained after finite element discretization in space) is written as a pair of first-order equations in terms of displacements and velocities. Then the solution is sought by minimizing the inner product of the residuals in the two equations (an unconventional approach) over typical time interval to obtain a symmetric set of algebraic equations involving displacements and velocities at two subsequent intervals. The new time integration scheme is termed the cross weighted-residual (CWR) time integration scheme because each of the two residuals takes the other one as a weight function in the minimization. The CWR time integration scheme is developed by using a uniform linear time approximation of the displacement and velocity fields to yield only a single step time integration scheme, which is comparable to the Newmark family of time integration scheme. A reduced integration technique is used to prevent velocity locking, which is caused by linear approximation of both the displacement and velocity fields. For the verification of the consistency and the stability, the CWR time integration scheme is tested with single-degree as well as multi-degree of freedom problems. The scheme performs extremely well compared with those of the well-known Newmark family of time integration schemes.

Modeling the damped dynamic behavior of a flexible pendulum

2019 ◽  
Vol 54 (2) ◽  
pp. 116-129 ◽  
Author(s):  
Roberto Ortega ◽  
Geraldine Farías ◽  
Marcela Cruchaga ◽  
Matías Rivero ◽  
Mariano Vázquez ◽  
...  
Keyword(s):  
High Speed ◽  
Time Integration ◽  
Integration Scheme ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Rayleigh Damping ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Damping Model

The focus of this work is on the computational modeling of a pendulum made of a hyperelastic material and the corresponding experimental validation with the aim of contributing to the study of a material commonly used in seismic absorber devices. From the proposed dynamics experiment, the motion of the pendulum is recorded using a high-speed camera. The evolution of the pendulum’s positions is recovered using a capturing motion technique by tracking markers. The simulation of the problem is developed in the framework of a parallel multi-physics code. Particular emphasis is placed on the analysis of the Newmark integration scheme and the use of Rayleigh damping model. In particular, the time step size effect is analyzed. A strong time step size dependency is obtained for dissipative time integration schemes, while the Rayleigh damping formulation without time integration dissipation shows time step–independent results when convergence is achieved.

Sign in / Sign up

Export Citation Format

Share Document