scholarly journals Bipenalty method for time domain computational dynamics

2009 ◽  
Vol 466 (2117) ◽  
pp. 1389-1408 ◽  
Author(s):  
Harm Askes ◽  
Miguel Caramés-Saddler ◽  
Antonio Rodríguez-Ferran
Keyword(s):  
Time Integration ◽  
Critical Time ◽  
Time Step ◽  
Beam Elements ◽  
Computational Dynamics ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
The Common ◽  
Critical Time Step ◽  
Better Than

Penalty functions can be used to add constraints to systems of equations. In computational mechanics, stiffness-type penalties are the common choice. However, in dynamic applications stiffness penalties have the disadvantage that they tend to decrease the critical time step in conditionally stable time integration schemes, leading to increased CPU times for simulations. In contrast, inertia penalties increase the critical time step. In this paper, we suggest the simultaneous use of stiffness penalties and inertia penalties, which is denoted as the bipenalty method . We demonstrate that the accuracy of the bipenalty method is at least as good as (and usually better than) using either stiffness penalties or inertia penalties. Furthermore, for a number of finite elements (bar elements, beam elements and square plane stress/plane strain elements) we have derived ratios of the two penalty parameters such that their combined effect on the critical time step is neutral. The bipenalty method is thus superior to using stiffness penalties, because the decrease in critical time step can be avoided. The bipenalty method is also superior to using inertia penalties, since the constraints are realized with higher accuracy.

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.

scholarly journals A Weighted Residual Parabolic Acceleration Time Integration Method for Problems in Structural Dynamics

2007 ◽  
Vol 7 (3) ◽  
pp. 227-238 ◽  
Author(s):  
S.H. Razavi ◽  
A. Abolmaali ◽  
M. Ghassemieh
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Time Integration ◽  
Critical Time ◽  
Linear Acceleration ◽  
Time Step ◽  
Time Integration Method ◽  
Acceleration Method ◽  
The Stability ◽  
Critical Time Step

AbstractIn the proposed method, the variation of displacement in each time step is assumed to be a fourth order polynomial in time and its five unknown coefficients are calculated based on: two initial conditions from the previous time step; satisfying the equation of motion at both ends of the time step; and the zero weighted residual within the time step. This method is non-dissipative and its dispersion is considerably less than in other popular methods. The stability of the method shows that the critical time step is more than twice of that for the linear acceleration method and its convergence is of fourth order.

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.

scholarly journals Damping Acoustic Modes in Compressible Horizontally Explicit Vertically Implicit (HEVI) and Split-Explicit Time Integration Schemes

2018 ◽  
Vol 146 (6) ◽  
pp. 1911-1923 ◽  
Author(s):  
Joseph B. Klemp ◽  
William C. Skamarock ◽  
Soyoung Ha
Keyword(s):  
Acoustic Waves ◽  
Acoustic Noise ◽  
Equations Of Motion ◽  
Time Integration ◽  
Time Step ◽  
Explicit Time Integration ◽  
Physical Interest ◽  
Acoustic Modes ◽  
Integration Schemes ◽  
Time Integration Schemes

Although the equations of motion for a compressible atmosphere accommodate acoustic waves, these modes typically play an insignificant role in atmospheric processes of physical interest. In numerically integrating the compressible equations, it is often beneficial to filter these acoustic modes to control acoustic noise and prevent its artificial growth. Here, a new technique is proposed for filtering the 3D divergence that may damp acoustic modes more effectively than filters previously implemented in numerical modes using horizontally explicit vertically implicit (HEVI) and split-explicit time integration schemes. With this approach, a divergence damping term is added as a final adjustment to the horizontal velocity at the new time level after completing the vertically implicit portion of the time step. In this manner, the divergence used in the filter term has exactly the same numerical form as that used in the discrete pressure equation. Analysis of the dispersion equation for this form of the filter documents its stability characteristics and confirms that it effectively damps acoustic modes with little artificial influence on the amplitude or propagation of the gravity wave modes that are of physical interest. Some specific aspects of the implementation of the filter in the Model for Prediction Across Scales (MPAS) are discussed, and results are presented to illustrate some of the beneficial aspects of suppressing acoustic noise.

EIGENFREQUENCY SHIFT IN THE NEWMARK TIME INTEGRATOR

2006 ◽  
Vol 06 (03) ◽  
pp. 431-436 ◽  
Author(s):  
HARM ASKES ◽  
ALEKSANDAR PAVIC
Keyword(s):  
Time Integration ◽  
Excitation Frequency ◽  
Continuous System ◽  
Time Discretization ◽  
Forced Vibrations ◽  
Technical Note ◽  
Time Step ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Numerical Time Integration

This technical note aims to clarify the influence of numerical time integration schemes (such as the Newmark method) on the eigenfrequency of the system. With a straightforward analysis of three consecutive time instants it is shown that the eigenfrequency of the time-discretized system is different from the eigenfrequency of the original (continuous) system, and that this frequency shift depends on the magnitude of the applied time step. As such, it affects both free and forced vibrations. In particular, for the analysis of forced vibrations at resonance the excitation frequency must be matched with the eigenfrequency of the time-discretized system rather than the eigenfrequency of the system prior to time discretization.

A Simple Explicit–Implicit Time-Marching Technique for Wave Propagation Analysis

2018 ◽  
Vol 16 (01) ◽  
pp. 1850082 ◽  
Author(s):  
Delfim Soares
Keyword(s):  
Wave Propagation ◽  
Time Integration ◽  
Critical Time ◽  
Implicit Time ◽  
Time Step ◽  
Stiffness Matrices ◽  
Time Integrators ◽  
Propagation Analysis ◽  
Time Marching ◽  
Critical Time Step

A new explicit–implicit time integration technique is proposed here for wave propagation analysis. In the present formulation, the time integrators of the model are selected at the element level, allowing each element to be considered as explicit or implicit. In the implicit elements, controllable algorithm dissipation is provided, enabling an [Formula: see text]-stable formulation. In the explicit elements, null amplitude decay is considered, enabling maximal critical time-step values. The new methodology renders a very simple and effective time-marching algorithm. Here, just displacement–velocity relations are considered, and no computation of accelerations is required. Moreover, explicit/implicit analyses can be carried out just by the tuning of local effective matrices, inputting or not stiffness matrices into their computations. At the end of the paper, numerical results are presented, illustrating the performance and potentialities of the new method.

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

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