Newmark Method (newmark + method)

Distribution by Scientific Domains


Selected Abstracts


Optimal time integration parameters for elastodynamic contact problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2001
A. Czekanski
Abstract In this paper, we employ the generalized- , time integration scheme for treating elastodynamic contact problems. The criteria invoked for the selection of the four time integration parameters are motivated by our desire to ensure that the solution is unconditionally stable, second-order accurate, provides optimal high-frequency dissipation and preserves the energy and momentum transfer in dynamic rigid impact problems. New closed-form expressions for the time integration parameters are determined in terms of user-specified high-frequency spectral radius. The selected parameters help in avoiding the spurious high-frequency modes, which are present in the traditional Newmark method. Copyright 2001 John Wiley & Sons, Ltd. [source]


A methodology for the formulation of error estimators for time integration in linear solid and structural dynamics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2006
I. Romero
Abstract In this article, we present a novel methodology for the formulation of a posteriori error estimators applicable to time-stepping algorithms of the type commonly employed in solid and structural mechanics. The estimators constructed with the presented methodology are accurate and can be implemented very efficiently. More importantly, they provide reliable error estimations even in non-smooth problems where many standard estimators fail to capture the order of magnitude of the error. The proposed methodology is applied, as an illustrative example, to construct an error estimator for the Newmark method. Numerical examples of its performance and comparison with existing error estimators are presented. These examples verify the good accuracy and robustness predicted by the analysis. Copyright 2005 John Wiley & Sons, Ltd. [source]


FEM simulation of turbulent flow in a turbine blade passage with dynamical fluid,structure interaction

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009
Lixiang Zhang
Abstract Results are described from a combined mathematical modeling and numerical iteration schemes of flow and vibration. We consider the coupling numerical simulations of both turbulent flow and structure vibration induced by flow. The methodology used is based on the stabilized finite element formulations with time integration. A fully coupled model of flow and flow-induced structure vibration was established using a hydride generalized variational principle of fluid and solid dynamics. The spatial discretization of this coupling model is based on the finite element interpolating formulations for the fluid and solid structure, while the different time integration schemes are respectively used for fluid and solid structure to obtain a stabilized algorithm. For fluid and solid dynamics, Hughes' predictor multi-corrector algorithm and the Newmark method are monolithically used to realize a monolithic solution of the fully coupled model. The numerical convergence is ensured for small deformation vibrating problems of the structure by using different time steps for fluid and solid, respectively. The established model and the associated numerical methodology developed in the paper were then applied to simulate two different flows. The first one is the lid-driven square cavity flow with different Reynolds numbers of 1000, 400 and 100 and the second is the turbulent flows in a 3-D turbine blade passage with dynamical fluid,structure interaction. Good agreement between numerical simulations and measurements of pressure and vibration acceleration indicates that the finite element method formulations developed in this paper are appropriate to deal with the flow under investigation. Copyright 2009 John Wiley & Sons, Ltd. [source]


An MPI Parallel Implementation of Newmark's Method

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 3 2000
Ali Namazifard
The standard message-passing interface (MPI) is used to parallelize Newmark's method. The linear matrix equation encountered at each time step is solved using a preconditioned conjugate gradient algorithm. Data are distributed over the processors of a given parallel computer on a degree-of-freedom basis; this produces effective load balance between the processors and leads to a highly parallelized code. The portability of the implementation of this scheme is tested by solving some simple problems on two different machines: an SGI Origin2000 and an IBM SP2. The measured times demonstrate the efficiency of the approach and highlight the maintenance advantages that arise from using a standard parallel library such as MPI. [source]