An Improved Sub-Step Composite Time Integration Formulation With Enhanced Performance on Linear and Nonlinear Dynamics

2021 ◽  
pp. 2150017
Author(s):  
W. B. Wen ◽  
S. Y. Deng ◽  
T. H. Liu ◽  
S. Y. Duan ◽  
W. Q. Hou ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Time Integration ◽  
Nonlinear Problems ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Promising Candidate ◽  
Simple Formulation ◽  
Time Integration Scheme ◽  
Linear And Nonlinear ◽  
Period Elongation

An improved time integration scheme is proposed for linear and nonlinear dynamics. The proposed scheme has two free parameters which control numerical dissipation and accuracy effectively. Basic properties including spectral stability, algorithmic accuracy, algorithmic damping, period elongation and overshooting behavior are investigated. The influences of algorithmic parameters on these properties are quantified. The effectiveness of the proposed scheme for linear and nonlinear dynamics is evaluated through some numerical examples. Analytical and numerical results demonstrate that the proposed scheme has the following significant characteristics: (1) desirable accuracy can be obtained for various linear and nonlinear problems, when compared with other effective schemes; (2) for nonlinear problems, new scheme also shows good performance; (3) the proposed scheme has simple formulation and good compatibility for various dynamic problems, and thus, is a promising candidate for practical analysis.

scholarly journals Numerical Investigation of an Academic Mistuned Bladed Disk Dynamics Accounting for Blade/Casing Contacts

2019 ◽  
Author(s):  
Jeanne Joachim ◽  
Florence Nyssen ◽  
Alain Batailly
Keyword(s):  
Time Integration ◽  
Synthesis Method ◽  
Aircraft Engine ◽  
Element Model ◽  
Integration Scheme ◽  
Bladed Disk ◽  
Structural Context ◽  
Time Integration Scheme ◽  
Blade Tip ◽  
Linear And Nonlinear

Abstract This contribution focuses on the combined analysis of mistuning and unilateral blade-tip/casing contacts. A 2D phenomenological finite element model of an aircraft engine fan stage is considered. It is reduced by means of the Craig-Bampton component mode synthesis method and contact treatment relies on a Lagrange multiplier algorithm within an explicit time-integration scheme. Blade-tip/casing contacts are initiated through the deformed shape of a perfectly rigid casing. Mistuning is accounted for on the blades only. Monte Carlo simulations are carried out in both linear and nonlinear configurations, which allows to compare amplifications predicted in both context due to mistuning. Following a thorough convergence analysis of the proposed numerical strategy, the influence of mistuning level as well as the configuration of the external forcing are investigated. Presented results underline the detrimental consequences of mistuning in a nonlinear structural context, yielding even higher vibration amplifications than in a linear context. A cross-analysis between linear and nonlinear computations reveals that no correlation is found between linear and nonlinear amplifications which suggests that the effect of existing strategies to mitigate vibration amplifications within a linear context may not be suitable within a nonlinear context.

An Explicit Time Integration Scheme Based on B-Spline Interpolation and Its Application in Wave Propagation Analysis

2017 ◽  
Vol 09 (08) ◽  
pp. 1750115 ◽  
Author(s):  
W. B. Wen ◽  
S. Y. Duan ◽  
Y. Tao ◽  
Jun Liang ◽  
Daining Fang
Keyword(s):  
Wave Propagation ◽  
Hyperbolic Equations ◽  
Spline Interpolation ◽  
Time Integration ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Weighted Residual Method ◽  
Explicit Time Integration ◽  
B Spline ◽  
Time Integration Scheme

An explicit time integration scheme for hyperbolic equations is proposed using B-spline interpolation and weighted residual method. It has simple formulation and calculation procedure. With one adjustable algorithmic parameter, new scheme has higher accuracy when compared with other excellent explicit schemes. New scheme has controllable and also desirable period elongation which is verified by theoretical analysis and numerical simulations. Especially, a demonstrative dispersion analysis coupled with the corresponding wave propagation demonstrate the desirable numerical dissipation property and the effectiveness of the proposed scheme for wave propagation problems.

A Novel Sub-Stepping Method with Numerical Dissipation Control for Time Integration of Highly Flexible Structures

2018 ◽  
Vol 10 (10) ◽  
pp. 1850106 ◽  
Author(s):  
Saeed Mohammadzadeh ◽  
Mehdi Ghassemieh
Keyword(s):  
Equilibrium Points ◽  
Flexible Structures ◽  
Time Integration ◽  
Single Step ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Step Method ◽  
Time Step ◽  
Time Increment ◽  
Time Integration Scheme

Sub-stepping time integration methods attempt to march each time step with multiple sub-steps. Generally, for the first sub-step, a single-step method is applied and the following sub-steps are solved using a method that utilizes the data obtained from two or three previous equilibrium points. Despite the robust stability in problems, control of numerical dissipation in sub-stepping schemes is a tough task due to applying different algorithms on a time increment. In order to overcome this insufficiency, a new sub-stepping time integration scheme, which uses two sub-steps in each time increment, is proposed. Newmark and quadratic acceleration methods are applied on the first and second sub-steps, respectively. Both methods utilize constant parameters that enable the control of numerical dissipation in the analysis. For the proposed method, the stability analysis revealed the unconditional stability region for the pertinent parameters. Additionally, the precision investigation disclosed an advantage of the proposed method with the presence of minor period elongation error. Finally, the application of the proposed method is illuminated via several numerical examples. In addition to numerical dissipation control, the proposed method proved to have an outstanding advantage over other methods in solving highly flexible structures more efficiently and more accurately.

Performance of Low-Dissipation Euler Fluxes and Preconditioned LU-SGS at Low Speeds

2011 ◽  
Vol 10 (1) ◽  
pp. 90-119 ◽  
Author(s):  
Keiichi Kitamura ◽  
Eiji Shima ◽  
Keiichiro Fujimoto ◽  
Z. J. Wang
Keyword(s):  
Time Derivative ◽  
Time Integration ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Steady Flows ◽  
Low Speed ◽  
Low Dissipation ◽  
Speed Flow ◽  
Time Integration Scheme

AbstractIn low speed flow computations, compressible finite-volume solvers are known to a) fail to converge in acceptable time and b) reach unphysical solutions. These problems are known to be cured by A) preconditioning on the time-derivative term, and B) control of numerical dissipation, respectively. There have been several methods of A) and B) proposed separately. However, it is unclear which combination is the most accurate, robust, and efficient for low speed flows. We carried out a comparative study of several well-known or recently-developed low-dissipation Euler fluxes coupled with a preconditioned LU-SGS (Lower-Upper Symmetric Gauss-Seidel) implicit time integration scheme to compute steady flows. Through a series of numerical experiments, accurate, efficient, and robust methods are suggested for low speed flow computations.

scholarly journals Numerical Investigation of a Mistuned Academic Bladed Disk Dynamics with Blade/Casing Contact

2020 ◽  
Author(s):  
Jeanne Joachim ◽  
Florence Nyssen ◽  
Alain Batailly
Keyword(s):  
Time Integration ◽  
Synthesis Method ◽  
Aircraft Engine ◽  
Element Model ◽  
Integration Scheme ◽  
Bladed Disk ◽  
Structural Context ◽  
Time Integration Scheme ◽  
Blade Tip ◽  
Linear And Nonlinear

Abstract This contribution focuses on the combined analysis of mistuning and unilateral blade-tip/casing contacts. A 2D phenomenological finite element model of an aircraft engine fan stage is considered. It is reduced by means of the Craig-Bampton component mode synthesis method and contact treatment relies on a Lagrange multiplier algorithm within an explicit time-integration scheme. Blade-tip/casing contacts are initiated through the deformed shape of a perfectly rigid casing. Mistuning is accounted for on the blades only. Monte Carlo simulations are carried out in both linear and nonlinear configurations, which allows to compare amplifications predicted in both context due to mistuning. Following a thorough convergence analysis of the proposed numerical strategy, the influence of mistuning level as well as the configuration of the external forcing are investigated. Presented results underline the detrimental consequences of mistuning in a nonlinear structural context, yielding even higher vibration amplifications than in a linear context. A cross-analysis between linear and nonlinear computations reveals that no correlation is found between linear and nonlinear amplifications which suggests that the effect of existing strategies to mitigate vibration amplifications within a linear context may not be suitable within a nonlinear context.

scholarly journals Performance of Composite Implicit Time Integration Scheme for Nonlinear Dynamic Analysis

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
William Taylor Matias Silva ◽  
Luciano Mendes Bezerra
Keyword(s):  
Transient Response ◽  
Time Integration ◽  
Nonlinear Dynamic Analysis ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Structural Dynamic ◽  
Implicit Time Integration ◽  
Time Integration Scheme

This paper presents a simple implicit time integration scheme for transient response solution of structures under large deformations and long-time durations. The authors focus on a practical method using implicit time integration scheme applied to structural dynamic analyses in which the widely used Newmark time integration procedure is unstable, and not energy-momentum conserving. In this integration scheme, the time step is divided in two substeps. For too large time steps, the method is stable but shows excessive numerical dissipation. The influence of different substep sizes on the numerical dissipation of the method is studied throughout three practical examples. The method shows good performance and may be considered good for nonlinear transient response of structures.

scholarly journals Structural Reliability Sensitivities under Nonstationary Random Vibrations

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Rita Greco ◽  
Francesco Trentadue
Keyword(s):  
Structural Reliability ◽  
Structural Parameters ◽  
Time Integration ◽  
Structural Response ◽  
Integration Scheme ◽  
Structural Systems ◽  
Frame Building ◽  
Time Integration Scheme ◽  
Noise Input ◽  
The Time Domain

Response sensitivity evaluation is an important element in reliability evaluation and design optimization of structural systems. It has been widely studied under static and dynamic forcing conditions with deterministic input data. In this paper, structural response and reliability sensitivities are determined by means of the time domain covariance analysis in both classically and nonclassically damped linear structural systems. A time integration scheme is proposed for covariance sensitivity. A modulated, filtered, white noise input process is adopted to model the stochastic nonstationary loads. The method allows for the evaluation of sensitivity statistics of different quantities of dynamic response with respect to structural parameters. Finally, numerical examples are presented regarding a multistorey shear frame building.

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