Simulating Maximum and Residual Displacements of RC Structures: II. Sensitivity

2011 ◽  
Vol 27 (4) ◽  
pp. 1203-1218 ◽  
Author(s):  
Ufuk Yazgan ◽  
Alessandro Dazio
Keyword(s):  
Damping Ratio ◽  
Time Integration ◽  
Integration Step ◽  
Discretization Scheme ◽  
Hysteretic Model ◽  
Step Size ◽  
Shake Table Tests ◽  
Rc Structures ◽  
Residual Displacements ◽  
Response History Analysis

The simulated response of a structure subjected to seismic excitation is sensitive to the idealizations made to model its response. This paper examines critical idealizations and assumptions that have a strong influence on the accuracy of the maximum and residual displacements predicted by response-history analysis. A set of shake table tests are numerically reproduced for this purpose. The investigated idealizations include the discretization scheme, the axial load, the steel hysteretic model, the viscous damping ratio, and the time-integration step size. The results indicate that the simulated residual displacements are significantly more sensitive to the model idealizations than the maximum displacements. It is found that the adopted discretization scheme and the utilized steel hysteresis model have very large influences on simulated residual displacements.

Newmark-Beta Method in Discrete Elastic Rods Algorithm to Avoid Energy Dissipation

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Weicheng Huang ◽  
Mohammad Khalid Jawed
Keyword(s):  
Energy Dissipation ◽  
Time Integration ◽  
Integration Scheme ◽  
Integration Step ◽  
Elastic Rods ◽  
Computationally Efficient ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Time Integration Scheme

Discrete elastic rods (DER) algorithm presents a computationally efficient means of simulating the geometrically nonlinear dynamics of elastic rods. However, it can suffer from artificial energy loss during the time integration step. Our approach extends the existing DER technique by using a different time integration scheme—we consider a second-order, implicit Newmark-beta method to avoid energy dissipation. This treatment shows better convergence with time step size, specially when the damping forces are negligible and the structure undergoes vibratory motion. Two demonstrations—a cantilever beam and a helical rod hanging under gravity—are used to show the effectiveness of the modified discrete elastic rods simulator.

A Quantitative Assessment of the Potential of Implicit Integration Methods for Molecular Dynamics Simulation

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Nick Schafer ◽  
Dan Negrut
Keyword(s):  
Molecular Dynamics ◽  
Md Simulation ◽  
Time Integration ◽  
Dynamics Simulation ◽  
Integration Step ◽  
Implicit Integration ◽  
Implicit Methods ◽  
Current Standard ◽  
Step Size ◽  
Computational Overhead

Implicit integration, unencumbered by numerical stability constraints, is attractive in molecular dynamics (MD) simulation due to its presumed ability to advance the simulation at large step sizes. It is not clear what step size values can be expected and if the larger step sizes will compensate for the computational overhead associated with an implicit integration method. The goal of this paper is to answer these questions and thereby assess quantitatively the potential of implicit integration in MD. Two implicit methods (midpoint and Hilber–Hughes–Taylor) are compared with the current standard for MD time integration (explicit velocity Verlet). The implicit algorithms were implemented in a research grade MD code, which used a first-principles interaction potential for biological molecules. The nonlinear systems of equations arising from the use of implicit methods were solved in a quasi-Newton framework. Aspects related to a Newton–Krylov type method are also briefly discussed. Although the energy conservation provided by the implicit methods was good, the integration step size lengths were limited by loss of convergence in the Newton iteration. Moreover, a spectral analysis of the dynamic response indicated that high frequencies present in the velocity and acceleration signals prevent a substantial increase in integration step size lengths. The overhead associated with implicit integration prevents this class of methods from having a decisive impact in MD simulation, a conclusion supported by a series of quantitative analyses summarized in the paper.

Simulating Maximum and Residual Displacements of RC Structures: I. Accuracy

2011 ◽  
Vol 27 (4) ◽  
pp. 1187-1202 ◽  
Author(s):  
Ufuk Yazgan ◽  
Alessandro Dazio
Keyword(s):  
Companion Paper ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Seismic Performance Assessment ◽  
Shake Table Tests ◽  
Rc Structures ◽  
Flexural Response ◽  
Bilinear Models ◽  
Residual Displacements ◽  
Global And Local

Estimation of likely global and local response measures plays an important role in seismic performance assessment. The capabilities and limitations of beam-column element modeling strategies in predicting the dynamic nonlinear flexural response of RC models are investigated in this study. For this purpose, 12 shake table tests are numerically reproduced. Correlations of the predicted deformations with the measured ones are evaluated. The results show that maximum displacements can be estimated with sufficient accuracy if the adopted hysteresis model takes into account stiffness degradation. However, accurate estimation of the residual displacements is found to be difficult to achieve. The results suggest that the assumed small-cycle behavior has a strong influence on the estimated residual displacements. Fiber-section models are found to provide relatively more accurate estimates of the residual displacements than modified Takeda hysteretic and bilinear models. A companion paper, Part II: Sensitivity, presents the sensitivity of the simulated displacements to a set of the model parameters and idealizations.

Residual displacements of RC structures as SDOF systems

2014 ◽  
Vol 44 (5) ◽  
pp. 713-734 ◽  
Author(s):  
Eftychia Liossatou ◽  
Michael N. Fardis
Keyword(s):  
Rc Structures ◽  
Residual Displacements

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Damping Ratio ◽  
Strong Dependence ◽  
Time Integration ◽  
Single Mode ◽  
Stick Slip ◽  
Friction Forces ◽  
Equivalent Damping ◽  
Damping Characteristics ◽  
Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

An Investigation into Nonlinearity of Foundation Soil of Gravity Retaining Wall Based on an Inversion Method

2012 ◽  
Vol 204-208 ◽  
pp. 557-561
Author(s):  
Hong Yan Xi ◽  
Jun Hua Zhang ◽  
Jing Sun ◽  
Jing Li ◽  
You Qing Wang ◽  
...  
Keyword(s):  
Shear Modulus ◽  
Shear Strain ◽  
Damping Ratio ◽  
Retaining Walls ◽  
Earthquake Ground Motion ◽  
Inversion Method ◽  
Dynamic Shear Modulus ◽  
Foundation Soil ◽  
Residual Displacements ◽  
Dynamic Nonlinearity

Strong earthquake ground motion leads to residual displacements of gravity retaining walls. Since large deformation occurs in foundation soil, nonlinear mechanical behavior should not be neglected in numerical modeling. The inversion methodology in geophysics is borrowed here to study the nonlinearity, i.e. the variation of shear modulus and damping ratio with the increase of shear strain of soil. A simplified model for the seismic displacement of retaining walls is combined with a genetic algorithm for the inversion. The dynamic shear modulus and damping ratio curves, representing the nonlinear property of foundation soil in a centrifuge test for gravity retaining walls, is obtained by the use of an inversion scheme. The result indicates that, for low level of shear strain, the shear modulus is larger than that used in the literature, implying that the model ground may be stiffer than expectation. For high level of shear strain, the inverted damping ratio is larger than the conventional one, which has efficiently suppressed an overestimation of seismic displacements. It is also displayed that the inversion method is an effective way to obtain quantitatively the dynamic nonlinearity of foundation soil of gravity retaining walls.

Effects of circumferential and axial grooves on the nonlinear oscillations of the full floating ring bearing supported turbocharger rotor

2018 ◽  
Vol 233 (5) ◽  
pp. 741-757 ◽  
Author(s):  
Congcong Zhang ◽  
Rixiu Men ◽  
Hong He ◽  
Wei Chen
Keyword(s):  
Finite Difference ◽  
Reynolds Equation ◽  
Nonlinear Oscillations ◽  
Time Integration ◽  
Response Analysis ◽  
Integration Step ◽  
Computationally Efficient ◽  
Fluid Forces ◽  
Transient Simulations ◽  
The Impact

It is seen that with the reduction in land areas owing to the floating-rings featured grooves, there is reduction in the load capacities and bearing torques of the oil-films, which have an influence on the nonlinear oscillations of turbocharger rotors. In the present paper, the impact of the reduced load capacities and bearing torques caused by circumferential or/and axial grooves in full-floating-ring bearings on the nonlinear oscillations of turbocharger rotors is investigated. The numerical solution of the Reynolds equation for full-floating-ring bearings with grooves by means of a finite difference or finite element approach imposes a prohibitive simulation times, sine in every time-integration step a direct discretization of the Reynolds equation has to be solved simultaneously with the rotor model. To be able to perform transient simulations, a computationally efficient full-floating-ring bearing model is mandatory. To surmount this problem, a very time-efficient but rather precise method is proposed. The major point of the proposed method is the manipulation of the Reynolds equation to allow a speed parameter varying within (−1, +1) to reflect the relative weights of the journal and floating ring’s rotation and squeezing effects. Given the diameter-to-length ratio of each fluid film, groove widths, and boundary conditions, the fluid force databases can be easily established by the finite difference method. During the transient response analysis, the required fluid forces and bearing torques from each film can be evaluated by interpolation using the existent forces and torques of the closest points in the databases. Using transient simulations with the proposed method, the effect of circumferential or/and axial grooves in full-floating-ring bearings on the amplitudes and frequencies of the nonlinear oscillations of turbocharger rotors is qualitatively investigated. It is shown that the reduction of the load capacities and bearing torques due to grooves exert a large influence on the nonlinear rotor oscillations.

Stability and Accuracy Analysis of Baumgarte’s Constraint Violation Stabilization Method

1995 ◽  
Vol 117 (3) ◽  
pp. 446-453 ◽  
Author(s):  
S. Yoon ◽  
R. M. Howe ◽  
D. T. Greenwood
Keyword(s):  
Equations Of Motion ◽  
Integration Step ◽  
State Variables ◽  
Stabilization Method ◽  
Lagrange Equations ◽  
Step Size ◽  
Constraint Violation ◽  
Truncation Errors ◽  
Numerical Stability Analysis ◽  
Stability And Accuracy

When Baumgarte’s Constraint Violation Stabilization Method (CVSM) is used in the simulation of Lagrange equations of motion with holonomic constraints, it is shown that, with suitable assumptions on the integration step size h and the eigenvalues (λ’s) of the linearized system, the constraint variables are effectively integrated by the same algorithm as that used for the state variables. A numerical stability analysis of the constraint violations can be performed using this so-called pseudo-integration equation. A study is also made of truncation errors and their modeling in the continuous time domain. This model can be used to determine the effectiveness of various constraint controls and integration methods in reducing the errors in the solution due to truncation errors. Examples are presented to illustrate the use of a higher-order truncation error model which leads to an accurate quantitative steady-state analysis of the constraint violations.

Separate Time Integration Based on the Hilber, Hughes, Taylor Scheme for Flexible Bodies With a Large Number of Modes

2020 ◽  
Vol 15 (6) ◽  
Author(s):  
Wolfgang Witteveen ◽  
Florian Pichler
Keyword(s):  
Time Integration ◽  
Flexible Multibody Dynamics ◽  
Integration Scheme ◽  
Step Size ◽  
Body Contact ◽  
Time Integration Scheme ◽  
Core Idea ◽  
Numerical Time Integration ◽  
Taylor Scheme ◽  
Local Deformations

Abstract In the current development of flexible multibody dynamics, the efficient and accurate consideration of distributed and nonlinear forces is an active area of research. Examples are, forces due to body-body contact or due to elastohydrodynamics (EHD). This leads to many additional modes for representing the local deformations in the areas on which those forces act. Recent publications show that these can be several hundred to several thousand additional modes. A conventional, monolithic numerical time integration scheme would lead to unacceptable computing times. This paper presents a method for an efficient time integration of such systems. The core idea is to treat the equations associated with modes representing local deformations separately. Using the Newmark formulas, a fixed point iteration is proposed for these separated equations, which can always be stabilized with decreasing step size. The concluding examples underline this property, as well as the fact that the proposed method massively outperforms the conventional, monolithic time integration with increasing number of modes.

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