scholarly journals Inconsistent Stability of Newmark's Method in Structural Dynamics Applications

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Richard Wiebe ◽  
Ilinca Stanciulescu
Keyword(s):  
Structural Dynamics ◽  
Finite Element Models ◽  
Interesting Phenomenon ◽  
Physical Systems ◽  
Stiffness Matrices ◽  
Time Integrators ◽  
Direct Interpretation ◽  
Time Marching ◽  
The Stability ◽  
Marching Scheme

The stability of numerical time integrators, and of the physical systems to which they are applied, are normally studied independently. This conceals a very interesting phenomenon, here termed inconsistent stability, wherein a numerical time marching scheme predicts a stable response about an equilibrium configuration that is, in fact, unstable. In this paper, time integrator parameters leading to possible inconsistent stability are first found analytically for conservative systems (symmetric tangent stiffness matrices), then several structural arches with increasing complexity are used as numerical case studies. The intention of this work is to highlight the potential for this unexpected, and mostly unknown, behavior to researchers studying complex dynamical systems, especially through time marching of finite element models. To allow for direct interpretation of our results, the work is focused on the Newmark time integrator, which is commonly used in structural dynamics.

scholarly journals Compressible and nonisothermal viscoelastic flow between eccentrically rotating cylinders

2021 ◽  
Author(s):  
A. T. Mackay ◽  
T. N. Phillips
Keyword(s):  
Unstructured Grid ◽  
Piecewise Linear ◽  
Compressible Fluids ◽  
Discrete Problem ◽  
Rotating Cylinders ◽  
Galerkin Finite Element ◽  
Viscoelastic Parameters ◽  
Time Marching ◽  
The Stability ◽  
Marching Scheme

AbstractA Taylor–Galerkin finite element time marching scheme is derived to numerically simulate the flow of a compressible and nonisothermal viscoelastic liquid between eccentrically rotating cylinders. Numerical approximations to the governing flow and constitutive equations are computed over a custom refined unstructured grid of piecewise linear Galerkin finite elements. An original extension to the DEVSS formulation for compressible fluids is introduced to stabilise solutions of the discrete problem. The predictions of two models: the extended White–Metzner and FENE-P-MP are presented. Comparisons between the torque and load bearing capacity predicted by both models are made over a range of viscoelastic parameters. The results highlight the significant and interacting effects of elasticity and compressibility on journal torque and resultant load, and the stability of the journal bearing system.

scholarly journals A locally defined time-marching technique for structural dynamics

2018 ◽  
Vol 211 ◽  
pp. 17004
Author(s):  
Delfim Soares ◽  
Tales Vieira Sofiste ◽  
Webe João Mansur
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Single Step ◽  
Numerical Dissipation ◽  
Structural Elements ◽  
Structural Element ◽  
Time Integrators ◽  
Step Procedure ◽  
Time Marching ◽  
Dynamics Analyses

In this work, a new time marching procedure is proposed for structural dynamics analyses. In this novel technique, time integration parameters are locally defined and different values may be attributed to each structural element of the model. In addition, the time integrators are evaluated according to the properties of the elements, and the user may select in which structural elements numerical dissipation will be introduced. Since the integration parameters are locally defined as function of the structural element itself, the time marching technique adapts according to the model, providing enhanced accuracy. The method is very simple to implement and it stands as an efficient, direct, single-step procedure. It is second order accurate, unconditionally stable, truly self-starting and it allows highly controllable algorithm dissipation in the higher modes. Numerical results are presented along the paper, illustrating the good performance of the new technique.

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.

The damped Crank–Nicolson time-marching scheme for the adaptive solution of the Black–Scholes equation

2015 ◽  
Vol 18 (4) ◽  
pp. 1-37 ◽  
Author(s):  
Christian Goll ◽  
Wolf Rannacher ◽  
Winnifried Woolner
Keyword(s):  
Black Scholes ◽  
Adaptive Solution ◽  
Time Marching ◽  
Marching Scheme ◽  
Crank Nicolson

scholarly journals Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

2021 ◽  
Vol 11 (8) ◽  
pp. 3421
Author(s):  
Cheng-Yu Ku ◽  
Li-Dan Hong ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Wei-Po Huang
Keyword(s):  
Porous Media ◽  
Time Domain ◽  
Numerical Solutions ◽  
Space Time ◽  
Two Dimensional ◽  
Transient Flows ◽  
Layered Porous Media ◽  
Time Marching ◽  
Time Basis ◽  
Marching Scheme

In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

scholarly journals Out-of-plane local mechanism analysis with finite element method

2021 ◽  
Vol 8 (1) ◽  
pp. 130-136
Author(s):  
Roberto Spagnuolo
Keyword(s):  
Finite Element ◽  
Masonry Walls ◽  
Finite Element Models ◽  
Mechanism Analysis ◽  
Fem Method ◽  
Local Mechanism ◽  
Out Of Plane ◽  
Smeared Crack ◽  
The Stability ◽  
No Tension Material

Abstract The stability check of masonry structures is a debated problem in Italy that poses serious problems for its extensive use. Indeed, the danger of out of plane collapse of masonry walls, which is one of the more challenging to evaluate, is traditionally addressed not using finite element models (FEM). The power of FEM is not properly used and some simplified method are preferred. In this paper the use of the thrust surface is suggested. This concept allows to to evaluate the eccentricity of the membrane stresses using the FEM method. For this purpose a sophisticated, layered, finite element with a no-tension material is used. To model a no-tension material we used the smeared crack method as it is not mesh-dependent and it is well known since the early ’80 in an ASCE Report [1]. The described element has been implemented by the author in the program Nòlian by Softing.

Validating and Updating Finite Element Models Using Experimental Measurements of Dynamics

1990 ◽  
Vol 204 (1) ◽  
pp. 45-50
Author(s):  
C F McCulloch ◽  
P Vanhonacker ◽  
E Dascotte
Keyword(s):  
Finite Element ◽  
Structural Dynamics ◽  
Model Updating ◽  
Measured Data ◽  
Physical Parameters ◽  
Experimental Measurements ◽  
Finite Element Models ◽  
Data Sets ◽  
Modal Data ◽  
Modelling Assumptions

A method is proposed for updating finite element models of structural dynamics using the results of experimental modal analysis, based on the sensitivities to changes in physical parameters. The method avoids many of the problems of incompatibility and inconsistency between the experimental and analytical modal data sets and enables the user to express confidence in measured data and modelling assumptions, allowing flexible but automated model updating.

Physical Realization of Generic-Element Parameters in Model Updating

2002 ◽  
Vol 124 (4) ◽  
pp. 628-633 ◽  
Author(s):  
H. Ahmadian ◽  
J. E. Mottershead ◽  
M. I. Friswell
Keyword(s):  
Model Updating ◽  
Finite Element Models ◽  
Physical Realization ◽  
Governing Equations ◽  
Stiffness Matrices ◽  
Model Predictions ◽  
Physical Effects ◽  
Realization Process ◽  
Physical Phenomena ◽  
Selection Of

The selection of parameters is most important to successful updating of finite element models. When the parameters are chosen on the basis of engineering understanding the model predictions are brought into agreement with experimental observations, and the behavior of the structure, even when differently configured, can be determined with confidence. Physical phenomena may be misrepresented in the original model, or may be absent altogether. In any case the updated model should represent an improved physical understanding of the structure and not simply consist of unrepresentative numbers which happen to cause the results of the model to agree with particular test data. The present paper introduces a systematic approach for the selection and physical realization of updated terms. In the realization process, the discrete equilibrium equation formed by mass, and stiffness matrices is converted to a continuous form at each node. By comparing the resulting differential equation with governing equations known to represent physical phenomena, the updated terms and their physical effects can be recognized. The approach is demonstrated by an experimental example.

Sign in / Sign up

Export Citation Format

Share Document