Unsymmetrical, Transient Heat Condition: Rotating Disk Applications

1970 ◽  
Vol 92 (1) ◽  
pp. 181-190 ◽  
Author(s):  
C. D. Mote
Keyword(s):  
Circular Disk ◽  
Rotating Disk ◽  
Transient Heat Conduction ◽  
The Finite Element Method ◽  
Time Step ◽  
Heat Condition ◽  
State Variable ◽  
General Utility ◽  
Finite Dimensional ◽  
Step Selection

The finite-element method is used in the development of a general, finite-dimensional, state variable formulation of transient heat conduction with surface diffusion. An explicit numerical scheme is used which provides a rational basis for the time-step selection. The general methods are applied in detail to the transient and steady-state conduction of a thin, uniform circular disk with uninsulated surfaces rotating past a stationary point source. The disk models examined illustrate the general utility of the formulation and discuss questions of concern in rotating disk heat transfer.

scholarly journals Effective Method for Analysis of Electrothermally Coupled Fields

1995 ◽  
Vol 2 (3) ◽  
pp. 219-225
Author(s):  
Jacek Korytkowski ◽  
Stanisław Wincenciak
Keyword(s):  
Physical Phenomenon ◽  
Three Dimensional ◽  
Main Idea ◽  
The Finite Element Method ◽  
Temperature Dependent ◽  
Time Step ◽  
Coupled Fields ◽  
Strongly Nonlinear ◽  
Step Selection ◽  
Raphson Method

An effective method is presented for solving a nonlinear system of partial differential equations that describe the time-dependent electrothermally coupled fields for passage of constant electric current in a three-dimensional conductive medium. A numerical model of this physical phenomenon was obtained by the finite element method, which takes into account the temperature-dependent characteristics describing the material parameters and conditions of heat transmission outside of the analyzed objects. These characteristics and conditions make the problem strongly nonlinear. The solution uses the Newton-Raphson method with the appropriate procedure for determining the Jacobian matrix elements. The main idea of the proposed method is the use of an automatic time step selection algorithm to solve heat conduction equations. The influence of the assumed accuracy value on the final result of the nonlinear calculation is discussed. The theoretical results were confirmed by the numerical experiments performed with selected physical objects.

Time step selection for 6-noded non-linear joint element in elasto-viscoplasticity analyses

1990 ◽  
Vol 10 (1) ◽  
pp. 33-58 ◽  
Author(s):  
Koji Sekiguchi ◽  
R.Kerry Rowe ◽  
Kwan Yee Lo
Keyword(s):  
Time Step ◽  
Non Linear ◽  
Joint Element ◽  
Selection For ◽  
Step Selection

GPU-Accelerated Efficient Implementation of FDTD Methods With Optimum Time-Step Selection

2014 ◽  
Vol 50 (2) ◽  
pp. 477-480 ◽  
Author(s):  
Theodoros T. Zygiridis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros D. Tsiboukis
Keyword(s):  
Efficient Implementation ◽  
Time Step ◽  
Optimum Time ◽  
Step Selection ◽  
Fdtd Methods

Comparison of Two Time-Integration Algorithms for an Anisotropic Damage Model Coupled with Plasticity

2015 ◽  
Vol 784 ◽  
pp. 292-299 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Marek Fassin ◽  
Stefanie Reese
Keyword(s):  
Evolution Equations ◽  
Damage Model ◽  
Time Integration ◽  
Three Dimensional ◽  
Anisotropic Damage ◽  
Euler Scheme ◽  
The Finite Element Method ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Integration Algorithms

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. (2000) are compared. Specifically, the standard implicit Euler scheme is compared to an algorithm which implicitly solves the elasto-plastic evolution equations and explicitly computes the damage update. To this end, a three dimensional bending example is solved using the finite element method and the results of the two algorithms are compared for different time step sizes.

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

scholarly journals Pounding Effects on the Earthquake Response of Adjacent Reinforced Concrete Structures Strengthened by Cable Elements

2014 ◽  
Vol 44 (2) ◽  
pp. 41-56 ◽  
Author(s):  
Angelos Liolios ◽  
Asterios Liolios ◽  
George Hatzigeorgiou ◽  
Stefan Radev
Keyword(s):  
Reinforced Concrete ◽  
Numerical Approach ◽  
Earthquake Response ◽  
Existing Buildings ◽  
The Finite Element Method ◽  
Time Step ◽  
Engineering Structures ◽  
Rc Structures ◽  
Incremental Approach ◽  
Rc Frames

Abstract A numerical approach for estimating the effects of pounding (seismic interaction) on the response of adjacent Civil Engineering structures is presented. Emphasis is given to reinforced concrete (RC) frames of existing buildings which are seismically strengthened by cable-elements. A double discretization, in space by the Finite Element Method and in time by a direct incremental approach is used. The unilateral behaviours of both, the cable-elements and the interfaces contact-constraints, are taken strictly into account and result to inequality constitutive conditions. So, in each time-step, a non-convex linear complementarity problem is solved. It is found that pounding and cable strengthening have significant effects on the earthquake response and, hence, on the seismic upgrading of existing adjacent RC structures.

Intelligent Time-Stepping for Practical Numerical Simulation

2021 ◽  
Author(s):  
Soham Sheth ◽  
Francois McKee ◽  
Kieran Neylon ◽  
Ghazala Fazil
Keyword(s):  
Heuristic Method ◽  
Simulation Models ◽  
Model Complexity ◽  
Large Field ◽  
Optimal Time ◽  
Time Step ◽  
Non Linear ◽  
Set Up ◽  
Reservoir Simulator ◽  
Step Selection

Abstract We present a novel reservoir simulator time-step selection approach which uses machine-learning (ML) techniques to analyze the mathematical and physical state of the system and predict time-step sizes which are large while still being efficient to solve, thus making the simulation faster. An optimal time-step choice avoids wasted non-linear and linear equation set-up work when the time-step is too small and avoids highly non-linear systems that take many iterations to solve. Typical time-step selectors use a limited set of features to heuristically predict the size of the next time-step. While they have been effective for simple simulation models, as model complexity increases, there is an increasing need for robust data-driven time-step selection algorithms. We propose two workflows – static and dynamic – that use a diverse set of physical (e.g., well data) and mathematical (e.g., CFL) features to build a predictive ML model. This can be pre-trained or dynamically trained to generate an inference model. The trained model can also be reinforced as new data becomes available and efficiently used for transfer learning. We present the application of these workflows in a commercial reservoir simulator using distinct types of simulation model including black oil, compositional and thermal steam-assisted gravity drainage (SAGD). We have found that history-match and uncertainty/optimization studies benefit most from the static approach while the dynamic approach produces optimum step-sizes for prediction studies. We use a confidence monitor to manage the ML time-step selector at runtime. If the confidence level falls below a threshold, we switch to traditional heuristic method for that time-step. This avoids any degradation in the performance when the model features are outside the training space. Application to several complex cases, including a large field study, shows a significant speedup for single simulations and even better results for multiple simulations. We demonstrate that any simulation can take advantage of the stored state of the trained model and even augment it when new situations are encountered, so the system becomes more effective as it is exposed to more data.

Energy Versus Stress Theories for Combined Stress—A Fatigue Experiment Using a Rotating Disk

1961 ◽  
Vol 83 (1) ◽  
pp. 10-14 ◽  
Author(s):  
W. N. Findley ◽  
P. N. Mathur ◽  
E. Szczepanski ◽  
A. O. Temel
Keyword(s):  
Fatigue Failure ◽  
Strain Energy ◽  
Fatigue Cracks ◽  
Circular Disk ◽  
Rotating Disk ◽  
Constant Load ◽  
Combined Stress ◽  
Combined Stresses ◽  
Critical Location ◽  
Fatigue Experiment

An experiment is described in which the strain energy at the critical location for fatigue failure is maintained constant while the stresses on a given plane of the material at the same location are caused to fluctuate. Apparatus developed to produce this condition consisted of a circular disk with a wide flanged rim which was loaded along a diameter by means of pivot-pad bearings. The disk was then rotated under a constant load to produce the desired fluctuation in stresses at the center of the disk while maintaining a constant strain energy at the center. The fact that fatigue cracks were developed in the region of constant strain energy was considered to indicate that a concept of a fluctuating strain energy as a basic theory of failure by fatigue under combined stresses is not tenable.

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