scholarly journals Application of discretization error estimators in stepped column buckling problems

2021 ◽  
Vol 37 (1) ◽  
Author(s):  
B. Souza ◽  
D. Fernades ◽  
C. Anflor ◽  
M. Morais
Keyword(s):  
Cross Section ◽  
Discretization Error ◽  
Error Estimator ◽  
Column Buckling ◽  
Error Estimators ◽  
Convergence Error ◽  
Solution Convergence ◽  
Richardson’S Extrapolation ◽  
The Finite Difference Method ◽  
Convergent Solution

In order to reduce the discretization error, in this paper, Richardson’s Extrapolation and Convergence Error Estimator were used to investigating the buckling problem convergence. The main objective was to verify the convergence order of the stepped column problem and to define a consistent moment of inertia at the point of variation of the cross-section. The variable of interest was the critical buckling load obtained by the Finite Difference Method. The convergent solution obtained errors less than 10-8, and this work showed that the best solution is not defined by excessive mesh refinement, but by the solution convergence analysis.

scholarly journals IMPROVING A POSTERIORI SPATIAL DISCRETIZATION ERROR ESTIMATION FOR SN TRANSPORT BY SINGULAR CHARACTERISTICS TRACKING

2021 ◽  
Vol 247 ◽  
pp. 03022
Author(s):  
Nathan H. Hart ◽  
Yousry Y. Azmy
Keyword(s):  
Error Estimate ◽  
Numerical Solution ◽  
Computational Cost ◽  
Discretization Error ◽  
Error Estimator ◽  
Approximation Procedure ◽  
Spatial Discretization ◽  
True Solution ◽  
Error Estimators ◽  
Singular Characteristics

Previously, we have developed a novel spatial discretization error estimator, the “residual source” estimator, in which an error transport problem, analogous to the discretized transport equation, is solved to acquire an estimate of the error, with a residual term acting as a fixed source. Like all error estimators, the residual source estimator suffers inaccuracy and imprecision in the proximity of singular characteristics, lines across which the solution is irregular. Estimator performance worsens as the irregularities become more pronounced, especially so if the true solution itself is discontinuous. This work introduces a modification to the residual approximation procedure that seeks to reduce the adverse effects of the singular characteristics on the error estimate. A partial singular characteristic tracking scheme is implemented to reduce the portion of the error in the numerical solution born by irregularities in the true solution. This treated numerical solution informs the residual approximations. The partial singular characteristic tracking scheme greatly enhances the numerical solution for a problem with prominent singular characteristics. The residual approximation and resultant residual source error estimate are likewise improved by the scheme, which only incurs the computational cost of an extra inner iteration.

Optimum Design of Columns Under Elastic Buckling

2012 ◽  
Author(s):  
Moataz A. M. Abd El Gawad ◽  
Hesham A. Hegazi ◽  
Sayed M. Metwalli
Keyword(s):  
Elastic Buckling ◽  
Control Points ◽  
Sectional Area ◽  
Cross Sectional ◽  
Column Buckling ◽  
B Spline ◽  
Buckling Constraints ◽  
Design Variables ◽  
The Finite Difference Method ◽  
Tapered Columns

In this paper, a generalized approach is developed to optimize column configuration subjected to buckling load. The configuration utilizes B-spline contour to provide more freedom to model the column shape. Previous columns in literature use tapered or parabolic tapered for configuration. This work considers hinged-hinged columns of circular solid cross-sectional area. Two sample applications are optimized using Genetic Algorithm with the finite difference method to satisfy the buckling constraints. The length and load are fixed. The objective is to minimize the volume considering the cross-sectional diameters as the design variables. B-Spline quadratic with three and five control points and cubic with five control points are applied. The proposed configuration is compared with tapered and parabolic tapered columns. Results show that continuity provides a better optimum against column buckling than other tapered columns. Even though volume is more than some configurations by about 1.67%, but those configurations would not satisfy buckling constraints over the entire length of the column.

Elastic-Plastic Torque Analysis of Notched Cross-Section Bars Using the Finite Difference Method

2008 ◽  
Vol 385-387 ◽  
pp. 869-872 ◽  
Author(s):  
Hui Peng Liu ◽  
Xiang Rong Fu ◽  
Song Cen ◽  
Xiu Gen Jiang ◽  
Jin San Ju ◽  
...  
Keyword(s):  
Stress Intensity ◽  
Cross Section ◽  
Finite Differences ◽  
Intensity Factors ◽  
Elastic Plastic ◽  
Numerical Tests ◽  
Finite Differences Method ◽  
New Strategy ◽  
Torque Analysis ◽  
The Finite Difference Method

A new strategy of finite differences method is proposed for analysis of notched cross-section bars under elastic-plastic torsion. Relation curves of the elastic-plastic torque responding with different positions, angles and lengths of the notches in one section are obtained by numerical tests. It can be seen that these relation curves exhibit obvious nonlinearity. Meanwhile, the stress intensity factors can also be easily calculated by utilizing the results of above finite differences method. It provides an effective way for solving such elastic-plastic fracture mechanics problem.

A POSTERIORI ERROR ESTIMATORS VIA BUBBLE FUNCTIONS

1996 ◽  
Vol 06 (01) ◽  
pp. 33-41 ◽  
Author(s):  
ALESSANDRO RUSSO
Keyword(s):  
Finite Element ◽  
Posteriori Error ◽  
Error Estimator ◽  
A Posteriori ◽  
A Posteriori Error Estimators ◽  
Element Space ◽  
A Posteriori Error ◽  
Error Estimators ◽  
Bubble Functions ◽  
Posteriori Error Estimators

In this paper we discuss a way to recover a classical residual-based error estimator for elliptic problems by using a finite element space enriched with bubble functions. The advection-dominated case is also discussed.

Parameter estimation in modelling the dynamics of fish stock biomass: are currently used observation-error estimators reliable?

1998 ◽  
Vol 55 (3) ◽  
pp. 749-760 ◽  
Author(s):  
Y Chen ◽  
N Andrew
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Likelihood Method ◽  
Fish Stock ◽  
Error Estimator ◽  
Observation Error ◽  
Estimation Errors ◽  
Abundance Index ◽  
Error Estimators ◽  
Production Models

Production models are used in fisheries when only a time series of catch and abundance indices are available. Observation-error estimators are commonly used to fit the models to the data with a least squares type of objective function. An assumption associated with observation-error estimators is that errors occur only in the observed abundance index but not in the dynamics of stock and observed catch. This assumption is usually unrealistic. Because the least squares methods tend to be sensitive to error assumptions, results derived from these methods may be unreliable. In this study, we propose a robust observation-error estimator. We evaluate the performance of this method, together with the commonly used maximum likelihood method, under different error assumptions. When there was only observation error in the abundance index, maximum likelihood tended to perform better. However, with both observation and process errors, maximum likelihood yielded much larger estimation errors compared with the proposed method. This study suggests that the proposed method is robust to error assumptions. Because the magnitude and types of error cannot often be specified with confidence, the proposed method offers a potentially useful addition to methods used to fit production models to abundance index and catch data.

scholarly journals Cell Conservative Flux Recovery and A Posteriori Error Estimate of Vertex-Centered Finite Volume Methods

2013 ◽  
Vol 5 (05) ◽  
pp. 705-727 ◽  
Author(s):  
Long Chen ◽  
Ming Wang
Keyword(s):  
Finite Volume ◽  
Control Volume ◽  
Mixed Finite Element ◽  
Posteriori Error ◽  
Finite Volume Methods ◽  
Posteriori Error Estimate ◽  
Error Estimator ◽  
A Posteriori ◽  
Error Estimators ◽  
Conservative Flux

AbstractA cell conservative flux recovery technique is developed here for vertex-centered finite volume methods of second order elliptic equations. It is based on solving a local Neumann problem on each control volume using mixed finite element methods. The recovered flux is used to construct a constant freea posteriorierror estimator which is proven to be reliable and efficient. Some numerical tests are presented to confirm the theoretical results. Our method works for general order finite volume methods and the recovery-based and residual-baseda posteriorierror estimators is the first result ona posteriorierror estimators for high order finite volume methods.

scholarly journals CALCULATION OF CENTRALLY COMPRESSED CONCRETE FILLED STEEL TUBULAR COLUMNS OF ANNULAR SECTION TAKING INTO ACCOUNT PHYSICAL NONLINEARITY

2021 ◽  
Vol 9 (3) ◽  
pp. 6-10
Author(s):  
Kazbek Khashkhozhev ◽  
Arthur Avakov
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Cross Section ◽  
Difference Method ◽  
Deformation Theory ◽  
Physical Nonlinearity ◽  
Short Term ◽  
Tubular Columns ◽  
Annular Section ◽  
The Finite Difference Method

In the article, the resolving equations are obtained for the calculation taking into account the physical nonlinearity and creep of centrally compressed concrete filled steel tubular columns of annular cross-section. The examples of the calculation of the bearing capacity with a short-term load are given. The solution was carried out numerically in the Matlab environment using the finite difference method. The deformation theory of plasticity by G.A. Geniev was used.

The Calculation of the Quasi-Three-Dimensional Flow in an Axial Gas Turbine

1975 ◽  
Vol 97 (2) ◽  
pp. 283-294 ◽  
Author(s):  
S. Biniaris
Keyword(s):  
Numerical Solution ◽  
Cross Section ◽  
Three Dimensional ◽  
Entire Region ◽  
Three Dimensional Flow ◽  
Total Enthalpy ◽  
Blade Thickness ◽  
Meridional Cross Section ◽  
The Finite Difference Method ◽  
The Stability

The flow is calculated within the entire region from far upstream to far downstream of the blade rows and this not only between the blade rows but especially within the blade passages. It is assumed that the flow is steady, adiabatic, and inviscid. However, compressibility, blade forces in all directions, blade thickness, and total enthalpy gradients are taken into account. The shape of the meridional cross section can be arbitrary. The blades can be either cylindrical or twisted. The numerical solution is based on the finite-difference method. The discretization error, the stability error, and the iteration error of the numerical solution are determined.

A Comparative Study of Flux Projection Type Error Estimators in Elasto-Plastic Finite Element Analysis

1994 ◽  
Author(s):  
Ravi P. Tetambe ◽  
Sunil Saigal
Keyword(s):  
Comparative Study ◽  
Adaptive Mesh Refinement ◽  
Two Dimensions ◽  
Total Strain ◽  
Deformation Analysis ◽  
Large Strains ◽  
Error Estimator ◽  
Energy Rate ◽  
Error Estimators ◽  
L2 Norm

Abstract This paper presents a comparative study of a series of flux projection type error estimators for elastio-plastic materials undergoing large strains and large rotations. The error estimators are: L2 norms of stress error, total strain error, equivalent strain error, incremental total strain error per load step, and energy rate norm error, respectively. Numerical examples are presented in two dimensions. The information provided by these error estimators may be used for adaptive mesh refinement and for subsequent data transfer (rezoning) in a large deformation analysis. The error estimators based on the energy rate and the incremental total strain were found to be accurate in the prediction of the discretization error for the test cases considered. The L2 norm of incremental strain error estimator consistently gave the most conservative estimate of error.

Sign in / Sign up

Export Citation Format

Share Document