scholarly journals A Radial Return Algorithm Application in Elastoplastic Frame Analysis Using Plastic Hinge Approach

2010 ◽  
Vol 2010 ◽  
pp. 1-22
Author(s):  
William Taylor Matias Silva ◽  
Luciano Mendes Bezerra
Keyword(s):  
Yield Surface ◽  
Plastic Hinge ◽  
General Function ◽  
Biaxial Bending ◽  
Solution Strategy ◽  
Framed Structures ◽  
Return Algorithm ◽  
Predictor Corrector ◽  
Raphson Method ◽  
Perfect Plastic

A new method is presented for first-order elastoplastic analysis of framed structures using a radial return predictor/corrector solution strategy. The proposed method assumes plastic hinge formation coupled with a yield surface. The yield surface is defined as a general function of axial force, shear forces, twisting, and biaxial bending moments on the cross-section of the frame. The material is regarded as linear and elastic-perfect plastic. The plastic deformations are governed by the normality criterion. Combining the Newton-Raphson method and the radial return algorithm, a consistent tangent modular matrix is proposed and fast and converging algorithms are presented. Examples demonstrate the accuracy and effectiveness of the proposed method.

Effect of MHD and Injection through one side of a long vertical channel embedded in porous medium with transpiration cooling

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
K. Govardhan ◽  
K. Kaladhar ◽  
G. Nagaraju ◽  
B. Balaswamy
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Similarity Transformation ◽  
Initial Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Transpiration Cooling ◽  
Transfer Rates ◽  
Predictor Corrector ◽  
Raphson Method

AbstractThis paper examines the effect of MHD, and injection through one side of a long vertical channel embedded in porous medium with transpiration cooling. The governing nonlinear partial differential equations have been transformed by similarity transformation into a set of ordinary differential equations, which are solved numerically by Adam-moultan Predictor-Corrector method with Newton-Raphson Method for missing initial conditions. Proflles of dimensionless velocity, temperature and concentration are shown graphically for different parameters entering into the analysis. Also the effects of the pertinent parameters on the heat transfer rates are tabulated. An analysis of the results obtained shows that the flow field is influenced appreciably by emerging parameters of the present study.

Elasto-Plastic Analysis of Steel Framed Structures Based on Rigid Body Rule and Plastic-Hinge Concept

2019 ◽  
Vol 19 (09) ◽  
pp. 1950104 ◽  
Author(s):  
Y. B. Yang ◽  
Zhao-Hui Chen ◽  
Y. C. Tao ◽  
Y. F. Li ◽  
M. M. Liao
Keyword(s):  
Rigid Body ◽  
Plastic Hinge ◽  
Computation Time ◽  
Trial And Error ◽  
Framed Structures ◽  
Plastic Analysis ◽  
Structural Engineers ◽  
Global And Local ◽  
Geometric Nonlinear Analysis ◽  
Mathematical Operations

Aimed at its elegance, the rigid-body-based procedure for geometric nonlinear analysis is extended to including the plastic-hinge concept for elasto-plastic analysis of framed structures. To this end, the rigid body test for initially stressed elements is first briefed, followed by derivation of the tangent stiffness of the 2D elasto-plastic beam element using the initial and full yield surfaces to consider gradual yielding of the cross-section. Of theoretical importance, the tangent and geometric stiffnesses are jointly tested by the rigid body rule for initially stressed elements. The above concepts are contained in the global and local strategies, respectively, for tracing the load–deflection curves and for performing the trial-and-error iterations. The former can deal with the formation of multi plastic hinges, in addition to multi-critical points, whereas the latter is strongly rooted in the rigid body rule and thus is free of fictitious forces (source of slow convergence). The accuracy and efficiency of the solutions obtained are confirmed by comparison with the existing ones. In conclusion, the procedure proposed in its entity makes the elasto-plastic analysis simpler and faster. The more complicated the problem is, the greater the saving in computation time using the proposed procedure. Since only minimal mathematical operations are required, this procedure has the potential of being widely accepted by structural engineers in routine analysis.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

The Solution Strategy as an Indicator of the Developmental Stage of Preschool Children’s Mental-Rotation Ability

2010 ◽  
Vol 31 (2) ◽  
pp. 95-100 ◽  
Author(s):  
Claudia Quaiser-Pohl ◽  
Anna M. Rohe ◽  
Tobias Amberger
Keyword(s):  
Preschool Children ◽  
Mental Rotation ◽  
Latent Class ◽  
Preschool Age ◽  
Stage Model ◽  
Solution Strategy ◽  
Thinking Aloud ◽  
Transition Analysis ◽  
Solution Strategies ◽  
Close Relationship

The solution strategies of preschool children solving mental-rotation tasks were analyzed in two studies. In the first study n = 111 preschool children had to demonstrate their solution strategy in the Picture Rotation Test (PRT) items by thinking aloud; seven different strategies were identified. In the second study these strategies were confirmed by latent class analysis (LCA) with the PRT data of n = 565 preschool children. In addition, a close relationship was found between the solution strategy and children’s age. Results point to a stage model for the development of mental-rotation ability as measured by the PRT, going from inappropriate strategies like guessing or comparing details, to semiappropriate approaches like choosing the stimulus with the smallest angle discrepancy, to a holistic or analytic strategy. A latent transition analysis (LTA) revealed that the ability to mentally rotate objects can be influenced by training in the preschool age.

On the Robustness of Solution Strategy Classifications

2010 ◽  
Vol 31 (2) ◽  
pp. 68-73 ◽  
Author(s):  
María José Contreras ◽  
Víctor J. Rubio ◽  
Daniel Peña ◽  
José Santacreu
Keyword(s):  
Individual Differences ◽  
Study Strategies ◽  
Solution Strategy ◽  
Specific Test ◽  
Spatial Tasks ◽  
The Stability ◽  
Strategy Changes ◽  
Over Time

Individual differences in performance when solving spatial tasks can be partly explained by differences in the strategies used. Two main difficulties arise when studying such strategies: the identification of the strategy itself and the stability of the strategy over time. In the present study strategies were separated into three categories: segmented (analytic), holistic-feedback dependent, and holistic-planned, according to the procedure described by Peña, Contreras, Shih, and Santacreu (2008) . A group of individuals were evaluated twice on a 1-year test-retest basis. During the 1-year interval between tests, the participants were not able to prepare for the specific test used in this study or similar ones. It was found that 60% of the individuals kept the same strategy throughout the tests. When strategy changes did occur, they were usually due to a better strategy. These results prove the robustness of using strategy-based procedures for studying individual differences in spatial tasks.

THE INFLUENCE OF THE WIND SPEED PREDICTION ERROR ON THE SIZE OF THE STORAGE CONTROLLED OPERATION ZONE IN THE SYSTEM WITH THE WIND GENERATOR

2020 ◽  
Vol 2020 (57) ◽  
pp. 35-41
Author(s):  
K.S. Klen ◽  
◽  
M.K. Yaremenko ◽  
V.Ya. Zhuykov ◽  
◽  
...  
Keyword(s):  
Wind Speed ◽  
Prediction Error ◽  
Average Energy ◽  
Interpolation Formula ◽  
Wind Speed Prediction ◽  
Wind Generator ◽  
Prediction Horizon ◽  
Speed Prediction ◽  
Using Data ◽  
Predictor Corrector

The article analyzes the influence of wind speed prediction error on the size of the controlled operation zone of the storage. The equation for calculating the power at the output of the wind generator according to the known values of wind speed is given. It is shown that when the wind speed prediction error reaches a value of 20%, the controlled operation zone of the storage disappears. The necessity of comparing prediction methods with different data discreteness to ensure the minimum possible prediction error and determining the influence of data discreteness on the error is substantiated. The equations of the "predictor-corrector" scheme for the Adams, Heming, and Milne methods are given. Newton's second interpolation formula for interpolation/extrapolation is given at the end of the data table. The average relative error of MARE was used to assess the accuracy of the prediction. It is shown that the prediction error is smaller when using data with less discreteness. It is shown that when using the Adams method with a prediction horizon of up to 30 min, within ± 34% of the average energy value, the drive can be controlled or discharged in a controlled manner. References 13, figures 2, tables 3.

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