Application of the R-Function Theory and Least Square Method for Torsion Problem with H-Shaped Cross-Section

2012 ◽  
Vol 217-219 ◽  
pp. 2313-2316
Author(s):  
Ping Ping Li ◽  
Hong Yuan ◽  
Shan Qing Li
Keyword(s):  
Boundary Condition ◽  
Cross Section ◽  
Stress Function ◽  
Present Method ◽  
Function Theory ◽  
Least Square Method ◽  
Least Square ◽  
Torsion Problem ◽  
Function Form ◽  
Shaped Cross Section

The R-function theory and least square method are employed to solve the torsion problem of the bar with H-shaped cross-section. When the least square method is used to solve the elastic torsion problem alone, the stress function can be set to meet the boundary condition, only with the simple cross-section such as the rectangle and ellipse. For the H-shaped cross-section, it is hard to find a stress function to meet the boundary condition. The R-function theory can solve the problem, and it can be used to describe H-shaped cross-section by implicit function form. Introducing the R-function theory can be easy to construct the stress function that satisfied the boundary of H-shaped cross-section. A numerical example demonstrates the feasibility and efficiency of the present method.

Application of the R-Function Theory and Variational Method for Torsion Problem with Complicated Cross-Section

2013 ◽  
Vol 353-356 ◽  
pp. 3320-3323 ◽  
Author(s):  
Shan Qing Li ◽  
Hong Yuan
Keyword(s):  
Boundary Condition ◽  
Variational Method ◽  
Cross Section ◽  
Stress Function ◽  
Present Method ◽  
Function Theory ◽  
Implicit Function ◽  
Torsion Problem ◽  
Function Form ◽  
Numerical Example

The R-function theory and variational method are employed to solve the torsion problem of the bar with a complicated cross-section. When the variational method is used to solve the elastic torsion problem alone, the stress function can be set to meet the boundary condition, only with the simple cross-section such as the rectangle and ellipse. For the complicated cross-section, it is hard to find a stress function to meet the boundary condition. The R-function theory can solve the problem, and it can be used to describe the complicated cross-section by implicit function form. Introducing the R-function theory can be easy to construct the stress function that satisfied the boundary of the complicated cross-section. A numerical example demonstrates the feasibility and efficiency of the present method.

Identification of Nonlinear Systems by Haar Wavelet

2004 ◽  
Author(s):  
Shy-Leh Chen ◽  
Keng-Chu Ho
Keyword(s):  
Nonlinear Systems ◽  
Least Square Method ◽  
Haar Wavelet ◽  
State Equation ◽  
Least Square ◽  
Algebraic Equations ◽  
Function Form ◽  
Unknown Parameters ◽  
Complete Orthogonal Basis ◽  
Unknown System

This study addresses the identification of autonomous nonlinear systems. It is assumed that the function form in the nonlinear system is known, leaving some unknown parameters to be estimated. It is also assumed that the free responses of the system can be measured. Since Haar wavelets can form a complete orthogonal basis for the appropriate function space, they are used to expand all signals. In doing so, the state equation can be transformed into a set of algebraic equations in unknown parameters. The technique of Kronecker product is utilized to simplify the expressions of the associated algebraic equations. Together with the least square method, the unknown system parameters are estimated. Several simulation examples verify the analysis.

Energy Saving in Mine Ventilation Roadway and its Optimization Model Solving

2013 ◽  
Vol 868 ◽  
pp. 291-295
Author(s):  
Jie Liu ◽  
Peng Yang ◽  
Wen Sheng Lv
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Least Square Method ◽  
Mine Ventilation ◽  
Least Square ◽  
Construction Costs ◽  
Maintenance Costs ◽  
Capital Construction ◽  
The Relationship ◽  
Power Costs

The paper is aimed at introducing our research of mathematical modelling of mine ventilation roadway optimal cross-section and its solving method. As we know, a rational cross-section should be determined to satisfy each intake and return airflow roadway based on the analysis of the relationship between ventilation cross-section and capital construction costs, in addition to maintenance costs and ventilation power costs. Reasonable selection of ventilation roadway cross-section is important to economic. The least square method is reasonable to build mathematical model for ventilation roadway costs. On the basis of previous studies, the relationship of capital construction costs and maintenance costs were further analyzed. Finally, considering the capital construction, maintenance and ventilation power costs three costs, the mathematical model was more accurate. Through researching a single ventilation roadway costs variation with the size of cross-section, cross-section size determined by considering time variable of costs was optimal, and built by this size could reduce economic investment. Hereby, it provides a solving method for the whole process of ventilation networks roadway cross-section optimization.

Analytical Solution of Lamb Wave Scattering at Plate End

2011 ◽  
Vol 199-200 ◽  
pp. 949-952 ◽  
Author(s):  
Fei Long Feng ◽  
Jian Zhong Shen ◽  
Jing Jun Deng ◽  
Qiu Ping Wang
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Lamb Wave ◽  
Wave Scattering ◽  
Least Square Method ◽  
Least Square ◽  
Matrix Elements ◽  
Scattering Coefficients ◽  
Reflection Matrix ◽  
Analytical Expressions

An analytical solution based on modal decomposition is presented to investigate Lamb wave scattering at plate end. Take boundary condition into biorthogonality relation, a matrix equation is established with all matrix elements have analytical expressions. The scattering feature is then expressed in matrix form, named as reflection matrix, which has explicit expression composed of those matrixes. Calculation examples have be implemented when antisymmetric modes are reflected. Scattering coefficients are figured out in a range when frequency-thickness product vary from 0 to 8kHzm, to prove the calculation efficiency. The calculation precision is very close to the least square method based on model discretization.

The Uniform Torsion of an Incomplete Tore

1949 ◽  
Vol 2 (3) ◽  
pp. 354 ◽  
Author(s):  
W Freiberger
Keyword(s):  
Boundary Condition ◽  
Cross Section ◽  
Stress Function ◽  
Resultant Force ◽  
Stress System ◽  
Helical Spring ◽  
Close Approximation ◽  
Torsion Function ◽  
Small Pitch ◽  
Single Force

A stress system is determined which gives as the resultant over any terminal cross-section a single force acting along the axis of the tore. This will yield a close approximation to the stresses in a helical spring of small pitch. The method used is that of finding a stress function analogous to the ordinary torsion function subject to a certain boundary condition and the problem is solved in toroidal harmonics. The stresses and resultant force are evaluated in term of the dimensions of the tore and compared with the results of known approximate theories.

Direct Assessment of Effective Renal Plasma Flow from Renoscintigraphy with a Gamma Camera and an On-Line Computer

1981 ◽  
Vol 20 (06) ◽  
pp. 274-278
Author(s):  
J. Liniecki ◽  
J. Bialobrzeski ◽  
Ewa Mlodkowska ◽  
M. J. Surma
Keyword(s):  
Count Rate ◽  
Renal Plasma Flow ◽  
Early Period ◽  
Least Square Method ◽  
Least Square ◽  
Uptake Coefficient ◽  
Positive Linear Correlation ◽  
On Line ◽  
Best Fit ◽  
Plasma Activity

A concept of a kidney uptake coefficient (UC) of 131I-o-hippurate was developed by analogy from the corresponding kidney clearance of blood plasma in the early period after injection of the hippurate. The UC for each kidney was defined as the count-rate over its ROI at a time shorter than the peak in the renoscintigraphic curve divided by the integral of the count-rate curve over the "blood"-ROI. A procedure for normalization of both curves against each other was also developed. The total kidney clearance of the hippurate was determined from the function of plasma activity concentration vs. time after a single injection; the determinations were made at 5, 10, 15, 20, 30, 45, 60, 75 and 90 min after intravenous administration of 131I-o-hippurate and the best-fit curve was obtained by means of the least-square method. When the UC was related to the absolute value of the clearance a positive linear correlation was found (r = 0.922, ρ > 0.99). Using this regression equation the clearance could be estimated in reverse from the uptake coefficient calculated solely on the basis of the renoscintigraphic curves without blood sampling. The errors of the estimate are compatible with the requirement of a fast appraisal of renal function for purposes of clinical diagknosis.

PENGARUH KNOWLEDGE MANAGEMENT, KOMPETENSI, MOTIVASI TERHADAP KINERJA KARYAWAN

2015 ◽  
Vol 5 (2) ◽  
pp. 1
Author(s):  
Miftahol Arifin
Keyword(s):  
Knowledge Management ◽  
Linear Regression ◽  
Significant Influence ◽  
Employee Performance ◽  
Least Square Method ◽  
Least Square ◽  
Analysis Tool ◽  
Ordinary Least Square ◽  
Competence Motivation ◽  
Performance Analyze

The purpose of this research is to analyze the influence of knowledge management on employee performance, analyze the effect of competence on employee performance, analyze the influence of motivation on employee performance). In this study, samples taken are structural employees PT.centris Kingdom Taxi Yogyakarta. The analysis tool in this study using multiple linear regression with Ordinary Least Square method (OLS). The conclusion of this study showed that the variables of knowledge management has a significant influence on employee performance, competence variables have an influence on employee performance, motivation variables have an influence on employee performance, The analysis showed that the variables of knowledge management, competence, motivation on employee performance.Keywords: knowledge management, competence, motivation, employee performance.

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