Newton-Raphson iterative method applied to circularly towed cable-body system

1979 ◽  
Vol 1 (2) ◽  
pp. 73-80 ◽  
Author(s):  
John W. Leonard
Keyword(s):  
Iterative Method ◽  
Body System ◽  
Newton Raphson ◽  
Towed Cable

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 130 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation is implicitly given in respect to the unknown flow friction factor λ; λ = ζ ( R e , ε * , λ ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. A common approach to solve it is through the Newton–Raphson iterative procedure or through the fixed-point iterative procedure. Both require in some cases, up to seven iterations. On the other hand, numerous more powerful iterative methods such as three- or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require, in the worst case, only two iterations to reach the final solution. The recommended representatives are Sharma–Guha–Gupta, Sharma–Sharma, Sharma–Arora, Džunić–Petković–Petković; Bi–Ren–Wu, Chun–Neta based on Kung–Traub, Neta, and the Jain method based on the Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between the iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

scholarly journals Fractional Newton-Raphson Method

2021 ◽  
Vol 8 (1) ◽  
pp. 1-13
Author(s):  
A. Torres-Hernandez ◽  
F. Brambila-Paz
Keyword(s):  
Fractional Calculus ◽  
Iterative Method ◽  
Complex Numbers ◽  
Initial Condition ◽  
The Real ◽  
Complex Roots ◽  
Newton Raphson ◽  
Roots Of A Polynomial ◽  
Raphson Method

The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the space of complex numbers given a real initial condition, which allows us to find both the real and complex roots of a polynomial unlike the classical Newton-Raphson method.

Elastodynamic Analysis of Towed Cable Systems by Global Nodal Position Vector Finite Element Method

2008 ◽  
Author(s):  
Zheng H. Zhu ◽  
Michael LaRosa ◽  
Feng J. Sun
Keyword(s):  
Finite Element ◽  
Cost Effective ◽  
Body Motion ◽  
Position Vector ◽  
Body System ◽  
Fe Method ◽  
Sea Trial ◽  
Design Engineers ◽  
Vector Finite Element ◽  
Towed Cable

The handling and control of towed cable and body systems onboard surface ships and submarines presents a significant technical challenge to design engineers in the defense and ocean industries. The current approaches rely heavily on the empirical methods and the time-consuming and costly prototype testing. Computer simulation provides a cost effective way to reduce the high risks associated with the towed cable/body system. However, the current dynamic analysis of towed cables is mostly done by the finite difference (FD) method in stead of the finite element (FE) method that is widely used in almost all engineering fields. This paper presents an alternative FE method to simulate the dynamics of towed cable and body system, in which the large rigid body motion is coupled with small elastic deformation. The newly derived FE method is formulated in terms of element nodal positions, which is different from the existing FE methods that use displacements. The alternative FE method solves for the cable position directly in order to eliminate accumulated numerical errors arising from existing FE methods that solve for displacements first in order to obtain the cable position over very long period of time. The alternative FE formulation is implemented and applied to real applications to demonstrate its robustness by comparing simulation results with the experimental and sea trial data.

Performance of textured foil journal bearing considering the influence of relative texture depth

2022 ◽  
pp. 135065012110729
Author(s):  
Guanghui Zhang ◽  
Kefan Xu ◽  
Jiazhen Han ◽  
Yanzhong Huang ◽  
Wenjie Gong ◽  
...  
Keyword(s):  
Iterative Method ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Surface Texturing ◽  
Static And Dynamic Characteristics ◽  
Foil Bearing ◽  
Newton Raphson ◽  
Maximum Increment

Both foil structure and surface texturing have been widely used to improve bearing performance. However, there is little research on their combination, namely, textured gas foil bearing. This paper adopts the Reynolds equation as the pressure governing equation of bump-type foil journal bearing to study the influence of textures located on the top foil. The Newton-Raphson iterative method and the perturbation method are employed to obtain static and dynamic characteristics, respectively. Thereafter, based on three texture distribution types, further analysis about the effect of the relative texture depth and the textured portion is carried out. The results indicate that an appropriate arrangement of textures could improve the performance of gas foil bearing. For #1 texture distribution, the maximum increment of load capacity could exceed 10% when ω  =  1.4 × 105 r/min, ε  =  0.2.

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation – Numerical Validation

2018 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation ζ is implicitly given in respect to the unknown flow friction factor λ ;  λ=ζ(Re,ε*,λ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. Common approach to solve it is through the Newton-Raphson iterative procedure or through the fixed-point iterative procedure. Both requires in some case even eight iterations. On the other hand numerous more powerful iterative methods such as three-or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require in worst case only two iterations to reach final solution. The recommended representatives are Sharma-Guha-Gupta, Sharma-Sharma, Sharma-Arora, Džunić-Petković-Petković; Bi-Ren-Wu, Chun-Neta based on Kung-Traub, Neta, and Jain method based on Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

A numerical model of a towed cable-body system

2000 ◽  
Vol 42 ◽  
pp. 362 ◽  
Author(s):  
C. K. H. Chin ◽  
R. L. May ◽  
H. J. Connell
Keyword(s):  
Numerical Model ◽  
Body System ◽  
Towed Cable

An iterative method for generating kinematically feasible interference-free robot trajectories

Robotica ◽  
1989 ◽  
Vol 7 (2) ◽  
pp. 119-127 ◽  
Author(s):  
R. O. Buchai ◽  
D. B. Cherchas
Keyword(s):  
Iterative Method ◽  
Quantitative Measure ◽  
Penalty Functions ◽  
Initial Estimate ◽  
Interference Constraints ◽  
Robot Trajectory ◽  
Point Motion ◽  
Newton Raphson ◽  
Point To Point ◽  
Raphson Method

SUMMARYThis paper proposes a method for finding an optimal geometric robot trajectory to perform a specified point-to-point motion without violating joint displacement limits or interference constraints. The problem is discretised, and a quantitative measure of interference is proposed. Constraint violations are represented by exterior penalty functions, and the problem is solved by iteratively improving an initial estimate of the trajectory. This is accomplished by numerically minimizing a cost functional using a modified Newton–Raphson method.

scholarly journals A New Accurate and Efficient Iterative Numerical Method for Solving the Scalar and Vector Nonlinear Equations: Approach Based on Geometric Considerations

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Grégory Antoni
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Accurate Solution ◽  
Extended Version ◽  
Root Finding ◽  
Newton Raphson ◽  
Stationary Type ◽  
Raphson Method

This paper deals with a new numerical iterative method for finding the approximate solutions associated with both scalar and vector nonlinear equations. The iterative method proposed here is an extended version of the numerical procedure originally developed in previous works. The present study proposes to show that this new root-finding algorithm combined with a stationary-type iterative method (e.g., Gauss-Seidel or Jacobi) is able to provide a longer accurate solution than classical Newton-Raphson method. A numerical analysis of the developed iterative method is addressed and discussed on some specific equations and systems.

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