MATLAB® Functions for Numerical Analysis and Their Applications in M&T

2021 ◽  
pp. 141-165
Keyword(s):  
Numerical Analysis ◽  
Friction Coefficient ◽  
Numerical Methods ◽  
Nonlinear Equations ◽  
Science And Engineering ◽  
Pressure Angle ◽  
Angle Function

The chapter presents the MATLAB® commands that realize numerical methods for solving problems arising in science and engineering in general and in the field of mechanics and tribology (M&T) in particular. The most commonly used commands along with some information on numerical methods are explained. The topics of the chapter include interpolation and extrapolation, solving nonlinear equations with one or more unknowns, finding minimum and maximum, integration, and differentiation. All described actions are explained by examples from the field of M&T. At the end of the chapter, applications are presented; they illustrate how to interpolate the friction coefficient data, calculate elongation of a scale with two springs, determine the maxima and minima of the pressure-angle function, and solve some other M&T problems.

scholarly journals Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Ali Özyapıcı ◽  
Zehra B. Sensoy ◽  
Tolgay Karanfiller
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Rate Of Convergence ◽  
Nonlinear Equations ◽  
Science And Engineering ◽  
Root Finding ◽  
Wide Range ◽  
Newton Raphson ◽  
Methods Numerical

In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of root-finding methods based on multiplicative and Volterra calculi is self-evident. Newton-Raphson, Halley, Broyden, and perturbed root-finding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, Newton-Raphson methods and consequently perturbed root-finding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed root-finding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods.

Upon Impact Numerical Modeling of Foam Materials

2017 ◽  
Vol 54 (2) ◽  
pp. 195-202
Author(s):  
Vasile Nastasescu ◽  
Silvia Marzavan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
General Character ◽  
Foam Material ◽  
Various Boundary Conditions ◽  
Specific Behaviour

The paper presents some theoretical and practical issues, particularly useful to users of numerical methods, especially finite element method for the behaviour modelling of the foam materials. Given the characteristics of specific behaviour of the foam materials, the requirement which has to be taken into consideration is the compression, inclusive impact with bodies more rigid then a foam material, when this is used alone or in combination with other materials in the form of composite laminated with various boundary conditions. The results and conclusions presented in this paper are the results of our investigations in the field and relates to the use of LS-Dyna program, but many observations, findings and conclusions, have a general character, valid for use of any numerical analysis by FEM programs.

Optimization of the Navy’s three-dimensional mine impact burial prediction simulation model, Impact35, using high-order numerical methods

2021 ◽  
pp. 154851292110286
Author(s):  
Athanasios Donas ◽  
Ioannis Famelis ◽  
Peter C Chu ◽  
George Galanis
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Prediction Model ◽  
Simulation Model ◽  
Three Dimensional ◽  
Simulation System ◽  
High Order ◽  
Alternative Methodology ◽  
Runge Kutta ◽  
Fifth Order

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

THE RESOLUTION CORRECTION IN THE SCINTILLATION SPECTROMETRY OF CONTINUOUS X RAYS

1958 ◽  
Vol 36 (12) ◽  
pp. 1624-1633 ◽  
Author(s):  
W. R. Dixon ◽  
J. H. Aitken
Keyword(s):  
Integral Equation ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Analytical Procedure ◽  
Pulse Height ◽  
Matrix Inversion ◽  
Height Distribution ◽  
X Rays ◽  
Smooth Solutions ◽  
Pulse Height Distribution

The problem of making resolution corrections in the scintillation spectrometry of continuous X rays is discussed. Analytical solutions are given to the integral equation which describes the effect of the statistical spread in pulse height. The practical necessity of making some kind of numerical analysis is pointed out. Difficulties with numerical methods arise from the fact that the observed pulse-height distribution cannot be defined precisely. As a result it is possible in practice only to find smooth "solutions". Additional difficulties arise if the numerical method is based on an invalid analytical procedure. For example matrix inversion is of doubtful value in making the resolution correction because there does not appear to be an inverse kernel for the integral equation in question.

Numerical Analysis of Air Measuring Station Location Optimization in Underground Mine Airway

2014 ◽  
Vol 960-961 ◽  
pp. 621-624
Author(s):  
Jing Zhao Zhang ◽  
Yong Sheng Yan ◽  
Zhen Guo Yan ◽  
Feng Liang Wu
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Underground Mine ◽  
Inlet Velocity ◽  
Location Optimization ◽  
Measuring Station ◽  
Numerical Tests ◽  
Station Location

The optimized air measuring station location of mine airway based on air fully developed was proposed and numerical tests were conducted with six models. The independence of air fully development and inlet velocity was analyzed which validated the models and the numerical methods. The results show that optimized air measuring station location in head entry is 132m-198m after the airway turning while 5.0m-10.1m before the airway turning in tail entry.

scholarly journals An Anatomical Study of Scilla (Scilloideae) Section Chionodoxa and Scilla bifolia in Turkey1

2017 ◽  
Vol 35 (0) ◽  
Author(s):  
H. YILDIRIM ◽  
K. YETISEN ◽  
A. ÖZDEMIR ◽  
C. ÖZDEMIR
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Analysis Of Variance ◽  
Leaf Anatomy ◽  
Pearson Correlation ◽  
Anatomical Study ◽  
Anatomical Variations ◽  
Vascular Bundles ◽  
Single Row ◽  
Scilla Bifolia

ABSTRACT In the present study Scilla luciliae, S. forbesii, S. sardensis, S. siehei, Scilla x allenii and S. bifolia are compared anatomically. Some differences have been found in root, scape, and leaf anatomy of the taxa, and commented. S. luciliae, S. forbesii, S. sardensis and S. siehei have a metaxylem at the center of the root, others have 3-4 number metaxylem. Vascular bundles in two row in S. luciliae and S. forbesii in a single row in S. sardensis, Scilla x allenii and S. bifolia though in three rows in S. siehei. Aerenchyma tissue is present in mesophyll of five taxa leaf except S. sardensis. The anatomical variations in the taxa have been investigated by means of numerical methods (Analysis of variance and Pearson correlation). By the analysis of the investigated taxa from 12 anatomy related characters, it has been also found that the results from numerical analysis of anatomy characters can provide additional evidences, which correspond to the anatomy for the recognition of the taxa.

scholarly journals Shamanskii Method for Solving Parameterized Fuzzy Nonlinear Equations

2020 ◽  
Vol 11 (1) ◽  
pp. 24-29
Author(s):  
Sulaiman Mohammed Ibrahim ◽  
Mustafa Mamat ◽  
Puspa Liza Ghazali
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Iteration Process ◽  
Benchmark Problems ◽  
Fuzzy Variables ◽  
Computationally Expensive ◽  
And Storage ◽  
Approximate Jacobian

One of the most significant problems in fuzzy set theory is solving fuzzy nonlinear equations. Numerous researches have been done on numerical methods for solving these problems, but numerical investigation indicates that most of the methods are computationally expensive due to computing and storage of Jacobian or approximate Jacobian at every iteration. This paper presents the Shamanskii algorithm, a variant of Newton method for solving nonlinear equation with fuzzy variables. The algorithm begins with Newton’s step at first iteration, followed by several Chord steps thereby reducing the high cost of Jacobian or approximate Jacobian evaluation during the iteration process. The fuzzy coe?cients of the nonlinear systems are parameterized before applying the proposed algorithm to obtain their solutions. Preliminary results of some benchmark problems and comparisons with existing methods show that the proposed method is promising.

scholarly journals Numerical analysis of axial fan characteristics

Mechanik ◽  
2018 ◽  
Vol 91 (7) ◽  
pp. 606-608
Author(s):  
Stanisław Wrzesień ◽  
Michał Frant ◽  
Maciej Majcher
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Flow Rate ◽  
Total Pressure ◽  
Volumetric Flow Rate ◽  
Total Efficiency ◽  
Axial Fan ◽  
Axial Fans ◽  
Basic Characteristics

The paper presents an analysis and comparison of basic characteristics of axial fans, both analytically and numerically. Such characteristics are: the characteristics of the total pressure, power and total efficiency as a function of the volumetric flow rate. The presented results showed significant quantitative and qualitative differences in the characteristics obtained by two methods. The usefulness of numerical methods in relation to the results of the initial analytical project was confirmed.

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