Wyniki wyszukiwania - BazTech

1

The finite difference method on adaptive mesh for singularly perturbed nonlinear 1D reaction diffusion boundary value problems

Duru Hakkı, Güneş Baransel

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 4

45--56

EN

In this paper, we study singularly perturbed nonlinear reaction-diffusion equations. The asymptotic behavior of the solution is examined. The difference scheme which is accomplished by the method of integral identities with using of interpolation quadrature rules with weight functions and remainder term integral form is established on adaptive mesh. Uniform convergence and stability of the difference method are discussed in the discrete maximum norm. The discrete scheme shows that orders of convergent rates are close to 2. An algorithm is presented, and some problems are solved to validate the theoretical results.

2

Linear and geometrically non-linear frequencies and mode shapes of beams carrying a point mass at various locations. An analytical approch and a parametric study

Adri A., Benamar R.

Diagnostyka

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2017

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Vol. 18, No. 2

13--21

EN

In the present paper, the frequencies and mode shapes of a clamped beam carrying a point mass, located at different positions, are investigated analytically and a parametric study is performed. The dynamic equation is written at two intervals of the beam span with the appropriate end and continuity conditions. After the necessary algebraic transformations, the generalised transcendental frequency equation is solved iteratively using the Newton Raphson method. Once the corresponding program is implemented, investigations are made of the changes in the beam frequencies and mode shapes for many values of the mass and mass location. Numerical results and plots are given for the clamped beam first and second frequencies and mode shapes corresponding to various added mass positions. The effect of the geometrical non-linearity is then examined using a single mode approach in order to obtain the corresponding backbone curves giving the amplitude dependent non-linear frequencies.

3

Postbuckling of an Imperfect Plate Loaded in Compression

Havran J., Psotny M.

Mechanics and Mechanical Engineering

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2016

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Vol. 20, nr 2

143--149

EN

The stability analysis of a plate loaded in compression is presented. The non–linear FEM equations are derived from the minimum total potential energy principle. The peculiarities of the effects of the initial imperfections are investigated using the user computer code. Special attention is paid to the influence of imperfections on the post– critical buckling mode. The FEM computer program using a 48 DOF element has been used for analysis. FEM model consists of 4x4 finite elements. Full Newton-Raphson procedure has been applied.

4

Metoda analizy zasilania w sieci COAX

Hoang N. L.

Elektronika : konstrukcje, technologie, zastosowania

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2014

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Vol. 55, nr 11

114-116

PL

Dostępowa sieć telekomunikacyjna bazująca na technologii koncentrycznych kabli współosiowych (ang. Coaxial Cable Network – COAX) jest obecnie jedną z najpopularniejszych sieci stosowanych w Polsce. Pomimo długiego czasu istnienia tej technologii zagadnienie planowania zasilania sieci COAX wciąż nie jest w pełni rozwiązane. W niniejszym artykule przedstawiamy sposób analizy aspektów zasilania sieci COAX bazujący na metodzie numerycznej Newtona-Raphsona.

EN

Telecommunications access network technology based on coaxial cables (COAX) is one of the most popular networks used in Poland. Despite the long existence of this technology, the problem of COAX network voltage planning is still not fully resolved. In this paper, we present a method for analyzing the voltage aspect of COAX network based on the numerical method of Newton-Raphson.

5

Wpływ zmiennego w czasie obciążenia zewnętrznego na parametry elastohydrodynamicznego (EHD) izotermicznego filmu olejowego

Buchalski K.

Autobusy : technika, eksploatacja, systemy transportowe

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2013

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R. 14, nr 3

1575-1583

PL

W artykule przedstawiono metodykę rozwiązania zagadnienia wpływu zmiennego w czasie obciążenia zewnętrznego na parametry izotermicznego (EHD) filmu, takie jak: rozkład ciśnienia i grubość filmu olejowego na długości strefy kontaktu. Rozpatrywany kontakt jest liniowym stykiem skoncentrowanym dwóch walców oddzielonych warstwą smaru. W wyniku badań otrzymano rozkłady ciśnienia i grubości filmu olejowego w funkcji zmian częstotliwości obciążenia zewnętrznego.

EN

This paper presents the methodology of solving the problem of variable external load which influence on the parameters of the isothermal (EHD) oil film such as pressure distribution and thickness of the oil film on the length of the contact zone. Contact is considered a concentrated line contact between two cylinders separated by a layer of grease. As a result of research received: pressure distributions and obtained oil film thickness as a function of the frequency change of the external load.

6

An efficient nonlinear analysis of 2D frames using a Newton-like technique

Mansouri I., Saffari H.

Archives of Civil and Mechanical Engineering

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2012

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Vol. 12, no. 4

485--492

EN

The Newton–Raphson method, which is based on the Taylor series and uses the tangent stiffness matrix, has been widely used to solve nonlinear problems. In this paper, a Newton-like algorithm is used for analyses involving geometric nonlinearity. This iterative technique that requires two initial guesses is known as two-point iterative method. In this method, a real function is assumed to approximate the tangent stiffness matrix of the structure. This paper, proposes an efficient function for reducing the computing time and, number of iterations in the Newton–Raphson method coupled with the two-point methodology. The computational nonlinear analysis on planar frames shows that the proposed strategy can reduce the computing time up to around 40%. Compared with the classic Newton–Raphson algorithm, the presented method proposes a methodology which also can reduce the number of iterations.

7

The polarization method combined with the Newton-Raphson technique in magnetostatic field problems

Kuczmann M.

Przegląd Elektrotechniczny

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2008

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R. 84, nr 12

198-201

EN

Nonlinear magnetic field problems can be solved by using the polarization method. After applying the Finite Element Method (FEM), a system of nonlinear equations can be derived, which can only be solved by iterative techniques. The fixed point iteration scheme and the Newton-Raphson technique are the most widely used algorithms to solve nonlinear equations. The first is known as a convergent, but slow algorithm, while the other is a fast solver, which convergence can be critical. This paper presents and compares the two methods.

PL

Nieliniowe problemy pola magnetycznego mogą być rozwiązywane przy użyciu metody polaryzacji. Po zastosowaniu MES otrzymuje się system równań nieliniowych, które mogą być rozwiązywane jedynie metodami iteracyjnymi. Schemat iteracyjny ustalonego punktu oraz technika Newtona-Raphsona są najczęściej stosowane w rozwiązywaniu równań nieliniowych. Pierwsze podejście daje algorytm zbieżny ale wolny, drugo zaś daje algorytm szybki ale na granicy zbieżności. W artykule przedstawiono i porównano te dwa podejścia.

8

Numerical estimation of temperature-dependent thermophysical parameters by means of the inverse method - 2D approach

Zmywaczyk J.

Archives of Thermodynamics

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2006

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Vol. 27, no. 2

37-54

EN

A modified Newton-Raphson method which has been proposed by Ching-yu Yang [3] to determine the temperature-dependent thermal conductivity and heat capacity from temperature measured at boundaries in a medium (ID case) has now been extended to estimate simultaneously the temperature dependent thermal conductivity k[r](T), k[x](T) and specific heat c[p](T) of an orthotropic material. It has been found that inverse solution of the problem was satisfactory if the degree of polynomials used to estimate the unknown parameters was not greater than three. In addition to this, a D-optimality criterion given by Beck [2] was utilised to determine the finał time of experiment t[f].

9

Effect of model parameters on elastohydrodynamic lubrication line contact with non-Newtonian Carreau viscosity model

Mongkolwongrojn M., Wongseedakeaw K., Yawong S., Jeenkour P., Aiumpornsin C.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no spec

255-261

EN

The compressible elastohydrodynamic (EHD) lubrication of two surfaces under line contact has been investigated in steady state operating conditions. The modified Reynolds equation with non-Newtonian fluids has been formulated using Carreau viscosity model. The simultaneous systems of modified Reynolds and elasticity equations with boundary conditions were solved numerically using Newton Raphson technique. The performance characteristics of the elastohydrodynamic lubrication under two surfaces in line contact were calculated and presented for varying the non-Newtonian Carreau viscosity model parameters. The pressure profile, film thickness profile, load capacity were investigated in both static and dynamic conditions. This simulation showed the significant effect of model parameters on elastohydrodynamic lubrication under heavy load conditions.

10

Metody energetyczna i Newtona-Raphsona w obliczeniach wytrzymałościowych nieliniowych konstrukcji prętowych

Wegner T. M.

Zeszyty Naukowe Politechniki Poznańskiej. Mechanika

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2000

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Nr 47

63-71

PL

W pracy przedstawiono zastosowanie metody energetycznej do budowy równań równowagi dowolnej konstrukcji prętowej. W przykładzie liczbowym konstrukcji prętowej nieliniowej geometrycznie otrzymany układ nieliniowych równań rozwiązano metodą Newtona-Raphsona. Uzyskane wyniki ilustrujące nieliniowe zależności przemieszczeń i odkształceń prętów w funkcji obciążenia konstrukcji przedstawiono na wykresie.

EN

This paper presents an application of strain energy method to build equilibrium equations of any truss. Newton-Raphson method solves the system of nonlinear equations obtained in a numerical example of geometrically nonlinear truss. Results illustrating the nonlinear relationships of displacements and strains of bars as functions of structure load are presented on a chart.

11

Metoda równoważenia harmonicznych

Kral J.

Elektrotechnika i Elektronika

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1999

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T. 18, z. 1

33--36

PL

W pracy przedstawiono metodą równoważenia harmonicznych (MRH) oraz jej usprawnienie z wykorzystaniem podprzestrzeni Kryłowa. Metoda równoważenia harmonicznych jest obecnie podstawową metodą analizy nieliniowych układów mikrofalowych pracujących w stanie ustalonym. Stosowana jest w czołowych komercyjnych symulatorach układów mikrofalowych, takich jak MDS firmy Hewlett Packard czy Serenadę firmy Compact-Software (obecnie Ansoft). W MRH obwód nieliniowy przedstawia siew postaci dwóch podobwodów: liniowego i nieliniowego. Istotą metody jest znalezienie takiego napięcia we wrotach łączących oba podobwody, dla którego odpowiedzi prądowe obu podobwodów są takie same. Przedstawiono sposób obliczania prądowego wektora błędu oraz sposób jego minimalizacji. Najszerzej obecnie stosowaną do tego metodąjest metoda Newtona-Raphsona. Wymaga ona obliczenia jakobianu w każdym kroku iteracyjnym. Przy dużych analizowanych układach stawia to duże wymagania co do pamięci operacyjnej i szybkości obliczeń komputera. Technika podprzestrzeni Kryłowa pozwala na znaczne zredukowanie wymaganej pamięci przy zachowaniu tej samej precyzji obliczeń i tej samej odporności na utratę zbieżności.

EN

Harmonic balance analysis and its improvement in the form of Krylov subspace have been presented. Nowadays harmonic balance method is the basic method for the analysis of non-linear microwave circuits working in steady state. It is used in the best general-purpose microwave simulators such as MDS of Hewlett Packard whether Serenadę of Com¬pact-Software (atpresent: Ansoft). In the analysis a non-linear circuit is divided into two sub-circuits: linear andnon--linear connected through a port. The idea of harmonic balance is to find a voltage waveform in the port that gives the same current in both the sub-circuits. The way of calculation of a current-error vector and its minimization is presented. The Newton-Raphson method is generally acknowledged as the most useful to minimize the error vector. It isprecise and robust but requires the storage of the Jacobian matrix in each step of iteration process. When the problem size becomes large the huge demandof computer resources is reąuired. This difficulty may be overcome making use of the Krylov sub-space techniquefor Jacobian matrix storage.

12

Efficient free vibration analysis of large structures with close or multiple natural frequencies. P. 1 : Undamped structures

Lee I. W., Jung H. J., Kim M. Ch.

Computer Assisted Mechanics and Engineering Sciences

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1999

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Vol. 6, No. 3-4

403-414

EN

An efficient numerical method which can calculate the eigenproblem for the large structural system with multiple or close natural frequencies is presented. The method is formulated by the accelerated Newton-Raphson method to the transformed problem. The method can calculate the natural frequencies and mode shapes without any numerical instability which may be encountered in the well-known methods such as the subspace iteration method or the determinant search method which has been widely used for solving eigenvalue problem. The efficiency of the method verified by comparing convergence and solution time for numerical examples with those of the subspace iteration method and the determinant search method.