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1
Content available remote Investigation of E-Cigarette Smoking Model with Mittag-Leffler Kernel
EN
Smoking is the most lethal social poisoning event. The World Health Organization defines smoking as the most important preventable cause of disease. Around 4.9 million people worldwide die from smoking every year. In order to analysis this matter, we aim to investigate an e-cigarette smoking model with Atangana-Baleanu fractional derivative. We obtain the existence conditions of the solution for this fractional model utilizing fixed-point theory. After giving existence conditions, the uniqueness of the solution is proved. Finally, to show the effect of the Atangana-Baleanu fractional derivative on the model, we give some numerical results supported by illustrative graphics.
PL
Obecnie trudno sobie wyobrazić inżyniera mechanika bez znajomości metod numerycznych (CAE). Powszechne korzystanie z komputerów i rozwój metod numerycznych przyczyniły się do zwiększenia jakości projektów inżynierskich. W artykule przedstawiono rozwój metod numerycznych i ich praktyczne zastosowania w budowie maszyn i pojazdów. Precyzja obliczeń oraz możliwość realizacji w rzeczywistości wirtualnej złożonych symulacji zwiększyła niezawodność produkowanych maszyn i pojazdów z jednoczesnym obniżeniem kosztów.
EN
Nowadays, is difficult to image mechanical engineer without skills of computer aided engineering (CAE) methods. Common use of computers, PC popularity and numerical methods development have been the reason of rapid growth of engineering design quality. Development of numerical methods and their practical applications in machine and vehicle building were presented. Precision of calculations as well as possibility of realization in virtual reality complex simulations increased reliability of produced machines and vehicles with simultaneous cost decreasing.
3
Content available Projekt konstrukcji przekrycia pływalni miejskiej
PL
Opracowano koncepcję architektoniczną obiektu pływalni miejskiej z dwoma wariantami konstrukcji przekrycia w postaci powłoki walcowej. Przeprowadzono analizę porównawczą sił wewnętrznych w powłoce uzyskanych metodą numeryczną i analityczną. Zwymiarowano żelbetową konstrukcję przekrycia powłokowego zgodnie z obowiązującymi eurokodami.
EN
The architectural and construction concept of the swimming pool with two types of cylindrical shell roof was designed. A comparative analysis of internal forces using a numerical and analytical method has been carried out. The reinforced structure of cylindrical shell roof has been designed according to required eurocodes.
PL
W artykule przedstawiono doświadczalne systemy występujące na rynku budowlanym, przeznaczone do ocieplania budynków od wewnątrz. Zaprezentowano wytyczne prawne dotyczące termoizolacji, powołując się na Dyrektywę Parlamentu Europejskiego oraz normy polskie. Zestawiono podstawową wiedzę na temat syntetycznych materiałów komórkowych i przedstawiono odmiany stosowane przy ocieplaniu od wewnątrz. Sklasyfikowano systemy ze względu na dyfuzję otwartą oraz zamkniętą. Wybrane parametry techniczne systemów przedstawiono w postaci wykresów. Przedstawiono algorytm postępowania w przypadku modelowania przegrody uwzględniające parametry klimatyczne, zacinające deszcze, występujące w danej okolicy, zawilgocenie budynku oraz magazynowanie ciepła i wilgoci przez przegrodę.
EN
The article presents experimental systems available on the construction market, intended for internal insulation of buildings. It describes legal guidelines for thermal insulation with reference to the Directive of the European Parliament as well as to Polish standards. It compiles basic knowledge on synthetic cellular materials and presents the variants used for internal insulation. It also contains a classification of the systems according to open and closed diffusion. Selected technical parameters of the systems have been presented in the form of charts. An algorithm of conduct in the case of partition modeling has been presented, taking into account climatic parameters, slanting rains occurring in a given area, moisture content of the building and storage of heat and moisture by the partition.
EN
The article is dedicated to the optimization problem of the regulated maintenance periodicity for military products operated according to their technical condition. The analytical method of optimization for the exponential law of the time distribution between failures and the numerical optimization method for the diffusion-monotonic law are taken into consideration. The search for the extreme value of the regulated maintenance periodicity for the diffusionmonotonic distribution law was conducted with the use of the numerical method applying Mathcad 15.0. The dependencies of both the technical utilization factor and its derivative on the regulated maintenance periodicity at certain values of the model parameters were obtained.
PL
W pracy podjęto problem optymalizacji okresowości obsługiwania planowego dla produktów wojskowych eksploatowanych według stanu technicznego. Rozważano analityczną metodę optymalizacji dla wykładniczego prawa rozkładu czasu między awariami oraz metodę numeryczną optymalizacji dla prawa dyfuzyjno-monotonicznego (za pomocą Mathcada 15.0). Uzyskano zależności zarówno współczynnika wykorzystania technicznego, jak i jego pochodnej od okresowości obsługiwania planowego przy określonych wartościach parametrów modelu.
6
PL
W pracy przedstawiono symulację numeryczną i analityczną temperatury twardnienia, odkształceń i naprężeń termicznych w fundamencie śluzy Sülfeld-Süd w Niemczech, której budowa zakończyła się w listopadzie 2008 r. Przedstawione wyniki dotyczą jednego z etapów budowy tego fundamentu o rzeczywistych wymiarach 41,5 x 26,5 m i grubości 2 m. Analizę numeryczną przeprowadzono w programie DIANA MES. Uzyskane wyniki zostały porównane z rzeczywistymi pomiarami temperatury, odkształceń i naprężeń w fundamencie śluzy.
EN
The study presents the numerical and analytical simulation of the hardening temperature, thermal strains and stresses in the foundation of the sluice Sülfeld-Süd in Germany, which construction process was completed in November 2008. The present study relates to a particular construction stage of this foundation with real dimensions of 41.5 x 26.5 m and a thickness of 2 m. The numerical analysis was performed in the software DIANA FEA. The obtained results are compared with actual measurements of temperature, strains and stresses in the sluice foundation.
7
EN
The paper presents a mathematical model of a complex electromechanical system. The electromechanical system features a deep-groove asynchronous motor, which drives a vertical pump. I this case the motor and pump are connected through a long shaft with distributed parameters. The motor is powered from a power transformer. The general model of the system was developed on the basis of interdisciplinary variational approaches. The final state equations are represented in the Cauchy normal form. This methodology gives the possibility of using both explicit and implicit numerical methods.
PL
W pracy przedstawiono model matematyczny złożonego układu elektromechanicznego, składającego się z głębokożłobkowego silnika asynchronicznego, który przez długi wał o parametrach rozłożonych napędza pompę pionową. Silnik zasilany jest z transformatora mocy. Ogólny model układu opracowano na podstawie interdyscyplinarnych podejść wariacyjnych. Końcowe równania stanu reprezentowane są w normalnej postaci Cauchy’ego, co daje możliwość wykorzystania zarówno jawnych, jak i ukrytych metod numerycznych.
EN
This paper proposes a method to numerically study viscous incompressible two-dimensional steady flow in a driven square cavity with heat and concentration sources placed on its side wall. The method proposed here is based on streamfunction-vorticity (Ψ-ξ) formulation. We have modified this formulation in such a way that it suits to solve the continuity, x and y-momentum, energy and mass transfer equations which are the governing equations of the problem under investigation in this study. No-slip and slip wall boundary conditions for velocity, temperature and concentration are defined on walls of a driven square cavity. In order to numerically compute the streamfunction Ψ, vorticityfunction ξ , temperature θ, concentration C and pressure P at different low, moderate and high Reynolds numbers, a general algorithm was proposed. The sequence of steps involved in this general algorithm are executed in a computer code, developed and run in a C compiler. We propose that, with the help of this code, one can easily compute the numerical solutions of the flow variables such as velocity, pressure, temperature, concentration, streamfunction, vorticityfunction and thereby depict and analyze streamlines, vortex lines, isotherms and isobars, in the driven square cavity for low, moderate and high Reynolds numbers. We have chosen suitable Prandtl and Schmidt numbers that enables us to define the average Nusselt and Sherwood numbers to study the heat ad mass transfer rates from the left wall of the cavity. The stability criterion of the numerical method used for solving the Poisson, vorticity transportation, energy and mass transfer has been given. Based on this criterion, we ought to choose appropriate time and space steps in numerical computations and thereby, we may obtain the desired accurate numerical solutions. The nature of the steady state solutions of the flow variables along the horizontal and vertical lines through the geometric center of the square cavity has been discussed and analyzed. To check the validity of the computer code used and corresponding numerical solutions of the flow variables obtained from this study, we have to compare these with established steady state solutions existing in the literature and they have to be found in good agreement.
EN
The present paper deals with an analysis of the combined effect of Joule heating and viscous dissipation on an MHD boundary layer flow and melting heat transfer of a micro polar fluid over a stretching surface. Governing equations of the problem are transformed into a set of coupled nonlinear ordinary differential equations by applying proper transformations and then they are solved numerically using the RKF-45 method. The method is verified by a comparison with the established results with limiting solution. The influence of the various interesting parameters on the flow and heat transfer is analyzed in detail through plotted graphs.
10
EN
The paper concerns an analysis for SubIval (the subinterval-based method for fractional derivative computations in initial value problems). A time step size adaptive solver is discussed, for which the formula of a local truncation error is derived. A general form for a system of linear equations is given for the considered class of problems (for which the analysis is performed in the paper). Two circuit examples are introduced to display the usefulness of the SubIval solver. For the examples that have been chosen it is possible to obtain referential solutions through completely different methods. The results obtained through the numerical solver are compared with evaluations of the referential solutions. The error estimation results obtained for the time steps of the SubIval solver are compared with the actual errors, being the differences between the numerical solutions and the referential solutions. The paper also contains a comparison of the accuracy of results obtained through the SubIval solver with the accuracies of other solvers.
EN
Solution of a dynamic system is commonly demanding when analytical approaches are used. In order to solve numerically, describing the motion dynamics using differential equations is becoming indispensable. In this article, Newton’s second law of motion is used to derive the equation of motion the governing equation of the dynamic system. A quarter model of the suspension system of a car is used as a case and sinusoidal road profile input was considered for modeling. The state space representation was used to reduce the second order differential equation of the dynamic system of suspension model to the first order differential equation. Among the available numerical methods to solve differential equations, Euler method has been employed and the differential equation is coded MATLAB. The numerical result of the second degree of freedom, quarter suspension system demonstrated that the approach of using numerical solution to a differential equation of dynamic system is suitable to easily simulate and visualize the system performance.
EN
The article presents the maps of xx stress component and compares values of analytical and numerical calculations for the stress intensity factor range of welded specimens with fillet welds which subjected to cyclic bending. The tests were performed under constant value of moment amplitude Ma = 9.20 Nm and stress ratio R = σmin/ σmax = -1. The specimens were made of drag steel rod S355. The specimens were solid and welded. The numerical models were simulated with ABAQUS suite and numerical calculations performed with FRANC3D software.
PL
Praca dotyczy zastosowania metody wielokrokowej Geara oraz wybranych metod niejawnych IRK do rozwiązania układu równań różniczkowych zwyczajnych, opisujących obwód zawierający cewkę nieliniową. Zostanie przedstawiony model takiej cewki oraz jej opis za pomocą wybranych zmiennych stanu. Zostanie również przedstawiony program do badania dynamiki cewki opracowany w języku C#, w którym zaimplementowano metody niejawne RK: RADAU IIA, Gaussa-Legendre'a, Lobatto III C oraz metody wielokrokowe.
EN
The work concerns the application of the multistep Gear and selected IRK implicit methods to solve the system of ordinary differential equations describing a circuit containing non-linear coil. In this paper - model of the coil and its description with the use of selected state variables will also be presented. This paper will also show application for dynamics examination of the circuit written in C#, in which the following implicit RK methods were implemented: Radau IIA, Gauss-Legendre, Lobatto III C and the multistep method.
PL
Wstęp i cele: W pracy przedstawiono wzory potęgowo-wykładnicze do obliczania przybliżonej wartości szybkości filtracji kłębuszkowej (GRF). Pokazano próbę klasyfikacji wartości referencyjnych poziomu kreatyniny oraz zakresów wartości GFR. W artykule podano przykłady obliczeń przybliżonej wartości filtracji kłębuszkowej dla wartości prawidłowych dla obu płci. Materiał i metody: Wykorzystano materiał teoretyczny z literatury przedmiotu. Zastosowano metodę analityczną i numeryczną z wykorzystaniem programu Mathematica. Wyniki: Obliczono analitycznie i numerycznie wartości poziomu kreatyniny dla przypadku wartości prawidłowych oraz nieprawidłowych. Używając program Mathematica opracowano interpreatcję graficzną wyników w postaci wykresów 2D oraz 3D. Wniosek: Zastosowanie programu numerycznego Mathematica pozwala na wykonanie symulacji zarówno numerycznej jak i graficznej wzoru potęgowo-wykładniczego określającego szybkość filtracji kłębuszkowej.
EN
Introduction and aim: The paper presents exponential and power formulas for calculation of glomerular filtration rate (GRF). An attempt was made to classify the reference values of creatinine level and ranges of GFR values. The article gives examples of calculations of the approximate value of glomerular filtration for both female and male. Material and methods: Theoretical material from the subject literature has been used. An analytical and numerical method have been applied using the Mathematica program. Results: Analytical and numerical values of creatinine values were calculated for the case of normal and abnormal values. Using the Mathematica program, graphical interpatation of results in the form of 2D and 3D charts was developed. Conclusion: The use of the numerical program Mathematica allows the simulation of both the numerical and graphical exponential and power formula determining the rate of glomerular filtration.
EN
In this paper we discuss different definitions of variable-order derivatives of high order and we propose accurate and robust algorithms for their approximate calculation. The proposed algorithms are based on finite difference approximations and B-spline interpolation. We compare the performance of the algorithms by experimental convergence order. Numerical examples are presented demonstrating the efficiency and accuracy of the proposed algorithms.
EN
Singular and hypersingular integral equations appear frequently in engineering problems. The approximate solution of these equations by using various numerical methods is well known. Here we consider the case where these equations are supplemented by inequality constraints-mainly parametric in equality constraints, but also the case of singular/hypersingular integral inequalities. The approach used here is simply to employ the computational method of quantifier elimination efficiently implemented in the computer algebra system Mathematica and derive the related set of necessary and sufficient conditions for the validity of the singular/hypersingular integral equation/inequality together with the related in equality constraints. The present approach is applied to singular integral equations/inequalities in the problem of periodic arrays of straight cracks under loading- and fracture-related inequality constraints by using the Lobatto-Chebyshev method. It is also applied to the hypersingular integral equation/inequality of the problem of a single straight crack under a parametric loading by using the collocation and Galerkin methods and parametric inequality constraints.
EN
The paper presents the design process of a radial-axial turbine working with SES36 working fluid. First, the mean-line design process is performed and then the geometry is developed. In the next stage the numerical verification is performed taking into account the real properties of the working fluid. The properties are implemented via a look-up table and by a modified Benedict-Webb-Rubin equation of state. The presented turbine is characterized by a very small stator outflow angle which is about 4.5◦ but despite this small value, the efficiency of the machine is relatively high and equal to about 88%. The influence of internal leakages has also been investigated.
EN
The propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. Two differential equations are contemplated for solving the problem for electromagnetic wave propagation: first – an equation for the electric field, second – an equation derived for a complex phase of an electric field. Both equations are solved by the use of a finite-difference method. The simulation error is estimated mathematically and investigated. The presented results for equations show that in order to establish a high accuracy computation a much smaller number of points is needed to solve the problem of X-ray waves propagation through a multi-lens system when the method for the second equation is used. The reason for such a result is that the electric field of a wave after passing through many lenses is a quickly oscillating function of coordinates, while the electric field phase is a quickly increasing, but not oscillating function. Therefore, a very detailed difference grid, which is necessary to approximate the considered electric field can be replaced by not such a detailed grid, when computations are made for the complex wave of the electric field. The simulation error of both suggested methods is estimated. It is shown that the derived equation for a phase function allows efficient simulation of propagation of X-rays for the multi-lens optical system.
EN
This paper deals with a measurement of the electric field intensity in the near field region with proposed autonomous electromagnetic (EM) field probe. This probe is specially designed to measure in the near distance from the sources of the EM field. The output from the probe is a voltage corresponding to the measured component of the electric field intensity. At the end we compared results from measurement of the components of the electric field intensity with the results from simulation based on the numerical method.
PL
Artykuł dotyczy pomiaru natężenia pola elektrycznego w strefie bliskiej za pomocą zaproponowanej autonomicznej sondy pola elektromagnetycznego (EM). Sonda ta została zaprojektowana specjalnie do pomiaru w strefie bliskiej źródła pola EM. Na wyjściu sondy otrzymuje się napięcie odpowiadające mierzonemu komponentowi natężenia pola elektrycznego. W artykule porównano rezultaty pomiarów komponentów natężenia pola elektrycznego z wynikami symulacji prowadzonych z wykorzystaniem metod numerycznych.
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