Wyniki wyszukiwania - BazTech

1

Thermal-electrical analogy in dynamic simulations of buildings: comparison of four numerical solution methods

Michalak Piotr

Journal of Mechanical and Energy Engineering

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2020

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Vol. 4, No 2

179--188

EN

The lumped capacitance method is widely used in dynamic modelling of buildings. Models differ in complexity, solution methods and ability to simulate transient behaviour of described objects. The paper presents a mathematical description of a simple 1R1C thermal network model of a building zone. Four numerical methods were applied to solve differential equation describing its dynamics. For validation purposes two test cases (600 and 900) from the BESTEST procedure were used. In both cases detailed results were given. Better ability of the simulation model to reproduce transient behaviour of the modelled buildings was noticed in case of the lightweight object (case 600). Annual heating and cooling demand was within the reference range for heavyweight one (case 900). The kind of the computation method had no significant effect on simulation results.

2

Solution approaches to differential equations of mechanical system dynamics: a case study of car suspension system

Terefe Tesfaye O., Lemu Hirpa G

Advances in Science and Technology. Research Journal

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2018

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Vol. 12, no 2

266--273

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.

3

A CFD model of a two-phase mixture flow in a test stand for air-borne particle analysis

Stachnik M., Czachor G., Jakubowski M.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2017

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nr 20(4)

343--358

EN

Farmers come across many materials which when being handled generate dust clouds. Even with low concentration these might pose risk of explosion and can carry dangerous microorganisms. To broaden the knowledge about fine dust particles sedimentation and analyze process of particles becoming air-borne, a tunnel air cleaner was designed. Based on the experiment, a CFX simulation was performed using the Eulerian approach and the CFX12.1 software. Presented model is a stedy state two-phase analysis of dust sedimentation. The results show mechanism of dust dispertion over large distance, such as regions of vorticity that seem to be main motor. Presented analysis emphasizes how easily small particles can become resuspended in the air and carried over distance. Acquired knowledge can be applied for safety regulation in many branches of agriculture.

4

Selected aspects of modelling a phenomena occurring with very large strain rates on the example of the shaped charge jet stream forming process and explosive formed projectiles

Panowicz R., Konarzewski M., Borkowski J., Milewski E.

Journal of KONES

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2015

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Vol. 22, No. 3

187--192

EN

During the process of the shaped charge jet stream formation and creation of the explosive formed projectiles, we have to deal with strain rates reaching level of 107 1/s and strains larger than in other dynamic phenomena. Therefore, the correct numerical analyses of such problems are especially demanding, both in terms of preparation of the numerical model and time needed for obtaining the solution. For their execution, both meshfree and Euler description based computational methods are used. Due to very large deformations and associated with them numerical analyses errors, computational methods based on the Lagrange description are not used. Description of the materials behaviour has to take into account influence of the strain rate in wide range of parameters. In most cases, it is realized by using in computational analyses Johnson-Cook or Steiberg-Green constitutive models. These models provide an accurate description of the material parameters not only in the wide range of strain rates, but also in large scope of strains and temperatures. Article presents results of the numerical analyses concerning the influence of selected numerical and geometric parameters of the system on the process of shaped charge jet stream formation and creation of explosive formed projectile.

5

Analysis of the influence of the finite elements mesh density on the determined shaped charge jet parameters

Panowicz R., Konarzewski M., Borkowski J., Milewski E.

Journal of KONES

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2015

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Vol. 22, No. 3

329--335

EN

Article presents results of numerical analyses of the finite elements mesh density influence on the shaped charge jet stream formation process and its selected parameters. Authors considered classical shaped charge, which consists of the plastic explosive material, copper liner and aluminium case. To properly described, material properties of the liner and case of the shaped charge, the Johnson-Cook material model was used. Detonation process was described using burn model approach. Behaviour of the detonation process products was described by commonly used John-Wilkins-Lee equation of state. Due to the nature of the presented phenomenon, in which we are dealing with large strains and strain rates, for its modelling authors utilized Euler description, implemented in the LS-Dyna software. In these method material flows by the finite elements and mesh is not deformed. Such approach allows for modelling phenomena where large and very large deformations occur. Unfortunately, it can result in a destabilizing of the systems energy balance. In order to minimize dissipation processes, in calculations was used second order scheme because of the spatial variables and time. Analyses were performed in axially symmetric setup, which was possible due to the symmetry of the analysed system. Influence of the finite elements size on the process of jet stream formation and its selected parameters was analysed.

6

Simplified 2D Transient Heat Transfer Simulation Using Gauss Error Function and FDM

du Plessis M.

Archives of Foundry Engineering

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2013

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Vol. 13, iss. 3 spec.

21--24

EN

This article documents the methodology used to compile a transient heat transfer simulation with the goal of calculating the time to full solidification or any specified temperature of a metal casting, this simulation may serves as a confirmation of Chvorinov's rule, furthermore the simulation will identify the heat transfer topography, allowing the user to identify the location of possible solidification errors, however for the purpose of simplification, only the liquid phase cooling of pure iron will be considered in this report. Euler methods will be discussed with special attention paid to explicit forward approximation and how Gaussian error can be used to simplify the simulation, in an attempt to reduce processing time. A look at the advantages and disadvantages of using this method will be considered and explanations given the decisions taken in the methodology of the simulation, the use of software will be discussed. The article will conclude with a look at the other applications for this simulation as well as the limits of this simulation.

7

Euler approximations can destroy unbounded solutions

Guy R. T., Misiurewicz M.

Fasciculi Mathematici

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2010

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Nr 44

43-52

EN

We show that there are ordinary differential equations in Rd with unbounded solutions, for which the difference equations obtained by using the forward Euler method have all solutions bounded.

8

Analysis Of Frame Stability As Safety Requirement

Holka H., Kukliński M.

Journal of Polish CIMAC

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2009

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Vol. 4, no 3

41-48

EN

This work is an analysis of an accident that occurred in a warehouse during loading of a new multi-level storing frame. The frame was designed in a professional design office with aid of computer program. It is of great importance to carry out checking procedures at various steps of the computerized design process. In this article two different methods were applied in order to calculate the critical buckling force. Then the results were compared. The Euler’s and the Rayleigh’s method yielded convergent results. The both methods proved that the critical buckling force would be exceeded if the frame was fully loaded. Since the frame began to incline when it was loaded only in 80%, other reasons of buckling must also be considered. Although we can’t eliminate designer’s mistake, it is more probable, that the buckling resistance of the frame was reduced by inappropriate operation of hydraulic stackers. The photographs show that the construction was so tightly loaded with palettes, that the overloading was the most probable cause of the catastrophe. The bending moment originated during the loading process could also reduce the buckling resistance of the construction.

9

Using the Euler's method to solve ordinary differential equations of higher order with a mixture of integer and Caputo derivatives

Błaszczyk T., Leszczyński J. S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2007

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Vol. 6, nr 1

31-40

EN

In this paper we present an application of the Euler's method to the numerical solution of fractional ordinary differential equations. These equations include both a classical differential operator of integer order and the fractional one defined in the Caputo sense. Our previous work was limited to the order of fractional derivative α ∈ (0,1) . This study considers numerical schemes for higher orders of a fractional derivative. We then compare our schemes with analytical solutions in order to show their good numerical precision.

10

Generalized Euler method for nonlinear first order partial differential functional equations

Kamont Z., Nadolski A.

Demonstratio Mathematica

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2005

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Vol. 38, nr 4

976-996

EN

Classical solutions of the local Cauchy problem on the Haar pyramid are approximated in the paper by solutions of suitable quasilinear systems of difference equations. The proof of the stability of the difference problem is based on a comparison technique with nonlinear estimates of the Perron type. This new approach to the numerical solving of nonlinear functional differential equations is generated by a quasilinearization method for initial problems. Numerical examples are given.

11

Mathematical model of architecture and learning processes of artificial neural networks

Bielecki A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2003

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Vol. 7, No 1

93-114

EN

A mathematical model of architecture and learning processes of multilayer artificial neural netwoks is discussed in the paper. Dynamical systems theory is used to describe the learning precess of networks consisting of linear, weakly nonlinear and nonlinear neurons. Conjugacy between a gradient dynamical system with a constant time step and a cascade generated by its Euler method theorem is applied as well.

12

Approximation of a Solidification Problem

Aboulaich R., Haggouch I., Souissi A.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 4

921-955

EN

A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocci, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al.., 1991; Saguez, 1980), or a control problem (El Bagdouri, 1987; Peneau, 1995; Saguez, 1980). In the present work, we provide a new formulation leading to a shape optimization problem. For a semidiscretization in time, we consider an Euler scheme. Under some restrictions related to stability conditions, we prove an L^2-rate of convergence of order 1 for the temperature. In the last part, we study the existence of an optimal shape, compute the shape gradient, and suggest a numerical algorithm to approximate the free boundary. The numerical results obtained show that this method is more efficient compared with the others.

13

Topological conjugacy of gradient cascades and learning process of a nonlinear neuron

Bielecki A.

Opuscula Mathematica

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2000

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Vol. 20

19-25

EN

This article discusses the topological conjugacy between a gradient dynamical system with a constant time step and a cascade generated by its Euler method. The result presented in this paper is that on a two-dimensional sphere a gradient dynamical system is, under some natural assumptions, correctly reproduced by Euler method for a time step sufficiently small. It means that the time-h-map of the induced dynamical system is globally topologically conjugate to discrete dynamical system obtained via Euler method. The presented theorem is applied to analysis of artificial nonlinear neuron learning process.

PL

W artukule rozważany jest problem topologicznego sprzężenia kaskady otrzymanej z równania gradientowego poprzez ustalenie kroku czasowego i kaskady generowanej przez metodę Eulera dla tego równania. Prezentowane twierdzenie mówi o tym, że na dwuwymiarowej sferze, przy pewnych naturalnych założeniach, dynamika układu gradientowego jest poprawnie odtwarzana przez metodę Eulera, jeśli jej krok czasowy jest dostatecznie mały. Oznacza to, że kaskada otrzymana przez ustalenie kroku czasowego jest globalnie topologicznie sprzężona z dyskretnym układem dynamicznym generowanym przez metodę Eulera. Prezentowane twierdzenie jest zastosowane do analizy procesu nauki nieliniowego neuronu.