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Analysis of pull-out maneuver for an aircraft represented by main wing and tailplane, using coupled Euler/flight dynamic model

Tomasz Iglewski Zdobysław Goraj
Archive of Mechanical Engineering | 2000 | vol. 47 | No 4 | 333-351
Keywords flight dynamics computational fluid dynamics grid generation finite differences method
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Abstract

The main aim of this analysis is to consider a mutual interference between aircraft motion and surrounding flow field. Euler flow model for inviscid, compressible gas and aircraft flight dynamics model was used to analyse quick dynamic manoeuvres. For such manoeuvres, aerodynamic hysteresis has a great influence on aircraft dynamics, which cannot be simulated with the assumption of quasi-steady aerodynamics. On the other hand, the aircraft motion as a rigid body strongly influences the flow field around itself. To account for this mutual interference, the Euler flow equations were used to obtain aerodynamic forces and moments acting on a simplified aircraft configuration (main wing+ tailplane only) during pull-out manoeuvre, and the flight dynamics equations of motion were used to describe dynamics of an aircraft. Initial conditions for the flight dynamics equation of motion were settled up coming from the solution of the Euler flow model. As a test case, a weak pull-out manoeuvre was selected. During this manoeuvre, the highest value of angle of attack doesn't exceed 12 degrees - the value which can be obtained from the classical approach based on flight dynamics equations of motion with quasisteady aerodynamics. However, coupled Euler flight dynamic model has much wider applicability, and can be used for the analysis of manoeuvres at high angles of attack, including large scale separation at sharp edges, unsteadiness and flow asymmetries even for symmetrical undisturbed flowficld case. This method, if successfully verified to a number of important flight manoeuvres (such as spin, Cobra manoeuvre, roll at high angles of attack and other) can open a new, very promising field in the analysis of aircraft dynamics.
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Authors and Affiliations

Tomasz Iglewski
Zdobysław Goraj

Combination of Artificial Neural Networks and Numerical Modeling for Predicting Deformation Modulus of Rock Masses

Narges Saadat Tayarani Saeed Jamali Mehdi Motevalli Zadeh
Archives of Mining Sciences | 2020 | vol. 65 | No 2 | 337-346 | DOI: 10.24425/ams.2020.133196
Keywords Artificial Neural Networks numerical simulation Finite Difference Method Deformation Modulus of Rock Mass Arch Dam
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Abstract

The deformation modulus of the rock mass as a very important parameter in rock mechanic projects generally is determined by the plate load in-situ tests. While this test is very expensive and time-consuming, so in this study a new method is developed to combin artificial neural networks and numerical modeling for predicting deformation modulus of rock masses. For this aim, firstly, the plate load test was simulated using a Finite Difference numerical model that was verified with actual results of the plate load test in Pirtaghi dam galleries in Iran. Secondly, an artificial neural network is trained with a set of data resulted from numerical simulations to estimate the deformation modulus of the rock mass. The results showed that an ANN with five neurons in the input layer, three hidden layers with 4, 3 and 2 neurons, and one neuron in the output layer had the best accuracy for predicting the deformation modulus of the rock mass.

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Authors and Affiliations

Narges Saadat Tayarani
Saeed Jamali
Mehdi Motevalli Zadeh

The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters

Ireneusz Winnicki Janusz Jasinski Slawomir Pietrek Krzysztof Kroszczynski
Advances in Geodesy and Geoinformation | 2022 | vol. 71 | No 2 | e23 | DOI: 10.24425/gac.2022.141176
Keywords transfer function finite element method finite difference methods matrices of the third-order Laplace filters modified differential equations
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Abstract

The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used third-order 3x3 pixels Laplace contour filters including the difference schemes used to derive them. The authors focused on the mathematical properties of the Laplace filters. The basic reasons of the differences of the properties were studied and indicated using their transfer functions and modified differential equations. The relations between the transfer function for the differential Laplace operator and its difference operators were described and presented graphically. The impact of the corner elements of the masks on the results was discussed. This is a theoretical work. The basic research conducted here refers to a few practical examples which are illustrations of the derived conclusions.We are aware that unambiguous and even categorical final statements as well as indication of areas of the results application always require numerous experiments and frequent dissemination of the results. Therefore, we present only a concise procedure of determination of the mathematical properties of the Laplace contour filters matrices. In the next paper we shall present the spectral characteristic of the fifth order filters of the Laplace type.
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Authors and Affiliations

Ireneusz Winnicki
1
ORCID: ORCID
Janusz Jasinski
1
ORCID: ORCID
Slawomir Pietrek
1
ORCID: ORCID
Krzysztof Kroszczynski
1
ORCID: ORCID
  1. Military University of Technology, Warsaw, Poland

The implicit numerical method for the one-dimensional anomalous subdiffusion equation with a nonlinear source term

Marek Błasik
Bulletin of the Polish Academy of Sciences Technical Sciences | 2021 | 69 | 6 | e138240 | DOI: 10.24425/bpasts.2021.138240
Keywords fractional derivatives and integrals integro-differential equations numerical methods finite difference methods
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Abstract

In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro-differential equation. As a result of the discretization of the integro-differential equation obtained an implicit numerical scheme which is the generalized Crank-Nicolson method. The implicit numerical schemes based on the finite difference method, such as the Carnk-Nicolson method or the Laasonen method, as a rule are unconditionally stable, which is their undoubted advantage. The discretization of the integro-differential equation is performed in two stages. First, the left-sided Riemann-Liouville integrals are approximated in such a way that the integrands are linear functions between successive grid nodes with respect to the time variable. This allows us to find the discrete values of the integral kernel of the left-sided Riemann-Liouville integral and assign them to the appropriate nodes. In the second step, second order derivative with respect to the spatial variable is approximated by the difference quotient. The obtained numerical scheme is verified on three examples for which closed analytical solutions are known.
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Bibliography

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  17.  M. Błasik, “A generalized Crank-Nicolson method for the solution of the subdiffusion equation,” 23rd International Conference on Methods & Models in Automation & Robotics (MMAR), pp.  726–729, 2018.
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  20.  K. Diethelm, The Analysis of Fractional Differential Equations. Berlin: Springer-Verlag, 2010.
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Authors and Affiliations

Marek Błasik
1
  1. Institute of Mathematics, Czestochowa University of Technology, al. Armii Krajowej 21, 42-201 Czestochowa, Poland

Analysis of traffic load effects in railway backfilled arch bridges

Tomasz Kamiński Czesław Machelski
Archives of Civil Engineering | 2022 | vol. 68 | No 2 | 243-260 | DOI: 10.24425/ace.2022.140640
Keywords field testing Finite Difference Method finite element method influence lines masonry arch bridge numerical analysis
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Abstract

The problem of the arch barrel deformation in railway backfilled arch bridges caused by their typical service loads is analysed. The main attention is paid to vertical or radial displacements of characteristic points of the arch barrel. In the study results of deflection measurements carried out on single and multi-span backfilled arch bridges made of bricks or plain concrete during passages of various typical railway vehicles are used. On the basis of such results empirical influence functions of displacements are being created. In the next step, the results are utilised to estimate bending effects within the arch. The paper includes different procedures based on measurements of displacements in various points and directions. Using empirical influence functions arbitrary virtual load cases may be also considered. In this manner the proposed methodology shows a potential to be an effective tool of comprehensive calibration of numerical models of backfilled arch bridges on the basic of field tests carried out under any live loads.
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Authors and Affiliations

Tomasz Kamiński
1
ORCID: ORCID
Czesław Machelski
1
ORCID: ORCID
  1. Wroclaw University of Science and Technology, Faculty of Civil Engineering, Wyb. Wyspianskiego 27, 50-370 Wrocław, Poland

Application of genetic algorithm for double-lap adhesive joint design

Sergei Kurennov Konstantin Barakhov Olexander Polyakov Igor Taranenko
Archive of Mechanical Engineering | 2023 | vol. 70 | No 1 | 27-42 | DOI: 10.24425/ame.2022.144074
Keywords adhesive joint genetic algorithm optimization finite difference method Goland-Reissner model
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Abstract

The problem of optimal design of symmetrical double-lap adhesive joint is considered. It is assumed that the main plate has constant thickness, while the thickness of the doublers can vary along the joint length. The optimization problem consists in finding optimal length of the joint and an optimal cross-section of the doublers, which provide minimum structural mass at given strength constraints. The classical Goland-Reissner model was used to describe the joint stress state. A corresponding system of differential equations with variable coefficients was solved using the finite difference method. Genetic optimization algorithm was used for numerical solution of the optimization problem. In this case, Fourier series were used to describe doubler thickness variation along the joint length. This solution ensures smoothness of the desired function. Two model problems were solved. It is shown that the length and optimal shape of the doubler depend on the design load.
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Bibliography

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Authors and Affiliations

Sergei Kurennov
1
ORCID: ORCID
Konstantin Barakhov
1
ORCID: ORCID
Olexander Polyakov
1
ORCID: ORCID
Igor Taranenko
1
ORCID: ORCID
  1. National Aerospace University “Kharkiv Aviation Institute”, Kharkiv, Ukraine

The mathematical characteristic of the fifth order Laplace contour filters used in digital image processing

Ireneusz Winnicki Slawomir Pietrek Janusz Jasinski Krzysztof Kroszczynski
Advances in Geodesy and Geoinformation | 2022 | vol. 71 | No 2 | e26 | DOI: 10.24425/agg.2022.141300
Keywords finite element method finite difference methods modified differential equations matrices of the fifth-order Laplace filters Taylor expansion of the transfer function
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Abstract

The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used fifth-order pixels Laplace filters including the difference schemes used to derive them (finite difference method – FDM and finite element method – FEM). The results of the research concerning third-order pixels matrices of the convolution Laplace filters used for digital processing of images were presented in our previous paper: The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters is presented byWinnicki et al. (2022). As previously, the authors focused on the mathematical properties of the Laplace filters: their transfer functions and modified differential equations (MDE). The relations between the transfer function for the differential Laplace operator and its difference operators are described and presented here in graphical form. The impact of the corner elements of the masks on the results is also discussed. A transfer function, is a function characterizing properties of the difference schemes applied to approximate differential operators. Since they are relations derived in both types of spaces (continuous and discrete), comparing them facilitates the assessment of the applied approximation method.
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Authors and Affiliations

Ireneusz Winnicki
1
ORCID: ORCID
Slawomir Pietrek
1
ORCID: ORCID
Janusz Jasinski
1
ORCID: ORCID
Krzysztof Kroszczynski
1
ORCID: ORCID
  1. Military University of Technology, Warsaw, Poland

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