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1

FPGA-based Low Latency Square Root CORDIC Algorithm

Węgrzyn Mariusz, Voytusik Stepan, Gavkalova Natalia

Journal of Telecommunications and Information Technology

|

2025

|

nr 1

21--29

EN

The coordinate rotation digital computer (CORDIC) algorithm is a popular method used in many fields of science and technology. Unfortunately, it is a time-consuming process for central processing units (CPUs) and graphics processing units (GPUs), and even for specialized digital signal processing (DSP) solutions. The CORDIC algorithm is an alternative for Newton-Raphson numerical calculation and for the FPGA based resource-expensive look-up-table (LUT) method. Various modifications of the CORDIC algorithm allow to speed up the operation of hardware in edge computing devices.With that context taken into consideration, this article presents a fast and accurate square root floating point (SQRT FP) CORDIC function which can be implemented in field programmable gate arrays (FPGAs). The proposed algorithm offers low-complexity, decent accuracy and speed, and is sufficient for digital signal processing (DSP) applications, such as digital filters, accelerators for neural networks, machine learning and computer vision applications, and intelligent robotic systems.

2

Wyznaczanie dużych ugięć płaskich struktur tekstylnych z wykorzystaniem energii potencjalnej układu

Szablewski Piotr

Przegląd Włókienniczy - Włókno, Odzież, Skóra

|

2024

|

nr 1

28--33

PL

Głównym tematem artykułu jest wykorzystanie metody energetycznej do rozwiązywania równań różniczkowych ciężkiej elastyki. Metoda ta może być z powodzeniem zastosowana do modelowania dużych ugięć, takich obiektów jak np. płaski pas tkaniny lub liniowy wyrób włókienniczy. Analiza problemu opiera się na zasadzie minimalizacji energii potencjalnej układu. Występujące w pracy zależności na energię potencjalną i energię zginania zostały podane w postaci ogólnej. Do minimalizacji energii potencjalnej wykorzystano rachunek wariacyjny. Wyniki uzyskane podczas analizy można wykorzystać np. do symulacji swobodnego układania tekstyliów płaskich, jak również zginania struktur liniowych.

EN

The main topic of the article is the use of the energy method to solve differential equations describing heavy elastica. This method can be successfully used to model large deflections such objects as a flat strip of fabric or a linear textile product. The analysis of the problem is based on the principle of minimizing the potential energy of the system. The relationships for potential energy and bending energy occurring in this work are given in general form. The calculus of variations was used to minimize the potential energy. The results obtained during the analysis can be used, for example, to simulate the free folding of flat textiles as well as the bending of linear textile structures.

3

Analysis of the Effectiveness of Using a High-Accuracy Numerical Algorithm in the Simulation of Two-Phase Flow Problems

Król Marcin

Problemy Mechatroniki : uzbrojenie, lotnictwo, inżynieria bezpieczeństwa

|

2024

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Vol. 15, Nr 3 (57)

9--30

EN

The continuous technical development of weapons and ammunition, as well as the growing requirements placed on new equipment, require the use of modern tools for their designing and testing. The analysis of the operation of powder propellant systems, which is the focus of interior ballistics, requires particularly specialised tools due to the complexity of the phenomena occurring during a shot. The development of numerical methods and the increase in the computing power of modern computers have enabled the modelling and simulation of highly complex physical problems and the development of numerical schemes with a theoretically arbitrary high order of accuracy. In this study, an attempt was made to develop a one-dimensional model of two-phase flows with a high order of solution accuracy in time, based on the finite volume method. The use of a two-phase flow model in the context of interior ballistics allows, among other things, the analysis of wave phenomena occurring during firing, which is crucial for safety reasons, especially in tank guns. The developed algorithm for solving two-phase systems was checked using recognised test problems for this type of model. The results of the work will be used to develop a numerical model to solve the main problem of interior ballistics.

PL

Ciągły rozwój techniczny broni i amunicji oraz rosnące wymagania stawiane nowym konstrukcjom wymuszają zastosowanie nowoczesnych narzędzi do ich projektowania i badania. Analiza działania prochowych układów miotających, będąca w centrum zainteresowania balistyki wewnętrznej, wymaga szczególnie wyspecjalizowanych narzędzi, ze względu na złożoność zjawisk zachodzących podczas strzału. Rozwój metod numerycznych oraz wzrost mocy obliczeniowej współczesnych komputerów umożliwił modelowanie i symulację wysoce złożonych problemów fizycznych oraz opracowanie schematów numerycznych o teoretycznie dowolnie wysokim rzędzie dokładności. W niniejszej pracy została podjęta próba opracowania jednowymiarowego modelu przepływów dwufazowych o wysokim rzędzie dokładności rozwiązania w czasie, na podstawie metody objętości skończonych. Zastosowanie modelu przepływów dwufazowych, w kontekście balistyki wewnętrznej, pozwala między innymi na analizę zjawisk falowych zachodzących podczas strzału, co jest niezwykle istotne ze względów bezpieczeństwa, w szczególności dla armat czołgowych. Opracowany algorytm rozwiązywania układów dwufazowych został sprawdzony z wykorzystaniem uznanych problemów testowych dla tego typu modeli. Wyniki pracy zostaną wykorzystane w celu opracowania modelu numerycznego służącego rozwiązaniu problemu głównego balistyki wewnętrznej.

4

The numerical methods for solving of the one-dimensional anomalous reaction-diffusion equation

Błasik Marek

Journal of Theoretical and Applied Mechanics

|

2024

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Vol. 62 nr 2

365--376

EN

This paper presents numerical methods for solving the one-dimensional fractional reaction- -diffusion equation with the fractional Caputo derivative. The proposed methods are based on transformation of the fractional differential equation to an equivalent form of a integro- -differential equation. The paper proposes an improvement of the existing implicit method, and a new explicit method. Stability and convergence tests of the methods were also conducted.

5

Possibilities of applying the extended Eyring rheological model in the technology of cement slurries used in oil drilling

Skrzypaszek Krzysztof

Journal of Geotechnology and Energy

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2024

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Vol. 41, no. 4

43--52

EN

This study explores the feasibility of implementing an extended Eyring rheological model to describe the dependence between shear stress and shear rate in cement slurries used in drilling technologies. Advances in cement slurry technology have rendered traditional mathematical models, particularly the widely used linear Bingham model recommended by the API RP 13D (American Petroleum Institute Recommended Practice 13D) standard, insufficient for accurately predicting flow resistance during pumping operations. A misalignment between the model and the actual behavior of cement slurries can result in significant errors, potentially increasing operational costs. By identifying and applying the relevant rheological model, it is possible to optimize the system’s performance, minimizing total pressure losses and thereby reducing overall drilling costs. This paper investigates the applicability of more sophisticated three-parameter rheological models, commonly utilized in other engineering disciplines, to address these challenges. Specifically, the extended Eyring model was adapted to the proprietary RheoSolution methodology developed by the Department of Drilling, Oil and Gas. To validate this approach, a series of laboratory tests were conducted on cement slurries widely used in the oil industry. The results were analyzed and compared against mathematical models recommended by the API standard. The findings confirm that the extended Eyring model offers superior accuracy in determining the rheological parameters of cement slurries for drilling applications, underscoring its potential as a robust tool for improving the efficiency of drilling operations.

6

Numerical and laboratory experimental analysis of the movement of silicone cleaning pigs through 90-degree bends pipe

Stetsiuk S.M., Doroshenko Ya.V., Filipchuk O.O., Daniv Z.V., Volovetskyi V.B.

Archives of Materials Science and Engineering

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2024

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Vol. 126, nr 2

65--77

EN

Purpose: Analysis of the stress-strain state of cylindrical cleaning pigs manufactured of hyperelastic material during their movement through the pipe bends of the pipelines, identification of maximum contact forces' points, and places of their separation from the inner wall. The effect of the dynamic friction coefficient between the pig's lateral surface and the pipeline's inner wall on the value of the maximum equivalent von Mises stresses in the pig is investigated – determination of the required pressure for the passage of the pig through pipeline bends. Design/methodology/approach: The finite element method performs numerical modelling of the pigs' movement through pipeline bends is performed. The non-linear properties of a hyperelastic pig material (a silicone compound with a hardness of 30 units on the Shore scale) are described by the potential Yeoh strain energy model. The contact interaction of the pig with the inner wall of the pipe bend is modelled by a surface-to-surface contact with dynamic friction coefficients of 0.1, 0.2, and 0.3 between them. For research, pigs with a length of 60 mm, 75 mm and 90 mm with a convex front and a concave rear end were manufactured and modelled. The experimental unit was designed and mounted from metal and glass pipes, between which pipe bends were placed with a bending angle of 90° and a bending radius of 1.5 DN. The metal pipeline has an internal diameter of 49 mm and a total length of 5.3 m, and the glass pipeline is 54 mm and 5 m, respectively. The experimental installation made of glass pipes was designed for visual observation of the dynamics of the pig movement through the glass pipeline bend and from metal – for measuring the pressure during the pig movement along the straight sections and the pipeline bend. To verify the correctness of the numerical modelling, the fully calculated deformations of the cleaning pigs in the bends of the pipeline were visualized and compared with photographs of the deformations of the pigs during their movement through the glass bends of the pipelines. Findings: The bending of the pig in the pipe bend and contact forces increase equivalent von Mises stresses in the pig. Moreover, during the movement of the pig in a pipe bend, the distribution of equivalent von Mises stresses in it, as well as its deformations, changes continuously. It depends on the stage at which it is located. Numerical modelling and experiments have established that when the pig is at the stage of movement in the middle part of the pipe bend, due to bending, its lateral surface is partially separated from the inner wall of the pipe bend. With this, on the convex side of the pipe bend, the pig is separated from the wall in the front and rear parts and on the concave side – in the middle part. This separation of the lateral surface of the pig from the inner wall of the pipe bend results in the formation of a gap and cross-flows through the pig, reducing the pressure drop on it, which can lead to its sticking. For pigs made of silicone compound with a hardness of 30 units on the Shore scale to pass pipeline bends with a bending angle of 90° and a bending radius of 1.5 DN, the pressure in the pig space shall be at least twice as high as the pressure required for the pig to move along a straight section of the pipeline. Research limitations/implications: Modelling and experimental studies were performed for pigs made of silicone compound. Therefore, subsequent studies will establish the influence of other hyperelastic materials' physical and mechanical properties on the pig movement along the pipeline bends. Practical implications: The results obtained in this study allow for determining the possibility of pigs passing through the pipeline bends of gas gathering systems at gas fields and gas networks, determining the necessary pressure for this and, if necessary, optimising the geometric shape and dimensions of the pigs passing through the pipe bends. Originality/value: The influence of the location of a solid pig made of hyperelastic material in the pipeline bend and the coefficient of dynamic friction on the stress-strain state of the pig is studied. The article contains original experimental units designed and installed to study the movement of pigs through pipeline bends.

7

Numerical Analysis of the Folding of Fabric Sheets Under Given Boundary Conditions

Szablewski Piotr

Przegląd Włókienniczy - Włókno, Odzież, Skóra

|

2023

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nr 6

36--42

EN

This paper deals with the numerical analysis of a stacking or folding of the flat textiles. This may be used for the solution of large deflection problems of flexible strips such as fabric sheets. It was assumed that during the run of bending phenomenon the flat strip of the fabric will be represented as its longitudinal section. The mathematical model of the fabric was presented as a flat deflection curve, i.e. heavy elastica. Elastica was described using the system of six first-order differential equations accompanied by a set of boundary conditions. The problem was solved by the numerical shooting method. The investigations can be used for simulation of fabric folding, stacking and for another applications from the field of textile mechanics.

PL

W artykule opisano analizę numeryczną procesu układania (składania) płaskich wyrobów tekstylnych. Przedstawiona metoda może być wykorzystana do rozwiązywania problemów dużych ugięć takich obiektów, jak np. płaski pas tkaniny. Założono, że w trakcie przebiegu zjawiska zginania płaski pas tkaniny będzie reprezentowany jako przekrój podłużny. Model matematyczny tkaniny przedstawiono w postaci płaskiej krzywej ugięcia, czyli ciężkiej elastyki. Elastyka została opisana za pomocą układu sześciu równań różniczkowych pierwszego rzędu wraz z zestawem odpowiednich warunków brzegowych. Problem rozwiązano numeryczną metodą strzału. Przeprowadzone badania i uzyskane wyniki można wykorzystać do symulacji układania tkanin oraz do innych zastosowań z zakresu mechaniki tekstyliów.

8

Water hummer in fluid networks

Osiadacz Andrzej J.

Gaz, Woda i Technika Sanitarna

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2023

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Nr 7-8

8--14

EN

The article discusses the problem of water hammer in fluid networks (gas, water supply and in pipelines transporting two-phase fluids. Mathematical models and selected computational algorithms are given.

PL

W artykule omówiono problem uderzenia hydraulicznego w sieciach płynowych (gazowych, wodociągowych oraz w rurociągach transportujących płyny dwufazowe. Podano modele matematyczne oraz wybrane algorytmy obliczeniowe.

9

Analytical and numerical analysis of damped harmonic oscillator model with nonlocal operators

Alharthi Nadiyah Hussain, Atangana Abdon, Alkahtani Badr S.

Demonstratio Mathematica

|

2023

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Vol. 56, nr 1

1--15

EN

Nonlocal operators with different kernels were used here to obtain more general harmonic oscillator models. Power law, exponential decay, and the generalized Mittag-Leffler kernels with Delta-Dirac property have been utilized in this process. The aim of this study was to introduce into the damped harmonic oscillator model nonlocalities associated with these mentioned kernels and see the effect of each one of them when computing the Bode diagram obtained from the Laplace and the Sumudu transform. For each case, we applied both the Laplace and the Sumudu transform to obtain a solution in a complex space. For each case, we obtained the Bode diagram and the phase diagram for different values of fractional orders. We presented a detailed analysis of uniqueness and an exact solution and used numerical approximation to obtain a numerical solution.

10

Influence of plunger motion profile of high pressure die casting on the casting porosity and solidification rate

Żak Katarzyna, Dańko Rafał, Żak Paweł L., Kowalczyk Wojciech

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2023

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Vol. 71, nr 5

art. no. e147339

EN

The high pressure die casting (HPDC) is a technique that allows us to produce parts for various sectors of industry. It has a great application in such sectors as automotive, energy, medicine, as the HPDC allows us to produce parts very fast and very cheaply. The HPDC casting quality depends on many parameters. The parameters among others, are cast alloy alloy metallurgy, filling system design, casting technology elements geometry and orientation, as well as, machine operation settings. In the article, different plunger motion schemes of the HPDC machine were taken into account. Analyses lead to learning about plunger motion influence on the casting porosity and solidification process run. Numerical experiments were run with the use of MAGMASoft® simulation software. Experiments were performed for industrial casting of water pump for automotive. Main parameter taken into account was maximal velocity of the plunger in the second phase. The analysis covered porosity distribution, feeding time through the gate, temperature field during whole process, solidification time. Cooling curves of the casting in chosen points were also analysed. Obtained results allow us to formulate conclusions that connect plunger motion scheme, gate solidification time and the casting wall thickness on the solidification rate and porosity of the casting.

11

Numerical investigation of noise generated by an axial fan installed in a pipeline

Romik Dawid

Vibrations in Physical Systems

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2022

|

Vol. 33, nr 1

art. no. 2022104

EN

The article presents the results of numerical calculations of noise generated by an axial fan installed in a ventilation duct with a circular cross-section. The research takes into account the installation of the axial fan due to the distance of the rotor from the curvature of the pipeline. The uRANS turbulent flow modeling methods were used in the calculations. The uRANS stands for the Navier-Stokes equation with Reynolds averaging in the version that takes into account the non-stationarity of the flow. The purpose of the work is to determine the sound power in the vicinity of the sound source. The decisive parameters affecting the noise emitted will be the length of the installation in front of and behind the rotor. The propagation of acoustic disturbances in the far field was modeled using the aeroacoustic analogy of Ffowcs-Williams and Hawkings. Based on the calculations, the directional characteristics of the sound source were determined.

12

Analiza porównawcza wybranych metod symulacji nieustalonego przepływu gazu w gazociągu

Osiadacz Andrzej J.

Gaz, Woda i Technika Sanitarna

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2022

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Nr 2

25--31

PL

Celem niniejszego artykułu jest porównanie wykorzystując prosty gazociąg dwóch różnych metod (metody charakterystyk oraz metody prostych) do symulacji nieustalonego przepływu gazu w sieciach gazowych. Założono, że nieustalony przepływ jest opisany przez układ równań quasi-liniowych hiperbolicznych. Rezultaty badań wykazały, że metoda prostych jest zdecydowanie bardziej przydatna do symulacji stanów nieustalonych.

EN

The purpose of this paper is to compare using simple gas pipeline two different numerical methods (the method of characteristics and the method of lines) which can be used for transient simulation of gas transmission networks. It was assumed that flow through the pipe is described by set of quasi-linear hyperbolic partial differentia equations. The results of investigations have shown that the method of lines is much more efficient for this purpose.

13

On the robustness of the topological derivative for Helmholtz problems and applications

Leugering Günter, Novotny Antonio André, Sokolowski Jan

Control and Cybernetics

|

2022

|

Vol. 51, No. 2

227--248

EN

We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(uɛ) with respect to a small hole Bɛ around a given point x0ɛ ∈ Bɛ ⊂ Ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole Bɛ. These parameters are either deliberately chosen in a certain range, as, e.g., the frequencies, or are known only up to some bounds. The problem arises as to whether one can obtain a uniform design using the topological gradient. We show that for 2-d and 3-d Helmholtz problems such a robust design is achievable.

14

Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation

Porwik Piotr

Archives of Control Sciences

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2022

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Vol. 32, No. 4

663--676

EN

In this paper, a class of linear Boolean functions is analyzed. The Boolean function can be represented as disjoint cubes or in the form of a truth vector. The primary purpose of this analysis is to decide whether an incompletely defined function can be extended to a complete linear form. A simple algorithm for generating all states of this function has been proposed if the Boolean function can have a full representation. The algorithm is beneficial for large functions. The proposed approach can be applied to completely and incompletely defined Boolean functions.

15

Matlab implementation of direct and indirect shooting methods to solve an optimal control problem with state constraints

Karbowski Andrzej

Journal of Automation Mobile Robotics and Intelligent Systems

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2021

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Vol. 15, No. 1

43--50

EN

The paper presents a general procedure to solve nume‐ rically optimal control problems with state constraints. It is used in the case, when the simple time discretization of the state equations and expressing the optimal cont‐ rol problem as a nonlinear mathematical programming problem is too coarse. It is based on using in turn two multiple shooting BVP approaches: direct and indirect. The paper is supplementary to the earlier author’s paper on direct and indirect shooting methods, presenting the theory underlying both approaches. The same example is considered here and brought to an end, that is two full listings of two MATLAB codes are shown.

16

Mathematical model bounds for maximizing the minimum completion time problem

Jemmali Mahdi, Alourani Abdullah

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 4

43--50

EN

This paper focuses on the parallel machine scheduling problem related to maximizing the minimum completion time. This problem affects several industrial applications. The application of this problem in real life is very impressive. This paper is based on the development of new lower bounds for the exact solution of the studied problem. It is shown in the literature that the problem is strongly NP-hard. The first developed lower bound is obtained by utilizing the probabilistic method to generate several solutions for the lower bound. The second is based on the knapsack problem with the iterative method. These numerical methods give new, better lower bounds.

17

A new numerical scheme for solving the two dimensional fractional diffusion equation

Altan Koç Dilara, Gülsu Mustafa

Journal of Applied Mathematics and Computational Mechanics

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2021

|

Vol. 20, nr 2

5--16

EN

In this study, the locally one dimensional (LOD) method is used to solve the two dimensional time fractional diffusion equation. The fractional derivative is the Caputo fractional derivative of order α. The rate of convergence of the finite difference method is presented. It is seen that this method is in agreement with the obtained numerical solutions with acceptable central processing unit time (CPU time). Error estimates, numerical and exact results are tabulated. The graphics of errors are given.

18

Zastosowanie metod numerycznych w projektowaniu rozdzielnic średniego napięcia

Kondratowicz-Kucewicz Beata, Krasuski Krzysztof, Hejduk Artur, Wojtasiewicz Grzegorz

Inżynieria Elektryczna

|

2021

|

nr 8

40--42

PL

Rozwój przemysłu oraz powiększanie obszarów miejskich powodują wzrost obciążenia sieci zasilającej i konieczność wdrożenia inteligentnych urządzeń i systemów sterowania zasilaniem odbiorców. Zmieniają się także oczekiwania odbiorców finalnych i zarówno oni, jak i dostawcy energii na całym świecie mają większą świadomość wpływu na środowisko procesów wytwarzania energii. W związku z tym sposób, w jaki się produkuje, rozdziela i zużywa energię musi również ewoluować. Aby sprostać tym wyzwaniom, sieci dystrybucyjne wyposaża się w nowoczesne, inteligentne rozwiązania, które podwyższają poziom efektywności i bezpieczeństwo użytkowania. Nowatorskie technologie, innowacyjne rozwiązania konstrukcyjne oraz nowoczesna architektura systemów lokalnej dystrybucji energii elektrycznej to cechy współczesnych sieci zasilających. Przetwarzanie energii elektrycznej, które odbywa się w węzłowych punktach sieci zasilającej zwanych stacjami elektroenergetycznym oraz rozdział energii w rozdzielnicach, są newralgiczne w całym procesie zasilania odbiorców energią elektryczną. Prawidłowe projektowanie, dobór urządzeń i aparatów dla rozdzielnic, stacji transformatorowych i nastawni może zatem zagwarantować bezpieczną pracę całej infrastruktury zasilającej, ale również zapewnić właściwą jakość dostarczanej energii elektrycznej.

19

An Introduction to the Special Issue on Numerical Techniques Meet with OR - Part II

Gürbüz Burcu, Weber Gerhard-Wilhelm

Foundations of Computing and Decision Sciences

|

2021

|

Vol. 46, No. 3

201--204

EN

The special issue: “Numerical Techniques Meet with OR” of the Foundations of Computing and Decision Sciences consists of two parts which are of the main theme of numerical techniques and their applications in multi-disciplinary areas. The first part of this special issue was already collected in the FCDS Vol. 46, issue 1. In this second part of our special issue editorial, a description of the special issue presents numerical methods which can be used as alternative techniques for Scientific Computing and led Operational Research applications in many fields for further investigation.

20

Numerical Analysis of Large Deflections of a Flat Textile Structure with Variable Bending Rigidity and Verification of Results Using Fem Simulation

Szablewski Piotr

Autex Research Journal

|

2021

|

Vol. 21, no. 1

108--114

EN

The paper presents the numerical modeling of large deflections of a flat textile structure subjected to a constant force acting on the free end. It was assumed that the examined structure is inextensible. The effect of the structure's own weight was also taken into account. In order to solve the problem, the flat textile structure was modeled using the heavy elastica theory. An important element of the analysis involves taking into account the variable bending rigidity of the examined textile structure along its length, which is often found in this type of products. The function of variable bending rigidity was assumed in advance. Numerical calculations were carried out in the Mathematica environment using the shooting method for the boundary value problem. The obtained results were verified using the finite element method.