scholarly journals A Symmetric Three-Layer Plate with Two Coaxial Cracks under Pure Bending

2021 ◽  
Vol 11 (6) ◽  
pp. 2859
Author(s):  
Mykhaylo Delyavskyy ◽  
Viktor Opanasovych ◽  
Roman Seliverstov ◽  
Oksana Bilash
Keyword(s):  
Strain State ◽  
Geometrical Parameters ◽  
Bending Moments ◽  
Algebraic Equations ◽  
Optimum Ratio ◽  
Pure Bending ◽  
Mechanical Quadrature ◽  
Linear Algebraic Equations ◽  
Crack Tips ◽  
Mechanical Quadrature Method

The purpose of this research was to investigate the effect of mechanical features and geometrical parameters on the stress–strain state of a cracked layered plate under pure bending (bending moments are uniformly distributed at infinity). The sixth-order bending problem of an infinite, symmetric, three-layer plate with two coaxial through cracks is considered under the assumption of no crack closure. By using complex potentials and methods of the theory of functions of a complex variable, the solution to the problem was obtained in the form of a singular integral equation. It is reduced to the system of linear algebraic equations and solved in a numerical manner by the mechanical quadrature method. The distributions of stresses and bending moments near the crack tips are shown. Numerical results are presented as graphical dependences of the reduced moment intensity factor on various problem parameters. In this particular case, the optimum ratio of layer thicknesses is determined.

Electromagnetic field of the circular magnetic source in biconical section

2020 ◽  
Vol 2020 (48) ◽  
pp. 5-10
Author(s):  
O.M. Sharabura ◽  
◽  
D.B. Kuryliak ◽  
Keyword(s):  
Field Pattern ◽  
Geometrical Parameters ◽  
Algebraic Equations ◽  
Axially Symmetric ◽  
Reduction Procedure ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Regularization Techniques ◽  
Far Field Pattern ◽  
Analytical Regularization

The problem of axially-symmetric electromagnetic wave diffraction from the perfectly conducting biconical scatterer formed by the finite cone placed in the semi-infinite conical region is solved rigorously using the mode-matching and analytical regularization techniques. The problem is reduced to the infinite systems of linear algebraic equations (ISLAE) of the second kind. The obtained equations admit the reduction procedure and can be solved with a given accuracy for any geometrical parameters and frequency. The numerical examples of the solution are presented. The analysis of the source location influences on the far-field pattern for different geometrical parameters of the bicone is carried out.

scholarly journals PLIENINIŲ TINKLINIŲ ARKINIŲ PĖSČIŲJŲ TILTŲ TINKLELIO LYGINAMOJI ANALIZĖ / COMPARATIVE NET ANALYSIS OF THE PEDESTRIAN STEEL NETWORK ARCH BRIDGES

2018 ◽  
Vol 10 (0) ◽  
pp. 1-6
Author(s):  
Sigutė Žilėnaitė
Keyword(s):  
21St Century ◽  
Strain State ◽  
Geometric Analysis ◽  
Search Pattern ◽  
Geometrical Parameters ◽  
Traffic Network ◽  
Bending Moments ◽  
Structural Form ◽  
Arch Bridges ◽  
Buckling Length

Network arch bridges as a new structural form were invented in the middle of 21st century, describing the row of hangers which intersect each other two or more times. The bending moments in the arch and grinder are approximately ten times smaller due to network hangers arrangement. Additionally, an arch buckling length is smaller comparing with traditional vertical hangers, due to the slope of hangers in the network. However, the search pattern of the net rational angle, other composite parameters, and strain-strain state includes only automotive and rail traffic network arched bridges. This paper presents a geometric analysis of the behaviour of network arch pedestrian steel bridges and geometrical parameters of hangers net. Santrauka Tinkliniai arkiniai tiltai – tai XX a. viduryje atsiradusi nauja konstrukcinė tilto forma, apibūdinama mažiausiai dviem eilėmis pasvirusių pakabų, prasilenkiančių viena su kita. Dėl kryžminio pakabų tinklelio arkoje ir standumo sijoje pasireiškia apie 10 kartų mažesni lenkimo momentai nei tradiciniame arkiniame tilte su vertikaliomis pakabomis. Taip pat dėl pasvirusių pakabų tokių tiltų arkos skaičiuojamasis ilgis yra mažesnis nei tradicinių. Pažymėtina, kad tinklelio racionalaus kampo bei kitų komponuojamųjų parametrų paieškos spektras daugelyje tyrimų apima tik automobilių ar geležinkelio eismo paskirties tinklinius arkinius tiltus. Šiame straipsnyje pateikta plieninių tinklinių arkinių pėsčiųjų tiltų elgsenos analizė ir pakabų tinklo geometrinių parametrų paieška.

Determination of the Stress State of the Layer with a Cylindrical Elastic Inclusion

2019 ◽  
Vol 968 ◽  
pp. 413-420
Author(s):  
Vitaly Yu. Miroshnikov ◽  
Alla V. Medvedeva ◽  
Sergei V. Oleshkevich
Keyword(s):  
Stress State ◽  
Reduction Method ◽  
Elastic Inclusion ◽  
Fourier Method ◽  
Theory Of Elasticity ◽  
Geometrical Parameters ◽  
Spatial Problem ◽  
Algebraic Equations ◽  
Linear Algebraic Equations

A spatial problem of the theory of elasticity for the layer with an infinite round cylindrical inclusion is investigated. At the boundaries of the layer, displacements are given. The cylindrical elastic inclusion is rigidly coupled with the layer and their boundary surfaces do not intersect. The solution to the spatial problem is obtained by the generalized Fourier method, with regard to the Lamé system of equations. The obtained infinite systems of linear algebraic equations are solved by a reduction method. As a result, the values ​​of displacements and stresses in the elastic body are determined. A comparative analysis of the stress state for different geometrical parameters is carried out, and a comparison is made with the stress state in the layer with a cylindrical cavity.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

scholarly journals Exact statistical solution for the hopping transport of trapped charge via finite Markov jump processes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrey A. Pil’nik ◽  
Andrey A. Chernov ◽  
Damir R. Islamov
Keyword(s):  
Charge Transport ◽  
Thin Layers ◽  
Jump Processes ◽  
Dielectric Films ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Statistical Solution ◽  
Linear Algebraic Equations ◽  
Special Cases ◽  
Thin Dielectric Films

AbstractIn this study, we developed a discrete theory of the charge transport in thin dielectric films by trapped electrons or holes, that is applicable both for the case of countable and a large number of traps. It was shown that Shockley–Read–Hall-like transport equations, which describe the 1D transport through dielectric layers, might incorrectly describe the charge flow through ultra-thin layers with a countable number of traps, taking into account the injection from and extraction to electrodes (contacts). A comparison with other theoretical models shows a good agreement. The developed model can be applied to one-, two- and three-dimensional systems. The model, formulated in a system of linear algebraic equations, can be implemented in the computational code using different optimized libraries. We demonstrated that analytical solutions can be found for stationary cases for any trap distribution and for the dynamics of system evolution for special cases. These solutions can be used to test the code and for studying the charge transport properties of thin dielectric films.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

scholarly journals Optimal Random Packing of Spheres and Extremal Effective Conductivity

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1063
Author(s):  
Vladimir Mityushev ◽  
Zhanat Zhunussova
Keyword(s):  
Effective Conductivity ◽  
Dimensional Space ◽  
Elementary Function ◽  
Voronoi Tessellation ◽  
Random Packing ◽  
Periodicity Cell ◽  
Algebraic Equations ◽  
Optimal Packing ◽  
Linear Algebraic Equations ◽  
Initial Location

A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) of composites with ideally conducting spherical inclusions is established. The location of inclusions of the optimal-design problem yields the optimal packing of inclusions. The geometrical-packing and physical-conductivity problems are stated in a periodic toroidal d-dimensional space with an arbitrarily fixed number n of nonoverlapping spheres per periodicity cell. Energy E depends on Voronoi tessellation (Delaunay graph) associated with the centers of spheres ak (k=1,2,…,n). All Delaunay graphs are divided into classes of isomorphic periodic graphs. For any fixed n, the number of such classes is finite. Energy E is estimated in the framework of structural approximations and reduced to the study of an elementary function of n variables. The minimum of E over locations of spheres is attained at the optimal packing within a fixed class of graphs. The optimal-packing location is unique within a fixed class up to translations and can be found from linear algebraic equations. Such an approach is useful for random optimal packing where an initial location of balls is randomly chosen; hence, a class of graphs is fixed and can dynamically change following prescribed packing rules. A finite algorithm for any fixed n is constructed to determine the optimal random packing of spheres in Rd.

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