scholarly journals ONE FEATURE OF THE CONSTRUCTIVE SOLUTIONS OF THE LATTICE GIRDER

2018 ◽  
Vol 14 (4) ◽  
pp. 90-97
Author(s):  
Mikhail N. Kirsanov
Keyword(s):  
Asymptotic Behavior ◽  
Analytical Form ◽  
Span Length ◽  
Induction Method ◽  
Particular Solutions ◽  
Computer Math ◽  
Lattice Girder

The problem of the deflection of a planar symmetric statically determinable truss with a double lattice depending on the number of panels was solved in an analytical form. The angle of inclination of the ascending and descending rods of the truss is different. A load is applied to the truss, evenly distributed over the nodes of the lower chord. Special operators of the Maple computer math system and the induction method were used to generalize individual particular solutions to an arbitrary case. Formulas are obtained for the forces the most compressed and stretched truss rods. Cases of kinematic variability of the structure are revealed. A picture of the possible speeds of truss nodes in these cases is constructed. The asymptotic behavior of the deflection is found with a large number of panels and a fixed span length. The deflection was determined by the formula of Maxwell – Mohr.

Analytical Calculation of Deformations and Kinematic Analysis of a Flat Truss with an Arbitrary Number of Panels

2021 ◽  
pp. 113-122
Author(s):  
М. Н. Кирсанов ◽  
О. В. Воробьев
Keyword(s):  
Kinematic Analysis ◽  
Arbitrary Number ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Analytical Calculation ◽  
Middle Part ◽  
Asymptotic Approximations ◽  
Induction Method ◽  
Particular Solutions

Постановка задачи. Разыскиваются аналитические зависимости прогиба и смещения опоры плоской фермы решетчатого вида от числа панелей. Ферма имеет сдвоенную решетку, прямолинейный нижний и приподнятый в средней части верхний пояс. Результаты. Для двух видов нагружения по формуле Максвелла-Мора получены аналитические зависимости прогибов конструкции от нагрузки, размеров и числа панелей. Для обобщения серии частных решений с различным числом панелей ферм на произвольный случай использован метод индукции и аналитические возможности системы компьютерной математики Maple. Для некоторых решений получены асимптотические приближения. Показано распределение усилий в элементах фермы. Выводы. Полученные формулы могут быть использованы в задачах оптимизации и как тестовые для оценки приближенных численных решений. Выявлены случаи геометрической изменяемости фермы при числе панелей, кратном трем. Приведен алгоритм выявления соответствующего распределения возможных скоростей шарниров. Statement of the problem. Analytical dependences of the deflection and displacement of the support of a flat lattice truss on the number of panels are being sought. The truss has a double lattice, a rectilinear lower belt and an upper belt raised in the middle part. Results. For two types of loading, according to the Maxwell-Mohr formula, analytical dependences of the deflections of the structure on the load, dimensions and number of panels are obtained. To generalize a series of particular solutions for trusses with different numbers of panels for an arbitrary case, the induction method and the analytical capabilities of the Maple computer mathematics system were used. For some solutions, asymptotic approximations are obtained. The distribution of forces in the rods of the structure is shown. Conclusions. The obtained formulas can be used in optimization problems and as test ones for evaluating approximate numerical solutions. Cases of geometric variability of the truss with the number of panels being a multiple of three are revealed. An algorithm for identifying the corresponding distribution of possible velocities of the joints is presented.

scholarly journals ANALYTICAL SOLUTION OF THE FREQUENCY OF THE LOAD OSCILLATION AT AN ARBITRARY GIRDER NODE IN THE SYSTEM MAPLE

2019 ◽  
pp. 3-3
Author(s):  
Mikhail N. Kirsanov ◽  
Dmitriy V. Tinkov
Keyword(s):  
Analytical Solution ◽  
Arbitrary Number ◽  
Analytical Form ◽  
Labor Costs ◽  
Induction Method ◽  
Regular Type ◽  
Final Formula ◽  
The Common ◽  
Two Stages ◽  
Elastic Lattice

Introduction. We study the oscillations of a massive load on a planar statically definable symmetric truss of a regular type with parallel belts. Truss weight is not included. Free vertical oscillations are considered. The stiffness of the truss rods is assumed to be the same, the deformations are elastic. Lattice of the truss is double with descending braces and racks. New in the formulation and solution of the problem is the analytical form of the solution, which makes it possible in practice to easily evaluate the frequency characteristics of the structure depending on an arbitrary number of truss panels and the location of the load. Materials and methods. The operators and methods of the system of computer mathematics Maple are used. To determine the forces in the rods, the knotting method is used. The common terms of the sequence of coefficients of solutions for different numbers of panels are obtained from solving linear homogeneous recurrent equations of various order, obtained by special operators of the Maple system. Dependence on two arbitrary natural parameters is revealed in two stages. First, solutions for fixed load positions are found, then these solutions are summarized into one final formula for frequency. Results. By a series of individual solutions to the problem of load oscillation using the double induction method, it was possible to find common members of all sequences. The solution is polynomial in both natural parameters. Graphs constructed for particular cases, showed the adequacy of the approach. The discontinuous non-monotonic nature of the intermittent change depending on the number of truss panels and some other features of the solution are noted. Conclusions. It is shown that the induction method, previously applicable mainly to statics problems with one parameter (number of truss panels), is fully operational to the problems of the oscillations of system with two natural parameters. It should be noted that significant labor costs and a significant increase in the time symbolic transformations in such tasks

scholarly journals Analytical calculation of the deflection of an externally statically indeterminate lattice truss

2019 ◽  
Vol 265 ◽  
pp. 05027
Author(s):  
Mikhail Kirsanov ◽  
Evgeny Komerzan ◽  
Olesya Sviridenko
Keyword(s):  
Arbitrary Number ◽  
Analytical Calculation ◽  
Linear Recurrence ◽  
System Of Equations ◽  
Induction Method ◽  
Particular Solutions ◽  
Recurrence Equations ◽  
Nonmonotonic Character

A scheme of a statically definable truss with additional supports is proposed. Derive formulas for the dependence of the deflection of the truss against the number of panels for three types of symmetrical loads. It is shown that for definite numbers of panels the determinant of the system of equations for the equilibrium of nodes degenerates. This indicates an instant changeability of the structure. To generalize particular solutions to an arbitrary number of panels, the induction method is applied. For this purpose, in the computer mathematics system Maple linear recurrence equations are constructed for the terms of a sequence of coefficients from individual solutions. The graphs of the dependences obtained indicate a nonmonotonic character of the solutions found and the possibility of optimizing the design by choosing the number of panels.

scholarly journals Analytical calculation of the combined suspension truss

2019 ◽  
Vol 265 ◽  
pp. 05025
Author(s):  
Mikhail Kirsanov ◽  
Dmitriy Tinkov ◽  
Oleh Boiko
Keyword(s):  
Analytical Calculation ◽  
Analytical Dependence ◽  
System Of Equations ◽  
Vertical Load ◽  
Induction Method ◽  
Uniform Loading ◽  
Number Of Solutions ◽  
Particular Solutions ◽  
Common Term ◽  
Cutting Out

An algorithm is given for obtaining the formula for the dependence of the deflection of a regular planar truss of an arched type with a suspended lower belt on the number of panels. The cases of uniform loading of the nodes of the upper and lower belts by a vertical load are considered. To generalize a number of solutions obtained in the system of computer mathematics Maple to an arbitrary case, an induction method was applied. For this purpose, for a sequence of coefficients of the particular solutions found, a common term is determined which is a solution of the recurrence equation. The deflection was determined with the help of Mohr's integral, which depends on the forces in the rods. Forces in a statically determinate construction were performed by cutting out nodes from the solution of a system of equations written in a matrix form. The analytical dependence of displacement of the mobile support on the number of panels is found.

On the influence of specimen thickness in TEM images of super-conducting vortices

1996 ◽  
Vol 54 ◽  
pp. 724-725
Author(s):  
J. Bonevich ◽  
D. Capacci ◽  
G. Pozzi ◽  
K. Harada ◽  
H. Kasai ◽  
...  
Keyword(s):  
Flux Line ◽  
Analytical Form ◽  
Realistic Model ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Flux Tubes ◽  
Analytical Expression ◽  
Flux Lines ◽  
Normal Core ◽  
Two Parameters

The successful observation of superconducting flux lines (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz and electron holography methods has presented several problems concerning the interpretation of the experimental results. The first approach has been to model the fluxon as a bundle of flux tubes perpendicular to the specimen surface (for which the electron optical phase shift has been found in analytical form) with a magnetic flux distribution given by the London model, which corresponds to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth, completely characterizes the superconducting fluxon. The obtained results have shown that the most relevant features of the experimental data are well interpreted by this model. However, Clem has proposed another more realistic model for the fluxon core that removes the unphysical limitation of the infinitely small normal core and has the advantage of being described by an analytical expression depending on two parameters (the coherence length and the London depth).

SH-Wave Scattering From the Interface Defect

2017 ◽  
Vol 5 (1) ◽  
pp. 45-50
Author(s):  
Myron Voytko ◽  
◽  
Yaroslav Kulynych ◽  
Dozyslav Kuryliak
Keyword(s):  
Half Space ◽  
Wave Diffraction ◽  
Scattered Field ◽  
Wave Scattering ◽  
Elastic Layer ◽  
Analytical Form ◽  
Structure Parameters ◽  
Sh Wave ◽  
Interface Defect ◽  
Hopf Method

The problem of the elastic SH-wave diffraction from the semi-infinite interface defect in the rigid junction of the elastic layer and the half-space is solved. The defect is modeled by the impedance surface. The solution is obtained by the Wiener- Hopf method. The dependences of the scattered field on the structure parameters are presented in analytical form. Verifica¬tion of the obtained solution is presented.

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