scholarly journals Calculation of plates in a geometrically nonlinear setting with the use of generalized equations of finite difference method

2018 ◽  
Vol 196 ◽  
pp. 01024 ◽  
Author(s):  
Natalia Uvarova ◽  
Radek Gabbasov
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Geometrically Nonlinear ◽  
Generalized Equations ◽  
Nonlinear Formulation ◽  
First Derivative ◽  
Equation Solving ◽  
Flexible Plates ◽  
Minimum Number ◽  
The Right

The article proposes a numerical method and an algorithm for analysis rectangular flexible plates in a geometrically nonlinear formulation. The generalized equations of the method of finite differences (MD) are used to solve the problem within the integrable region taking into account the discontinuities of the desired function, its first derivative and the right part of the original differential equation. Solving differential equations of the problem, composed with respect to the desired functions of deflection and stress are reduced to the 4th differential equations of the second order, which are solved numerically. As an example, a square plate loaded with a uniformly distributed load is considered. The results of the calculation with a minimum number of partitions are compared with the known analytical solution of A. S. Volmir [1] and indicate the possibility of using the numerical method for solving problems in a nonlinear formulation.

scholarly journals NUMERICAL METHOD OF CALCULATION OF ROUND PLATES IN A GEOMETRICALLY NONLINEAR STATEMENT

Vestnik MGSU ◽  
2017 ◽  
pp. 631-635
Author(s):  
Radek Fatykhovich Gabbasov ◽  
Natalia Borisovna Uvarova
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Geometrically Nonlinear ◽  
Method Of Calculation ◽  
First Order ◽  
Nonlinear Statement ◽  
Minimum Number ◽  
Dead Loading ◽  
The Right ◽  
The Given

The article considers the axisymmetric problem about the calculation of round plates with dead loading in a geometrically nonlinear system. To solve the problem some generalized equations of finite difference method (FMD) are needed that allow to solve tasks within intergrable scope taking into account discontinuities of the required function, its first-order derivative and the right-hand side of the primitive differential equation. Resolvent differential equations of the question comprised fractionally the required function of the inflection and stresses are reduced to four differential equations, two of which are linear of the first-order and two are nonlinear of the second order. The obtained system of differential equations is solved numerically. The proposed method is shown with the example of calculation of a round plate; the given data are taken from work [1]. The calculation data with the minimum number of partitions are compared to the known solution of A.S. Vol’mir [1] and they indicate the possibility of using a numerical method for handling the problem in nonlinear statement.

scholarly journals A numerical method for friction problems with multiple contacts

1996 ◽  
Vol 37 (3) ◽  
pp. 288-308 ◽  
Author(s):  
David E. Stewart
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Static Friction ◽  
Previous Method ◽  
High Order Accuracy ◽  
Order Accuracy ◽  
First Order ◽  
Multiple Contacts ◽  
Contact Surfaces ◽  
The Right

AbstractFriction problems involving “dry” or “static” friction can be difficult to solve numerically due to the existence of discontinuities in the differential equations appearing in the right-hand side. Conventional methods only give first-order accuracy at best; some methods based on stiff solvers can obtain high order accuracy. The previous method of the author [16] is extended to deal with friction problems involving multiple contact surfaces.

scholarly journals Vibrations of dam–plate of a hydro-technical structure under seismic load

2021 ◽  
Vol 264 ◽  
pp. 05057
Author(s):  
A Tukhtaboev ◽  
Sergey Leonov ◽  
Fozil Turaev ◽  
Kudrat Ruzmetov
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Numerical Method ◽  
Quadrature Formulas ◽  
Seismic Load ◽  
Geometrically Nonlinear ◽  
Material Parameters ◽  
Weakly Singular ◽  
Technical Structure ◽  
Nonlinear Statement

In present paper, the problem of the vibration of a viscoelastic dam-plate of a hydro-technical structure is investigated, based on the Kirchhoff-Love hypothesis in the geometrically nonlinear statement. This problem is reduced to a system of nonlinear ordinary integro-differential equations by using the Bubnov-Galerkin method. The resulting system with a weakly-singular Koltunov-Rzhanitsyn kernel is solved using a numerical method based on quadrature formulas. The behavior of the viscoelastic dam-plate of hydro-technical structure is studied for the wide ranges of physical, mechanical, and geometrical material parameters.

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

Filippov solutions of vector Dirichlet problems

2020 ◽  
Vol 70 (2) ◽  
pp. 401-416
Author(s):  
Hana Machů
Keyword(s):  
Differential Equations ◽  
The State ◽  
State Variables ◽  
Dirichlet Problems ◽  
Filippov Solutions ◽  
Natural Notion ◽  
Growth Restrictions ◽  
The One ◽  
The Right ◽  
Effective Growth

Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.

An implicit multistep numerical method for real-time simulation of stiff systems

SIMULATION ◽  
2021 ◽  
pp. 003754972110216
Author(s):  
Zhang Lei ◽  
Li Jie ◽  
Wang Menglu ◽  
Liu Mengya
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Real Time ◽  
Physical System ◽  
Physical Models ◽  
Stiff Systems ◽  
Real Time Simulation ◽  
Stiff Ordinary Differential Equations ◽  
Root Finding ◽  
Time Simulation

Simulating a physical system in real-time is widely used in equipment design, test, and validation. Though an implicit multistep numerical method excels at solving physical models that are usually composed of stiff ordinary differential equations, it is not suitable for real-time simulation because of state discontinuity and massive iterations for root finding. Thus, a method based on the backward differential formula is presented. It divides the main fixed step of real-time simulation into limited minor steps according to computing cost and accuracy demand. By analyzing and testing its capability, this method shows advantage and efficiency in real-time simulation, especially when the system contains stiff equations. A simulation application will have more flexibility while using this method.

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