# Sergey Viktorovych ChoporovZaporizhzhya National University · Faculty of Mathematics

Sergey Viktorovych Choporov

Doctor of Engineering

## About

42

Publications

6,101

Reads

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19

Citations

Citations since 2016

Introduction

My research is devoted to the following problems:
- computer-aided design
- meshing
- finite element method
- parallel computing
- machine learning

Additional affiliations

Education

September 2002 - July 2007

## Publications

Publications (42)

Context. For computer modeling of complex objects and phenomena of various nature, in practice, the numerical finite element method is often used. Its software implementation (especially for the study of new classes of problems) is a rather laborious process. The high cost of software development makes the development of new approaches to improving...

The deniable encryption algorithms productivity increasing is investigated in this paper. This investigation is relevant because of effective schemes for information and its users protection. But these algorithms is very complex and lumped. It really affects them. That's why deniable encryption algorithms have not been widespread in data processing...

In the process of designing structures from inhomogeneous materials, there is the need to build discrete models that consider the peculiarities of the geometrical shape of subdomains from different materials. The first stage in the modeling of such structures is the construction of a geometric model. In order to describe the shapes of inhomogeneous...

Context. Unauthorized access to well-protected information and telecommunication systems is a topical problem in the information security field [1]. For this problem solving, it is proposed to use the deniable encryption mechanisms, which allows its
managers to object to the existence of data, ensure their confidentiality and protect the informatio...

Свідоцтво про реєстрацію авторського права. Комп'ютерна система "Система тріангуляції двовимірних геометричних областей, заданих із застосуванням R-функцій"

This paper describes equations for buckling anal-
ysis of the circular symmetrical sandwich plates with iso-
tropic face sheets and the nonlinear elastic core material.
The total potential energy equation of circular sandwich
plate is obtained. We use the Ritz method and the method
of consecutive loading to reduce variational problem to
algebra...

Software design patterns are general reusable object-oriented solution. In software engineering, patterns have been proven to offer many benefits. Scientific software also becomes more object-oriented and the importance of design patterns increases. We present a set of design patterns for object-oriented scientific software. Particularly we develop...

When using many modern methods of automatic generation of surface meshes of implicitly defined geometric objects, the accuracy of approximation in the vicinity of surface singularities (holes, breaks, etc.) is lost. To improve surface meshes of geometric objects, various methods of smoothing are used. The existing smoothing methods are focused on t...

The finite element method is the most successful numerical method for simulation of mechanical problems. It can be viewed as a virtual machine that automates simulation taking as input geometry of a domain, meshing the domain into finite elements of the same shape and producing a system of discrete equations. Implementations of the finite element m...

Context. The present article deals with the problem of representation of solids in computer-aided design. The object of the study is a process of representation of solids in computer-aided design.
Objective. The objective of the study is the development of a hybrid representation scheme which uses implicit functions, R-operations and parametric fun...

This paper compares the analytical model of the axisymmetric bending of a circular sandwich plate with the finite element method (FEM) based numerical model. The differential equations of the bending of circular symmetrical sandwich plates with isotropic face sheets and a nonlinear elastic core material are obtained. The perturbation method of a sm...

Herein paper compares the analytical model with the FEM based numerical model of the axisymmetric bending of circular sandwich plates. Also, the paper describes equations of the circular symmetrical sandwich plates bending with isotropic face sheets and the nonlinear elastic core material. The method of constructing an analytical solution of nonlin...

This article describes the problem of unstructured quadrilateral mesh generation and smoothing. During automatic mesh generation, in general, non-convex quadrilaterals can be obtained near boundaries of non-convex regions. We suggest the smoothing algorithm that refines meshes using local minimization of an area functional. The area functional for...

Surface triangular meshing is an actual problem in the areas of computer graphics and numerical analysis. Typically, a surface is specified by a parametric equation. Meshes are being generated in a 2D parameter space and mapped to a surface. Some surfaces have very geometrically and topologically complex borders (e.g. holes, perforations, etc.). In...

Numerical simulations are now widely employed in various engineering fields. A lot of numerical simulations uses models based on partial differential equations (PDE). In the most frequently used numerical methods (e.g. the finite element method), a continuous problem is replaced by a discrete model. The discrete model approximates solution of the i...

Numerical simulations are now widely employed in various engineering fields. A lot of numerical simulations uses models based on partial differential equations (PDE). In the most frequently used numerical methods (e.g. the finite element method), a continuous problem is replaced by a discrete model. The discrete model approximates solution of the i...

In herein paper is described the problem of triangular mesh generation for complex geometrical domain. Functional approach is used for a geometrical object representation. Vladimir Rvachev's R‑functions are used also. Functional approach is based on implicit functions and logical operations (negation, conjunction and disjunction) over these functio...

In the herein paper is decried the domain specific language for the finite element analysis of thin layered plates using computer aided engineering. The main objective of the paper is development of domain specific language for thin plates and shells analysis using the Finite element method. The first-order shear deformation theory of thin layered...

Objective: to build a model of reconstruction of the coracoclavicular ligament in cases of the acromioclavicular joint injuries and to determine the position of point for the fixateur on the clavicle ensuring minimal forces in the artificial ligament. Model of the acromioclavicular joint represented as a system of interacting rigid rods was taken a...

Sandwich structures are common used in aircraft and shipbuilding, aerospace industry, civil engineering, electronics and other industries. Therefore the problem of developing effective methods for determining the stress-strain state of sandwich structural elements is urgent. There is a need summarizing the classical theories using the improved mode...

The paper describes equations of circular symmetrical sandwich plates bending for plates with isotropic outer layers and nonlinear elastic filler. Two computer models of circular sandwich plates are proposed: 1) analytical model on the basis of Maple CAS, 2) threedimensional FEM-model. We compare results of analytical model with results of numerica...

The finite element method is a powerful tool for the numerical simulation of a wide range of problems. Implementation of the finite element method in CAD systems on the basis of modern computers allows researchers to solve large scale problems. The article describes parallel algorithms for assembly of stiffness matrix and for solution of linear equ...

Nowadays engineers and researchers are faced with solving very complex problems in a mathematical modeling and design. Numerical analysis naturally finds applications in all fields of engineering and the physical sciences. The finite element method is a powerful tool for the numerical simulation of a wide range of problems. Implementation of the fi...

An algebraic approaches for movement of finite element nodes are described in the article. Proposed approaches are based on directed smoothing. Author describe some properties of proposed functions for smoothing.

The functional approach is one of the most general approaches in geometrical modeling. The functional approach describes complex geometrical objects (like engines, aircrafts, etc.) using mathematical formulas. A popular method for representation geometrical object in mathematical formulas uses implicit functions. These implicit functions can be con...

The problem of functional modeling of smooth conjugation of different elements of constructions is described in the article. Authors propose functional models of most-used types of smooth conjugations of planar objects. Examples of models of 3D bodies on the basis of developed models of planar conjugations are described in the article.

R-ФУНКЦИЙ В работе рассмотрена проблема геометрического моделирования сложных объектов на базе теории R-функций. Предложен подход к формализации описания геометрической модели на основе проблемно-ориентированного языка. Ил.: 2. Библиогр.: 9 назв. Ключевые слова: геометрическая модель, R-функция, проблемно-ориентированный язык. Постановка проблемы....

The problem of mathematical modeling of geometrical objects on the basis of R-functions is described in the article. Author propose an approach for generation of nonuniform hexahedral element meshes.

This article deals with the problem of geometrical modeling of complex objects with using Rvachev functions. We suggest an approach to discretization of received geometrical models on quadrilaterals and hexahedral element meshes. The proposed approach has been realized in CAD-system.

## Questions

Question (1)

Our team is develop software for shells FEA. In present I develop buckling analysis module for shells.

I use assembly of flat quadrilaterals with six degrees of freedom for stress-strain analysis. In local coordinates element stiffness matrix is presented by SciLab codes:

[N, dNdXi, dNdEta, jacobian, dNdX, dNdY] = isoQuad4(nodes, quads, elnum, xi, eta)

Bm = [dNdX(1) 0 0 0 0 0 dNdX(2) 0 0 0 0 0 dNdX(3) 0 0 0 0 0 dNdX(4) 0 0 0 0 0;

0 dNdY(1) 0 0 0 0 0 dNdY(2) 0 0 0 0 0 dNdY(3) 0 0 0 0 0 dNdY(4) 0 0 0 0;

dNdY(1) dNdX(1) 0 0 0 0 dNdY(2) dNdX(2) 0 0 0 0 dNdY(3) dNdX(3) 0 0 0 0 dNdY(4) dNdX(4) 0 0 0 0]; // membrane part

Bf = [0 0 0 dNdX(1) 0 0 0 0 0 dNdX(2) 0 0 0 0 0 dNdX(3) 0 0 0 0 0 dNdX(4) 0 0;

0 0 0 0 dNdY(1) 0 0 0 0 0 dNdY(2) 0 0 0 0 0 dNdY(3) 0 0 0 0 0 dNdY(4) 0;

0 0 0 dNdY(1) dNdX(1) 0 0 0 0 dNdY(2) dNdX(2) 0 0 0 0 dNdY(3) dNdX(3) 0 0 0 0 dNdY(4) dNdX(4) 0]; // bending part

Bc = [0 0 dNdX(1) N(1) 0 0 0 0 dNdX(2) N(2) 0 0 0 0 dNdX(3) N(3) 0 0 0 0 dNdX(4) N(4) 0 0;

0 0 dNdY(1) 0 N(1) 0 0 0 dNdY(2) 0 N(2) 0 0 0 dNdY(3) 0 N(3) 0 0 0 dNdY(4) 0 N(4) 0]; // shear part

local = local + thickness * Bm' * Df * Bm * jacobian * wi * wj + (thickness**3 / 12) * Bf' * Df * Bf * jacobian * wi * wj + kappa * thickness * Bc' * Dc * Bc * jacobian * wi *wj

.......

element_stiffness_in_global = T' * local * T

where T - [24x24] cosinesses matrix of transformation from global coordinates to local coordinates.

I obtain displacements and stress tensor elements that close to analytical and numerical results (ansys) for test task (cylindrical shell under external pressure).

How I can build geometric stiffness matrix for linear buckling analysis?

## Projects

Projects (4)

All Dear Colleagues–Collaborators and Their Laboratories are invited to attach to this project Their old, new, and future works or messages about the stability of plates, shells (cylindrical, spheral, conical, et cetera ... shells), and panels made of metals, composites, concrete, bricks (masonry), wood, et cetera ... in elastic, elastic-plastic and plastic states ...
... if any RSGate Member wants to be added to the project as the Collaborator (at least a co/authorship of one work about the "Stability of Plates" would be required), He needs to be a follower of a member ... , sorry ... , but in another way, the system of the project doesn't recognize Him, and He can't be added ... ,
... if any Dear Colleague–Collaborator of the Project wants to add other Colleagues, which work on the stability (at least the co/authorship of one work about the "Stability of Plates" would be required) ... - don't hesitate to invite them ...
The main rules of our Project are as follows:
1. every Colleague–Collaborator of our Project should attach at least 1 work about "Stability of Plates" or a message about it,
2. every Colleague–Collaborator of our Project should follow each other,
3. every Colleague–Collaborator of our Project should read and recommend, if only would be so possibility regarding a scientific level of researches, all works with each other,
4. every Colleague–Collaborator of our Project should comment works to each other if only would be a reason to do that - comments naturally may be critical but with respect to authors,
5. every Colleague–Collaborator of our Project should cite each other - if only would be so possibility regarding research works of each one, i.e. in every new work attached to our Project should be cited a big number, e.g. 100 works of Collaborators of our Project,
6. every Colleague–Collaborator of our Project should collaborate and write common (with the Collaborators as co-authors) papers, books, ... and other kinds of works, if only would be so possibility,
7. if any Colleague–Collaborator of our Project has a possibility to help to publish works (e.g. as a member of a scientific journal or publishing house editorial board) should give massage about it in the "goal of the project" or in "updates" in our Project,
8. if any Colleague–Collaborator knows about a conference with "Stability of Plates" as a panel or topic - He should inform us in the "goal of the project" or in "updates" in our Project ...
I hope that the above rules of our Project would help us to get success in our scientific work ... , every one of us would like that His work would be noted, read, recommended, commented, discussed, and cited ... , but somebody should do that ...
All Dear Colleagues – Collaborators are invited to be added to the Stability of Structures’s Lab regarding the rules of the Lab:
https://www.researchgate.net/lab/Stability-of-Structuress-Lab-Krzysztof-Murawski
Faithfully Yours
Krzysztof Murawski

All Dear Colleagues – Collaborators and Their Laboratories are invited to attach to this project Their old, new and future works or messages about Stability of Structures, especially: buckling, wrinkling, crimpling, crumpling ... and their energy absorption as well as about dynamic stability, slope stability .. of axially and non-axially loaded structures like columns, tubes, pipes, beams, plates, boxes, tanks, silos, pales, poles, pillars, conical shells, thin-walled structures as well as nanostructures, foams, gels.. et cetera .. made of metals, wood, plywood, bamboo, bones, composite, laminate, glass, ceramic, gypsum, concrete, rock, brick .. et cetera ..
If any RSGate Member wants to be added to the project as the Collaborator (at least a co/authorship of one work about the stability and following of 50 Members of the Project would be required), He needs to be a follower of a member of the project ... , sorry ... , but in another way, the system of the project doesn't recognize Him, and He can't be added ...
Naturally, all Dear Colleagues–Collaborators are asked to add every Colleague, which works on the stability (at least the co/authorship of one work about the stability and following of 50 Members of the Project would be required) ... - and don't hesitate to invite them ...
Dear Colleagues–Collaborators, I would like to thank You very much for Your current engagement in our Project, but let me allow to remind You what does mean "Collaboration" in the case of our Project, i.e.:
1. every Colleague–Collaborator of our Project should attach at least 1 work about "Stability of Structures" or a message about it,
2. every Colleague–Collaborator of our Project should follow each other (at least 50 Members of the Project),
3. every Colleague–Collaborator of our Project should read and recommend, if only would be so possibility regarding a scientific level of researches, all works with each other,
4. every Colleague–Collaborator of our Project should comment works to each other if only would be a reason to do that - comments naturally may be critical but with respect to authors,
5. every Colleague–Collaborator of our Project should cite each other - if only would be so possibility regarding research works of each one, i.e. in every new work attached to our Project should be cited a big number, e.g. 100 (a minimum number: 50) works of Collaborators of our Project,
6. every Colleague–Collaborator of our Project should collaborate and write common (with the Collaborators as co-authors) papers, books, ... and other kinds of works, if only would be so possibility,
7. if any Colleague–Collaborator of our Project has a possibility to help to publish works about "Stability of Structures" (e.g. as a member of a scientific journal or publishing house editorial board) should give massage about it in the "goal of the project" or in "updates" in our Project,
8. if any Colleague–Collaborator knows about a conference with "Stability of Structures" as a panel or topic - He should inform us in the "goal of the project" or in "updates" in our Project ...
I hope that the above rules of our Project would help us to get success in our scientific work ... , every one of us would like that His work would be noted, read, recommended, commented, discussed, and cited ... , but somebody should do that ...
Simultaneously I would like to note that renunciation of the rules of the Project, can be taken by other Collaborators as a kind of dishonesty, especially when a Collaborator would like to obtain a lot of "Reads", "Recommendations" and "Citations", but self doesn't take any so activity .

The goal of the project is the development of effective methods for the cloud CAE software. Particularly, suitable for cloud computing meshing techniques and FEA algorithms will be developed. Problems of using HPC in the CAE software design arise in the project. Design patterns for scientific software will be also developed.
This project continues our previous researches devoted to geometric modelling and meshing problems.