Change search
ReferencesLink to record
Permanent link

Direct link
Solution to boundary-contact problems of elasticity in mathematical models of the printing-plate contact system for flexographic printing
Karlstad University, Faculty of Technology and Science.
2007 (English)Doctoral thesis, monograph (Other scientific)
Abstract [en]

Boundary-contact problems (BCPs) are studied within the frames of

classical mathematical theory of elasticity and plasticity

elaborated by Landau, Kupradze, Timoshenko, Goodier, Fichera and

many others on the basis of analysis of two- and three-dimensional

boundary value problems for linear partial differential equations.

A great attention is traditionally paid both to theoretical

investigations using variational methods and boundary singular

integral equations (Muskhelishvili) and construction of solutions

in the form that admit efficient numerical evaluation (Kupradze).

A special family of BCPs considered by Shtaerman, Vorovich,

Alblas, Nowell, and others arises within the frames of the models

of squeezing thin multilayer elastic sheets. We show that

mathematical models based on the analysis of BCPs can be also

applied to modeling of the clich\'{e}-surface printing contacts

and paper surface compressibility in flexographic printing.

The main result of this work is formulation and complete

investigation of BCPs in layered structures, which includes both

the theoretical (statement of the problems, solvability and

uniqueness) and applied parts (approximate and numerical

solutions, codes, simulation).

We elaborate a mathematical model of squeezing a thin elastic

sheet placed on a stiff base without friction by weak loads

through several openings on one of its boundary surfaces. We

formulate and consider the corresponding BCPs in two- and

three-dimensional bands, prove the existence and uniqueness of

solutions, and investigate their smoothness including the behavior

at infinity and in the vicinity of critical points. The BCP in a

two-dimensional band is reduced to a Fredholm integral equation

(IE) with a logarithmic singularity of the kernel. The theory of

logarithmic IEs developed in the study includes the analysis of

solvability and development of solution techniques when the set of

integration consists of several intervals. The IE associated with

the BCP is solved by three methods based on the use of

Fourier-Chebyshev series, matrix-algebraic determination of the

entries in the resulting infinite system matrix, and

semi-inversion. An asymptotic theory for the BCP is developed and

the solutions are obtained as asymptotic series in powers of the

characteristic small parameter.

We propose and justify a technique for the solution of BCPs and

boundary value problems with boundary conditions of mixed type

called the approximate decomposition method (ADM). The main idea

of ADM is simplifying general BCPs and reducing them to a chain

of auxiliary problems for 'shifted' Laplacian in long rectangles

or parallelepipeds and then to a sequence of iterative problems

such that each of them can be solved (explicitly) by the Fourier

method. The solution to the initial BCP is then obtained as a

limit using a contraction operator, which constitutes in

particular an independent proof of the BCP unique solvability.

We elaborate a numerical method and algorithms based on the

approximate decomposition and the computer codes and perform

comprehensive numerical analysis of the BCPs including the

simulation for problems of practical interest. A variety of

computational results are presented and discussed which form the

basis for further applications for the modeling and simulation of

printing-plate contact systems and other structures of

flexographic printing. A comparison with finite-element solution

is performed.

Place, publisher, year, edition, pages
Fakulteten för teknik- och naturvetenskap , 2007. , 151 p.
Karlstad University Studies, ISSN 1403-8099 ; 2007:8
Keyword [en]
boundary-contact problem, elasticity, integral equation, approximate decomposition
National Category
Computational Mathematics
Research subject
URN: urn:nbn:se:kau:diva-773ISBN: 978-91-7063-110-8OAI: diva2:6493
Public defence
2007-04-25, Andersalen, 11D 121, Universitetsgatan 2, 651 88 Karlstad, 13:00
Available from: 2007-04-03 Created: 2007-04-03

Open Access in DiVA

fulltext(5650 kB)1007 downloads
File information
File name FULLTEXT01.pdfFile size 5650 kBChecksum SHA-1
Type fulltextMimetype application/pdf

By organisation
Faculty of Technology and Science
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 1007 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 482 hits
ReferencesLink to record
Permanent link

Direct link