Application of Minimax Method for Calculation of Viscoelastic Material Functions and Relaxation Spectra of Polymer Melts and Solutions
Titel:
Application of Minimax Method for Calculation of Viscoelastic Material Functions and Relaxation Spectra of Polymer Melts and Solutions
Auteur:
Yanovksy, Yu. G. Basistov, Yu. A.
Verschenen in:
International journal of polymeric materials
Paginering:
Jaargang 33 (1996) nr. 3-4 pagina's 235-256
Jaar:
1996-06-01
Inhoud:
Many publications were devoted to the problem of finding methods for calculating the distribution function of relaxation time spectra Hx(τ) for viscoelastic media. Direct calculations of this function on the basis of known relations of the linear theory of viscoelasticity connected with the solution of Fredholm integral equations of the first kind involve serious difficulties. At the same time, numerical approaches to determining the function H(τ) based on the use of experimentally determined material functions were proposed in a number of recent publications. Since the accuracy of calculating the functions depends directly on the confidence of determining the primary experimental data that generally always contain errors of a statistical nature, a number of authors employ smoothing numerical methods of determining the material functions, or ones that fail to react to the appearance of rough errors. These methods include methods of regularization and maximum of entropy. However, they have a number of serious shortcomings limiting the possibilities of their successful use. In the present work, we propose to employ a different numerical method for these purposes, namely, the minimax technique. In our opinion, it is more accurate, rapid, and universal. We consider a scheme of constructing an algorithm, give examples of solving test problems showing how the algorithm functions in various extreme hypothetic situations. The results of the numerical calculations of the function H(τ) for a real object, viz. polybutadiene are based on experiments run in a rotary viscometer Rheotron of the firm Brabender.
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