Nelineární modelování průmyslových textilních výrobků

Abstract

This work focuses mainly on ways of creating a mathematical model, which could describe the mechanical behaviour of textiles accurately, because textiles are very specific in their mechanical behaviour due to their relatively low stiffness, especially flexural stiffness. These phenomena are not present in common problems solved by mathematical modelling which forms quite a challenge for this work. The specific behaviour of textiles is caused not only by the materials they consist of, but by the manufacture process as well, which is totally different when compared to metals. Because the manufacture is so specific, a significant portion of this paper focuses on a brief description of the process as well as an analysis of the influence of single parts of the manufacture on the mechanical behaviour. This chapter includes an experiment on finding mechanical data of a particular textile product which is later analysed in a specific problem. A whole chapter is dedicated to a comparison of various options of mathematical models when used for textiles with references to other authors. These models are in many cases actually tested on specific cases with their conclusions related to suitability for the case in this paper. As stated above, the main criteria are the accuracy in describing the specific mechanical behaviour of textiles, especially the negligible flexural stiffness. This work follows a previous research, which made the author choose a specific approach known as fluid structure interaction in search of a more accurate description of the problem in the previous research. The fluid structure interaction is a very special case of a mathematical model, because it combines both the fluid and solid mechanics, which are often treated separately. A large part of the paper is then focused to a brief description of the algorithms regarding both these fields of study, which are in this case interconnected. These algorithms are then used in simple problems which are programmed. Conclusions from these problems are a great benefit to the research as a focus of this paper. Finally, the particular case of a flexible water tank bladder is analysed using commercial software with student license. The problem includes measuring of the geometry of the product, using the experimentally found data for the material and using the initial conditions to achieve a comparable behaviour to the previous study. The results are then compared to the methods used in previous study as well as to an actual experiment for finding the shape of the bladder. Alas, a limited supply of the textile product allows only non-destructive experiments. Before the conclusions, the work summarizes potential use of the method researched here in another, more complicated problems, which are not verified