5. Admissible
values for the shape parameters
Values
of the shape parameters A and B in Equation (5) cannot be
arbitrary. In other words, these parameters cannot take the full range of
values. Below there is a precise definition of the interval of admissible
values of A and B. The existence of immovable supporting plane,
as in Figure 1, leads to the geometrical condition 
for 
. Besides, from the inextensibility we have
that 
for . Take into consideration
dimensionless form of the variables and 
, we have
From
hole area of a and b we choose only such values so that the
inequalities (13) are satisfied. These inequalities have been calculated
numerically. For example the extreme values of a and b are as
follows:
. Admissible area of a
and b have been show in Figure 8.
After
analyzing the states of equilibrium it should be remembered that values of a
and b should be from admissible area which is presented in
Figure 8. Admissible are of a and b should be superimposed
on the graphs from Figures 6-7.
6. Conclusions
Above-mentioned
method of analyzing of a flat textile structure loaded by compression force and
deadweight has been presented for the bending curve given by formula (5).
Thanks to different parameters A and B we can simulate different
shapes of bending curve (such as in the reality). Similarly, it can be carried
out for different shapes of bending curve. For solving the problem the Ritz
energetic method has been applied. Similar way to solving of the problem we can
find in work [5] for the one-dimension problem. Due to nonlinearity numerical
methods have been applied. These methods can be used without any problem for
multi-dimension tasks with more than two shape parameters.
References
- Dym
C.L., Stability Theory and Its Applications to Structural Mechanics,
Leyden Noordhoff Int. Publishing, 1974.
- Naleszkiewicz
J., Problems of Elastic Stability, PWN, Warsaw, 1958.
- Forray
M.J., Variational Calculus in Science and Engineering, McGraw-Hill, New York, 1968.
- Timoshenko
S.P., Gere J.M., Theory of Elastic Stability, McGraw-Hill, New York, 1961.
- Szablewski
P., Analysis of the Stability of a Flat Textile Structure, AUTEX Research
Journal, Vol.6, No.4, 2006, p. 204-215.
About
the Author:
The
author is associated with Technical University of Łdź, Department of
Technical Mechanics and Informatics, Lodz, Poland.
To read more articles on Textile,
Industry,
Technical
Textile, Dyes
& Chemicals, Machinery,
Fashion,
Apparel,
Technology,
Retail,
Leather,
Footwear & Jewellery, Software
and General
please visit http://articles.fibre2fashion.com
To promote your company, product and services via promotional article, follow
this link: http://www.fibre2fashion.com/services/article-writing-service/content-promotion-services.asp
