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International Journal of Engineering Mathematics
Volume 2017, Article ID 7159738, 8 pages
https://doi.org/10.1155/2017/7159738
Research Article

Modelling of the Deformation Diffusion Areas on a Para-Aramid Fabric with B-Spline Curves

1Department of Mathematics, Bitlis Eren University, Bitlis, Turkey
2Department of Mathematics, Uludağ University, Bursa, Turkey
3Department of Mathematics, Ege University, İzmir, Turkey

Correspondence should be addressed to Hatice Kuşak Samancı; moc.oohay@sumat_hatice

Received 6 June 2016; Revised 29 August 2016; Accepted 15 September 2016; Published 20 February 2017

Academic Editor: Giuseppe Carbone

Copyright © 2017 Hatice Kuşak Samancı et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The geometrical modelling of the planar energy diffusion behaviors of the deformations on a para-aramid fabric has been performed. In the application process of the study, in the experimental period, drop test with bullets of different weights has been applied. The B-spline curve-generating technique has been used in the study. This is an efficient method for geometrical modelling of the deformation diffusion areas formed after the drop test. Proper control points have been chosen to be able to draw the borders of the diffusion areas on the fabric which is deformed, and then the De Casteljau and De Boor algorithms have been used. The Holditch area calculation according to the beams taken at certain fixed lengths has been performed for the B-spline border curve obtained as a closed form. After the calculations, it has been determined that the diffusion area where the bullet with pointed end was dropped on a para-aramid fabric is bigger and the diffusion area where the bullet with rounded end was dropped is smaller when compared with the areas where other bullets with different ends were dropped.