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

Hatice Kuşak Samancı,Filiz Yağcı,Ali Çalişkan

doi:10.1155/2017/7159738

Hatice Kuşak Samancı, Filiz Yağcı + Show 1 more

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https://doi.org/10.1155/2017/7159738

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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.

Highlights

The exploration of the use of parametric curves and surfaces can be viewed as the origin of Computer Aided Geometric Design (CAGD)
Scouring/Water repellent treatment we have focused on a type of para-aramid fabric and we have investigated geometrical modelling of the planar energy diffusion behaviors of the deformations on the ballistic fabric
The data of the Holditch areas that were found by using spline method after the geometric modelling study for each tip are given

Summary

Introduction

The exploration of the use of parametric curves and surfaces can be viewed as the origin of Computer Aided Geometric Design (CAGD). The major breakthroughs in CAGD were undoubtedly the theory of Bezier surfaces and Coons patches, later combined with B-spline methods. Gordon and Riesenfeld proposed curves and surfaces which use basis splines as blending functions. These are called B-spline curves and surfaces. B-spline curves are expressed as a convex combination of polygon vertex position vectors and have the variation diminishing property. In plane geometry Holditch Theorem states if a chord of fixed length is allowed to rotate inside a convex closed curve the locus of a point on the chord a distance p from one end and a distance q from the other is a closed curve whose area is less than that of the original curve by πpq. While not mentioned by Holditch, the proof of the theorem requires an assumption that the chord be short enough that the traced locus is a simple closed curve [3]

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