Abstract

Deflection analysis of yarns of a bi-axial woven composite plate under tensional loading is investigated in this article. A unit part of the warp yarn which is limited by two adjacent weft yarns is modeled by a curved beam. Using the Winkler theory of curved beams, the strain energy under the tensile loading is derived. Initial shape of yarns is chosen to be arc shaped. The deflection analysis is accomplished by making use of energy method. First, the external work of the horizontal (or tensile) force and also the vertical contacting force is evaluated. Second, using the variational method the governing equations and boundary conditions are derived and then solved to find out the displacement fields exactly. Finally, making use of the continuity of the deflection of two contacting yarns at the contacting point the vertical contacting force is obtained. It must be mentioned that shear forces and slipping of contacting yarns are disregarded here. The validation of the work is performed by comparison of results with the semi circle beam (yarn) which is found in some usual text books.