Geometric analysis of fishnet model in spherical draping of orthogonal fabric sheet

To describe geometric behavior of an orthogonal fabric sheet draped over a sphere theoretically, a new method to determine the net position on the sphere with fishnet model was present by using coordinate transformation, and in-plane shear deformation of the fabrics and bending curvatures of tows were derived. Node positions in symmetric planes and node position in other region under local coordinate system were determined with constant arc length condition. The net coordinate on the sphere in global coordinate was obtained by coordinate transformation method, and in-plane shear deformation of the fabrics and bending curvatures of tows in two directions were calculated with the deformed net. The numeric examples show that draping deformation is related to neither net size, nor sphere radius when net size is far smaller than that of sphere radius. The distributions of shear deformation and bending deformation are only dependent on two spherical coordinates of the deformed nets.