Geometric analysis of fishnet model in spherical draping of orthogonal fabric sheet
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摘要: 为了从理论上表征平面正交织物球面成型后的几何特征, 提出基于坐标变换求解渔网模型的新方法, 确定单层正交平面织物在球面上铺覆成型后的网格位置、 织物剪切变形和纱线弯曲变形。依据弧长不变条件确定方形织物完全包覆球面后的对称面上的网格位置和局部坐标系下中间网格的位置, 利用坐标变换获得中间网格在整体坐标系成型球面上的坐标位置; 根据变形前后的网格形状确定织物面内剪切变形和两个方向纱线的弯曲曲率, 为织物的球面成型性评价提供几何参数。通过实例证明了当网格尺寸远小于球体半径时铺覆变形程度与网格 尺寸无关, 也与球体半径无关。铺覆后织物的剪切变形和纱线弯曲变形分布只与织物在球面上的球坐标位置有关。Abstract: 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.
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Keywords:
- draping /
- formability /
- textile /
- preform /
- coordinate transformation
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