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Elliptic Integral Solutions of the Large Deflection of a Fiber Cantilever with Circular Wavy Crimp###

机译:圆形波浪压接的纤维悬臂梁大挠度的椭圆积分解###

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摘要

Solutions for the two-dimensional deflection of a crimped fiber cantilever with circular wavy crimp are obtained for a one-end clamped boundary under a concentrated inclined load direction. The fiber is regarded as a linear elastic material, and crimp is described as a combination of semicircular arcs smoothly connected with each other with a constant curvature of the same magnitude and alternative sign. The inclined load direction is also taken into account. Consequently, the solutions are expressed as the recursive forms of elliptic integrals transformed in two different ways. These solutions contain two different transformed parameters involved with material and geometric parameters. We validate the accuracy of our model by comparing it with former results for one-element straight and semicircular beams, calculate a two-element solution, and obtain the shapes. Our results have both technical and mathematical significance. They are directly applicable to cable applications, reinforcing fibers in textile composites, and wavy fabrics or yarns. Our mathematical techniques also enable us to consider three further research topics―the multiplicity of solutions, stability evaluations of our model, and extensible elastica problems.
机译:对于在集中的倾斜载荷方向下的一端夹持边界,获得了具有圆形波浪形卷曲的卷曲纤维悬臂的二维挠度解。纤维被视为线性弹性材料,压接被描述为半圆弧的组合,这些圆弧彼此平滑地连接,并具有相同幅度和其他符号的恒定曲率。还考虑了倾斜的载荷方向。因此,解表示为以两种不同方式转换的椭圆积分的递归形式。这些解决方案包含涉及材料和几何参数的两个不同的转换参数。通过将其与一元直梁和半圆梁的先前结果进行比较,验证模型的准确性,计算二元解,并获得形状。我们的结果具有技术和数学意义。它们直接适用于电缆应用,纺织复合材料中的增强纤维以及波浪形织物或纱线。我们的数学技术还使我们能够考虑三个进一步的研究主题:解的多样性,模型的稳定性评估以及可扩展的弹性问题。

著录项

  • 来源
    《Textile Research Journal》 |2003年第1期|p.47-54|共8页
  • 作者单位

    Department of Material Engineering, Seoul National University, Seoul 151-742, South Korea;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 纺织工业、染整工业;
  • 关键词

  • 入库时间 2022-08-18 00:11:15

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