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A. Magnusson, M. Ristinmaa, C. Ljung (2001)
Behaviour of the extensible elastica solutionInternational Journal of Solids and Structures, 38
J. Jung, T. Kang, Kyungwoo Lee (2003)
Elliptic Integral Solutions of the Large Deflection of a Fiber Cantilever with Circular Wavy CrimpTextile Research Journal, 73
H. Ramsey (1988)
A theory of thin rods with application to helical constituent wires in cablesInternational Journal of Mechanical Sciences, 30
Extensible elastica solutions of two-dimensional deflection of crimped fiber cantilever of circular wavy crimp were obtained for one end clamped boundary under concentrated, inclined and dead tip load Fiber was also regarded as a linear elastic material. Crimp was described as a combination of semicircular arcs smoothly connected with each other having constant curvature of all the same magnitude and alternative sign. Also the inclined load direction was taken into account. The solutions were expressed as the recursive forms of integrals in two different cases, which can also be transformed to elliptic integrals respectively. Comparing the data with inextensible ones was carried out. Consequently in the solution, the normal strain of neutral axis is expressed in terms of cross-sectional area, second moment of area and normalized load parameter. Examples of the circular cross-sectioned fiber are presented. As a result, the differences of normalized load between inextensible and extensible elastica solutions when the radius ratio becomes 0.1 were maximum Λ=0.1.
Fibers and Polymers – Springer Journals
Published: Mar 1, 2005
Keywords: Extensible elastica; Dead tip load; Crimp; Recursive form; Elliptic integrals
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