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

Abstract

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 conc ntrated 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 ext ensible elastica problems.