Large Deflections of Statically Loaded Coplanar Fibers Using Normal and Tangential Displacements

摘要

The increased use of fibrous materials in engineering applications makes the quantitative analysis of the mechanical behavior of a statically loaded fiber important. Through an assumed idealized fiber, the analysis of fiber deflection becomes a problem of finding the deflection of a thin circular rod subjected to a variety of static loadings. Thin flexible bars easily undergo large deflections; thus elementary strength of materials is not applicable. Even classical theory of linear elasticity because of its assumptions of small displacements is rendered useless. This report deals with two-dimensional deflections of statically loaded thin rods. The purpose is to find the deflected curve as a function of the undeflected shape and the imposed loads. The solution is in terms of normal and tangential displacements from points on the original undeflected curve. Five nonlinear differential equations are derived and solved for several loadings and end conditions on an analog computer. Results are presented in graphical form. (Author)