Abstract
Abstract The paper presents the numerical modeling of large deflections of a flat textile structure subjected to a constant force acting on the free end. It was assumed that the examined structure is inextensible. The effect of the structure's own weight was also taken into account. In order to solve the problem, the flat textile structure was modeled using the heavy elastica theory. An important element of the analysis involves taking into account the variable bending rigidity of the examined textile structure along its length, which is often found in this type of products. The function of variable bending rigidity was assumed in advance. Numerical calculations were carried out in the Mathematica environment using the shooting method for the boundary value problem. The obtained results were verified using the finite element method.
Highlights
Deflection of cantilever beams has been the subject of numerous analyses to date
Dado and AL‐Sadder [4] presented a new technique for the large deflection analysis of nonprismatic cantilever beams based on the integrated least‐square error of the nonlinear governing differential equation in which the angle of rotation is represented by a polynomial
AL‐Sadder and AL‐Rawi [8] developed quasilinearization finite differences for the large deflection analysis of nonprismatic slender cantilever beams subjected to various types of continuous and discontinuous external variable distributed and concentrated loads in the horizontal and vertical global directions
Summary
Deflection of cantilever beams has been the subject of numerous analyses to date. A good example of a cantilever beam subjected to a vertical concentrated force at the free end can be found in the book Mechanics of materials [1], as well as in many other textbooks on physics and mechanics. Belendez et al [21] analyzed large deflections of a uniform cantilever beam under the action of a combined load consisting of a uniformly distributed load and an external vertical concentrated load applied at the free end This analysis obtained a numerical solution using an algorithm based on the Runge– Kutta–Felhberg method and compared the numerical results with experimental results. Bisshopp and Drucker [23] provided a solution for the large deflection of a cantilever beam subjected to one concentrated load, acting vertically downward at the free end of the beam, in terms of elliptic integrals These two works [22,23] are based on the fundamental Bernoulli–Euler theorem, which states that the curvature is proportional to the bending moment. The obtained results will be verified using the FE method (FEM)
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