The static WKB solution to catenary problems with large sag and bending stiffness
type: Item
instance of: scholarly article
title: The static WKB solution to catenary problems with large sag and bending stiffness
zbMATH Open document ID: 1407.74048
DOI: 10.1155/2014/231726
author: Chanping Pan
author: YuHung Hsu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: Large sag with a bending stiffness catenary is a subject that draws attention in the realm of fatigue analysis, estimation of suspension cable sag for bridge cable hoisting, and ocean engineering of the employment of mooring systems. However, the bending stiffness is the cause of boundary layers at the anchorage of cables, thereby finding a solution of the differential equation can be extremely difficult. Previous studies have tackled this problem with the perturbation method; yet, due to the complexity of the matching process and solution finding, the method might not be an ideal solution for engineering applications. Moreover, the finite difference method and the finite element method in numerical analysis can often be ineffective because of inappropriate parameter configuration and the drastic variation of functions in the boundary layers. Therefore, this study proposed a novel bending moment expression of a large sag catenary. The expression was derived from the sag identified using bending moment equations, and a solution was found by applying the WKB method (Wentzel-Kramers-Brillouin method) to overcome the complex problem of boundary layers. Consequently, a simple solution of various mechanical properties in a cable with bending stiffness and large sag could be obtained.
Mathematics Subject Classification ID: 74K05
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 7015943
Wikidata QID: Q59064009
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/231726
OpenAlex ID: W2146891551
cites work: Q3997900
cites work: Multiple scale and singular perturbation methods
cites work: The effect of bending stiffness on inextensible cables
cites work: Bending boundary layers in a moving strip
cites work: Matched asymptotic expansions for bent and twisted rods: Applications for cable and pipeline laying
cites work: Transient Fokker-Planck-Kolmogorov equation solved with smoothed particle hydrodynamics method
description: scientific article; zbMATH DE number 7015943