Analytical and numerical analysis of a continuous model of a flexible suspension element under vertical loads

Abstract

Conducting static analysis to determine operational characteristics of a flexible element is a crucial stage in the design of suspension engineering structures. Considering the structural features and production requirements for computational accuracy, the use of theoretical foundations of the catenary method is adopted as a rational approach for the static analysis of suspension systems. Based on the principles of the developed algorithm and the proposed approach to modelling and calculating suspension structures, the geometric and force parameters of a supporting element, positioned within a single span and loaded by the combined action of uniformly distributed and concentrated vertical loads, have been determined. The parameters of the supporting element were established by constructing and solving systems of transcendental equations. Due to the lack of widely used modern software complexes that would allow researchers to solve systems of this type of equations, this paper demonstrates that the required results can be obtained by employing application computer software (using the method of successive approximations with a pre-defined accuracy, which ensures minimal labour and time expenditure) or by using computational algorithms of spreadsheet processors (applying the graphical-analytical method, which is labour-intensive but allows for the establishment of the uniqueness of the problem's solution). The paper presents schematic diagrams illustrating the vertical load, tensions, and sag of the supporting element, along with the results of numerical modelling (illustrated by a specific example).