Comparative assessment of the contending force and placement methods for weightless sagging cables

Abstract

Sagging elastic cables are inherently nonlinear structures due to the presence of self-weight apart from the presence of conventional physical and geometrical nonlinearities. Recently, authors have proposed a force method of weightless sagging elastic cables with linear tension–extension relations and undergoing small elastic displacements to focus explicitly on their characteristic ‘configurational’ nonlinearity. This force method is based upon the rate-type constitutive equations and third-order differential equations of motion. Existing displacement method is reconstructed here for the physically linear weightless sagging elastic cables undergoing finite elastic displacements. In place of nodal forces in force method, deformed state nodal placements are the primary variables in this placement method. Rate-type constitutive equations for two-node weightless planar sagging elastic cables are derived. The objective of the present paper is to compare and contrast these two contending methods in reference to their underlying hypotheses, analytical reach, and quantitative predictions of structural response. Possible equivalence of the proposed third-order and the popular incremental second-order differential equation of motion are explored. Theoretical significance of the present paper is critically evaluated.