Computational methods for the zero-stress state and the pre-stress state of tensile cable-net structures

Abstract

This paper proposes an extended design concept and mechanical description for cable-net structures, including 10 states and 15 procedures which are defined according to their physical nature and analytical capabilities. In the pre-stress release analysis, an iterative computational method is developed for the inverse evaluation from the equilibrium state to the zero-stress state, which adopts the least norm least square approach (LNLS) to the compatibility equation because of the indeterminate property of a cable-net structure. In the pre-tensioning development analysis, another iterative computational method is developed for the positive problem from the zero-stress state to the actual pre-stress state by moving the boundary joints, in which the explicit governing equations are formulated based on the particular energy function and a feasible self-stress mode is adopted to avoid the singularity of the initial stiffness matrix. To implement these methods, Matlab algorithms are developed and two examples are investigated. By comparing the results of the iterative method with those of the dynamic relaxation method, this study determines that they are comparable with each other, which validates the efficiency and accuracy of these iterative methods.