Ultimate Force Boundary of Trusses

Abstract

In this paper, we introduce an effective way of limit analysis on the bearing capacity of given trusses. To illustrate the maximum external forces that a truss can carry on different directions, we propose the concept of ultimate force boundary (UFB) which is usually a closed polygon for a 2D truss and a closed polygonal mesh for a 3D truss. We prove that UFB is convex, and we introduce an efficient algorithm to compute the precise UFB based on its convexity. UFB can be used as direct visualization of bearing capacity of trusses and also provides insight of reducing the complexity of continuous boundary condition in truss optimization.