Optimal Design of Non-linear Truss Structures considering Progressive Collapse

Abstract

In this paper, a methodology is proposed to evaluate the optimal design of truss structures considering progressive collapse. This methodology combines Total-Lagrangian formulation for material and geometrical nonlinear analysis, using nodal positions and log-strain measure; the Systematic Reliability-based Approach to Progressive Collapse method; and risk-optimization formulation. Two benchmark examples are analyzed and discussed. The results demonstrate the accuracy, robustness, and efficiency of the proposed methodology in evaluation the optimal design of truss structures subjected to progressive collapse. It is shown that material behavior (elastic, elastoplastic, and hyperelastic) and rate of loading (step and linear load) can lead to different optimal design configurations. In the hyperstatic example, the coefficient of vulnerability identifies the most critical bar for each truss configuration. The most vulnerable bars in the reference design become less vulnerable in the optimal design, leading to load redistribution, or alternate load paths, which reduce the probability of occurrence of progressive collapse.