Robust limit analysis theory for computing worst-case limit loads under uncertainties

TL;DR

This paper introduces a comprehensive theoretical framework for robust limit analysis that accounts for uncertainties in material properties and loading conditions, enabling more reliable structural safety assessments.

Contribution

It develops generic robust limit analysis formulations, models uncertain strength properties, and provides tractable reformulations for numerical implementation, advancing the field of structural safety under uncertainty.

Findings

Robust limit analysis formulations for uncertain material strength

Numerical methods using conic programming for implementation

Applications to structures with uncertain loads and material properties

Abstract

This work proposes a novel theoretical framework of robust limit analysis i.e. the computation of limit loads of structures in presence of uncertainties using limit analysis and robust optimization theories. We first derive generic robust limit analysis formulations in the case of uncertain material strength properties. We discuss various ways of modeling uncertain strength properties and introduce the notion of robust strength criteria. We formulate static and adjustable robust counterparts of the corresponding uncertain limit analysis problems. Depending on the chosen strength uncertainty model, we also discuss tractable reformulations or approximations which can be implemented numerically using conic programming solvers. Building upon these results, we also derive robust limit analysis formulations in presence of loading uncertainties. Finally, various applications illustrate the versatility of the proposed framework including the derivation of a robust Mohr-Coulomb criterion with uncertain cohesion and friction angle, the computation of limit load of a structure subject to the partial loss of some components, or the limit load of a truss structure under multiple load uncertainties.