On the effect of boundary condition uncertainty on robust topology optimization of aerospace structures

Abstract

Uncertainty quantification (UQ) within topology optimization (TO) is a growing trend, with designers recognizing that deterministic analysis does not reflect the natural variabilities found in real-world structural performance. Thus far the majority of works have dealt with uncertain loading and material properties; however, minimal research has considered uncertain boundary conditions (BCs), which play a vital role for static and dynamic analysis involving compliance and natural frequency objectives and/or constraints. BCs uncertainty is studied in this paper by assuming a random percentage of a cantilever can be freed to rotate and/or translate in space. This is firstly demonstrated through a case study on a flat plate wing where the frequency gap between two modes is maximized, and secondly through optimizing the wing of a sensorcraft where compliance is minimized. A robust objective is formulated via a weighted sum of the mean and standard deviation, which is approximated efficiently using a Non-Intrusive Polynomial Chaos Expansion (NIPC). Both studies demonstrate the pitfalls of a deterministic optimum in dealing with uncertain BCs, and how using Robust TO (RTO) can effectively reduce the variance and worst-case performance of the objective. Experimental validation for the flat plate wing is also undertaken to ensure practical feasibility of the RTO topologies and to provide motivation to study BCs uncertainty further.