Bayesian robust optimisation of buckling loads of trusses with random imperfections

Structural optimisation with linear responses is a highly active research field with broad applications. In practice, nonlinear structural behaviour and random imperfections different from the ideal design often need to be considered. Optimised lightweight structures, such as truss-based shallow domes and slender towers, are usually prone to sudden failure through buckling so that structural nonlinearities must be taken into account. Additionally, imperfections, like perturbations in geometry or material properties, can drastically reduce the buckling load of a structure compared to that of the perfect structure. Therefore, without the consideration of nonlinearities and imperfections, standard deterministic optimisation of the linear structure gives a design with lower safety and less robustness against uncertainties, yielding the necessity of robust optimisation. In this thesis, we propose a novel and efficient framework for robust structural optimisation with nonlinearities and random imperfections, with applications to sizing optimisation of buckling loads of truss structures. In robust optimisation, the objective is the weighted sum of the expectation and standard deviation of buckling loads, where the weighting is controlled by a chosen trade-off parameter. The probability distribution of buckling loads is estimated by sampling from imperfections with a known probability distribution and performing nonlinear finite element evaluations for each sample individually. However, using standard nonlinear finite element methods to trace the equilibrium paths for buckling loads is computationally expensive, especially when many random samples and finite element evaluations are required. Besides, as the objective function is expensive with no closed-form and the computation of its derivatives is costly, traditional gradient-based optimisation approaches are unsuitable. To address the aforementioned problems, we first employ the extended system method to directly compute stability points and buckling loads, which avoids the expensive computation of tracing the equilibrium paths. Furthermore, the extended system method is used to devise an efficient algorithm for computing the buckling load distribution for structures with random imperfections. Secondly, we adopt quasi-Monte Carlo sampling, i.e. Sobol sampling, to generate samples with better uniformity thanpseudorandom samples, which significantly reduces the number of samples and finite element evaluations thus further improving efficiency. Thirdly, we apply the Bayesian optimisation with a Gaussian process surrogate model and the iterative domain shrinkage scheme for the described robust optimisation problem. Compared to traditional gradient-based optimisation approaches, Bayesian optimisation is exceptionally well suited for expensive black-box objective functions as it does not require gradients.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2024

Author dc:creator

• Liu, Tianyi

Advisor dc:contributor.advisor

• Cirak, Fehmi

• Bayesian optimisation
• Computational mechanics
• Extended system method
• Gaussian process
• Robust optimisation
• Sobol sampling
• Uncertainty quantification

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/ed0d4930-a817-48bb-adb5-9080df2ba80d/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.112607

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/374591