Bayesian Reconstruction of Goal Orientated Error Fields in Large Aerospace Finite Element Models

Bonney, Matthew S.; Evans, Richard; Rouse, James; Jones, Arthur; Hamadi, Maxime

Abstract

A major difficulty in the mechanical simulation of large aerospace structures is the multi-scale nature of modern designs due to, at least in part, the increased use of composite materials. "Thin" materials are typically idealised by shell elements in order to make simulations computationally tractable, however this significantly limits the fidelity of solutions. Through thickness stress states, for example, are important in predicting delam-ination but are known to be poorly approximated by shell element. To solve this issue, a multi-scale methodology , such as MARQUESS, is required to accurately model these systems. This work is focused on the application of a goal oriented error estimator methodology in MARQUESS to suggest confidence bounds of "hot-spot" predictions. The goal oriented error esti-mator uses the combination of dual formulations and Zienkiwicz-Zhu recovery to estimate volume averaged errors at training locations in a candidate structure. Bayesian recovery processes are then used to approximate full error fields from local solutions. This es-timator is applied to two systems, one 2D system and one full 3D system, both modelled using shell elements. The 2D system investigates the mesh refinement to denote the convergence properties of the estimator. For the 3D system, the Gaussian process is used to reduce the number of dual problems from 1, 300 to 100 simulations with only small differences from the full simulations. This work demonstrates the initial implementation of this non-intrusive estimator to denote the error associated with the modelling in the macro-level scale.

Citation

Bonney, M. S., Evans, R., Rouse, J., Jones, A., & Hamadi, M. (2020). Bayesian Reconstruction of Goal Orientated Error Fields in Large Aerospace Finite Element Models. In Proceedings of AerospaceEurope Conference 2020

• Conference Name: AerospaceEurope Conference 2020 (AEC2020)
• Start Date: Feb 25, 2020
• End Date: Feb 28, 2020
• Acceptance Date: Nov 18, 2019
• Online Publication Date: Feb 28, 2020
• Publication Date: Feb 28, 2020
• Deposit Date: Jul 15, 2020
• Publicly Available Date: Jul 21, 2020
• Book Title: Proceedings of AerospaceEurope Conference 2020
• Keywords: GOEE; Aerospace Structures; Bayesian Response Sur- face; MARQUESS; Zienkiwicz-Zhu Recovery; Finite Element Method
• Public URL: https://nottingham-repository.worktribe.com/output/4768617
• Related Public URLs: https://aerospace-europe2020.eu/