Abstract
In this work, a method for the application of multi-fidelity modeling to the reliability analysis of 2D elastostatic structures using the boundary element method (BEM) is proposed. Reliability analyses were carried out on a rectangular plate with a center circular hole subjected to uniaxial tension using Monte Carlo simulations (MCS), the first-order reliability method (FORM), and the second-order reliability method (SORM). Two BEM models were investigated, a low-fidelity model (LFM) of 20 elements and a high-fidelity model (HFM) of 100 elements. The response of these models at several design points was used to create multi-fidelity models (MFMs) utilizing second-order polynomial response surfaces and their reliability, alongside that of the LFM and the HFM, was evaluated. Results show that the MFMs that directly called the LFM were significantly superior in terms of accuracy to the LFM, achieving very similar levels of accuracy to the HFM, while also being of similar computational cost to the LFM. These direct MFMs were found to provide good substitutes for the HFM for MCS, FORM, and SORM.
Highlights
All engineering parameters have uncertainties in their values, it is important that these are considered during the design process
Multi- ̄delity modeling is used in combination with reliability analyses performed using Monte Carlo simulations (MCS), First-order reliability method (FORM), and second-order reliability method (SORM)
It can be seen from thisgure that SORM follows MCS much more closely than FORM, suggesting that SORM provides a much more accurate approximation for the failure domain than FORM
Summary
All engineering parameters have uncertainties in their values, it is important that these are considered during the design process. Huang and Aliabadi[6] addressed a more complex problem involving the reliability analysis of 2D cracked structures using the dual boundary element method (DBEM).[8] The sensitivity of the stress intensity factors with respect to several random variables, including crack length and fracture toughness, was calculated using the IDM and compared to those obtained from thenite di®erence method (FDM) with both the DBEM and the FEM and with MCS. The computational cost of performing reliability analyses on 2D elastostatic structures using the BEM through the application of multi- ̄delity modeling is investigated. The aim is to use MFMs to obtain similar accuracy to the HFM but at much less computational cost, greatly improving the e±ciency of the reliability analysis procedures using MCS, FORM, and SORM. A second objective involves quantifying this improvement in e±ciency for each of these three methods, determining the extent to which each of these methods benet from the application of multi- ̄delity modeling
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