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Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring

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Abstract

This paper presents a new computational method for forward uncertainty quantification (UQ) analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs. The method consists of a generalized polynomial chaos expansion (GPCE) for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set. In the reanalysis, we employ substructuring for a structure to isolate its local regions that vary due to random inputs. This allows for avoiding repeated computations of invariant substructures while generating the input-output data set. Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy. Consequently, the GPCE with the static reanalysis method can achieve significant computational saving, thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs. The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses (FEAs). We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional (all-dependent) random inputs.

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Authors and Affiliations

  1. Department of Automotive Engineering, Hanyang University, Seoul, 04763, Republic of Korea

    D. Lee

  2. School of Mechanical Engineering, Chungnam National University, Daejeon, 34134, Republic of Korea

    S. Chang

  3. Department of Mechanical, Robotics and Energy Engineering, Dongguk University, Seoul, 04620, Republic of Korea

    J. Lee

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  1. D. Lee
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  2. S. Chang
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  3. J. Lee
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Correspondence to J. Lee.

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Conflict of interest The authors declare no conflict of interest.

Additional information

Project supported by the National Research Foundation of Korea (Nos. NRF-2020R1C1C1011970 and NRF-2018R1A5A7023490)

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Lee, D., Chang, S. & Lee, J. Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring. Appl. Math. Mech.-Engl. Ed. 45, 819–836 (2024). https://doi.org/10.1007/s10483-024-3108-8

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  • DOI: https://doi.org/10.1007/s10483-024-3108-8

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Chinese Library Classification

2010 Mathematics Subject Classification

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