A novel univariate dimension‐reduction based interval finite element method for static response prediction of uncertain structures
To eliminate the errors caused by the conventional interval perturbation finite element method due to classic interval arithmetic and neglect of higher‐order terms, we propose a novel univariate dimension‐reduction based interval finite element method to predict the static response bounds of structu...
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Published in | International journal for numerical methods in engineering Vol. 124; no. 12; pp. 2709 - 2730 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Hoboken, USA
John Wiley & Sons, Inc
30.06.2023
Wiley Subscription Services, Inc |
Subjects | |
Online Access | Get full text |
ISSN | 0029-5981 1097-0207 |
DOI | 10.1002/nme.7225 |
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Summary: | To eliminate the errors caused by the conventional interval perturbation finite element method due to classic interval arithmetic and neglect of higher‐order terms, we propose a novel univariate dimension‐reduction based interval finite element method to predict the static response bounds of structures with uncertain but bounded parameters. First, a univariate dimension‐reduction algorithm is derived using the generalized Taylor expansion. The global stiffness matrix is expressed as the sum of the median and the univariate disturbance radius. Compared with Taylor expansion approximation, the univariate dimension‐reduction approximation has higher accuracy and does not increase the amount of calculation. Then the inverse of the interval global stiffness matrix is approximated as an improved Neumann series. Higher‐ order terms are included by summing up the geometric terms in the Neumann series. Finally, the improved interval algorithm is used to solve the upper and lower bounds of the structural displacement response and the element stress response. The dependence between the interval parameters is accounted in comparison with the classic interval algorithm. The accuracy and effectiveness of the new method are validated by numerical cases on 2D truss, 3D frame and truck frame with multiple interval parameters. |
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Bibliography: | Funding information Innovative Research Foundation of Ship General Performance, Grant/Award Number: 33122125; National Natural Science Foundation of China, Grant/Award Number: 51775230 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
ISSN: | 0029-5981 1097-0207 |
DOI: | 10.1002/nme.7225 |