On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of Structures
The main aim of this work was to investigate a numerical error in determining limit state functions, which describe the extreme magnitudes of steel structures with respect to random variables. It was assisted here by the global version of the response function method (RFM). Various approximations of...
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| Format: | Article |
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MDPI AG
2021-10-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/21/10179 |
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| author | Bartłomiej Pokusiński Marcin Kamiński |
| author_facet | Bartłomiej Pokusiński Marcin Kamiński |
| author_sort | Bartłomiej Pokusiński |
| collection | DOAJ |
| description | The main aim of this work was to investigate a numerical error in determining limit state functions, which describe the extreme magnitudes of steel structures with respect to random variables. It was assisted here by the global version of the response function method (RFM). Various approximations of trial points generated on the basis of several hundred selected reference composite functions based on polynomials were analyzed. The final goal was to find some criterion—between approximation and input data—for the selection of the response function leading to relative a posteriori errors less than 1%. Unlike the classical problem of curve fitting, the accuracy of the final values of probabilistic moments was verified here as they can be used in further reliability calculations. The use of the criterion and the associated way of selecting the response function was demonstrated on the example of steel diagrid grillages. It resulted in quite high correctness in comparison with extended FEM tests. |
| first_indexed | 2024-03-10T06:06:30Z |
| format | Article |
| id | doaj.art-672639a22cb1473f8d6e72561203314e |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T06:06:30Z |
| publishDate | 2021-10-01 |
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| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-672639a22cb1473f8d6e72561203314e2023-11-22T20:28:59ZengMDPI AGApplied Sciences2076-34172021-10-0111211017910.3390/app112110179On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of StructuresBartłomiej Pokusiński0Marcin Kamiński1Department of Structural Mechanics, Faculty of Civil Engineering, Architecture and Environmental Engineering, Łódź University of Technology, 90-924 Łódź, PolandDepartment of Structural Mechanics, Faculty of Civil Engineering, Architecture and Environmental Engineering, Łódź University of Technology, 90-924 Łódź, PolandThe main aim of this work was to investigate a numerical error in determining limit state functions, which describe the extreme magnitudes of steel structures with respect to random variables. It was assisted here by the global version of the response function method (RFM). Various approximations of trial points generated on the basis of several hundred selected reference composite functions based on polynomials were analyzed. The final goal was to find some criterion—between approximation and input data—for the selection of the response function leading to relative a posteriori errors less than 1%. Unlike the classical problem of curve fitting, the accuracy of the final values of probabilistic moments was verified here as they can be used in further reliability calculations. The use of the criterion and the associated way of selecting the response function was demonstrated on the example of steel diagrid grillages. It resulted in quite high correctness in comparison with extended FEM tests.https://www.mdpi.com/2076-3417/11/21/10179response predictionlimit state functionresponse function methodprobabilistic direct integration approachsteel diagrid structures |
| spellingShingle | Bartłomiej Pokusiński Marcin Kamiński On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of Structures Applied Sciences response prediction limit state function response function method probabilistic direct integration approach steel diagrid structures |
| title | On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of Structures |
| title_full | On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of Structures |
| title_fullStr | On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of Structures |
| title_full_unstemmed | On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of Structures |
| title_short | On Selecting Composite Functions Based on Polynomials for Responses Describing Extreme Magnitudes of Structures |
| title_sort | on selecting composite functions based on polynomials for responses describing extreme magnitudes of structures |
| topic | response prediction limit state function response function method probabilistic direct integration approach steel diagrid structures |
| url | https://www.mdpi.com/2076-3417/11/21/10179 |
| work_keys_str_mv | AT bartłomiejpokusinski onselectingcompositefunctionsbasedonpolynomialsforresponsesdescribingextrememagnitudesofstructures AT marcinkaminski onselectingcompositefunctionsbasedonpolynomialsforresponsesdescribingextrememagnitudesofstructures |