Planar Cross-Sectional Fitting of Structural Members to Numerical Simulation Results Obtained from Finite Element Models with Solid or Shell Elements
Modeling complex conditions involving extensive engineering structures with large numbers of beams and columns often requires a mixture of analytical modeling based on beam theory and numerical simulations involving finite element models composed of solid or shell elements. However, high levels of d...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
|
| Series: | Buildings |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-5309/15/5/797 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850030341261099008 |
|---|---|
| author | Xuan Zhang Shifa Xia Huanchen Li Fengwei Shi En-Feng Deng Meng Li |
| author_facet | Xuan Zhang Shifa Xia Huanchen Li Fengwei Shi En-Feng Deng Meng Li |
| author_sort | Xuan Zhang |
| collection | DOAJ |
| description | Modeling complex conditions involving extensive engineering structures with large numbers of beams and columns often requires a mixture of analytical modeling based on beam theory and numerical simulations involving finite element models composed of solid or shell elements. However, high levels of deformation in the planar configuration of cross-sections arising under extreme external loads, such as intensive earthquakes, explosions, and hurricanes, greatly complicates the task of fitting the numerical simulation results to the planar cross-sections required by beam theory. The present work addresses this issue by proposing a fitting method based on a least squares approximation method. The fitting problem is first transformed into a process of solving a cubic equation whose coefficients are integrals over the simulated cross-section. The solution of the cubic equation is defined using explicit formulae developed for calculating the integrals over the surfaces of single solid or shell elements lying within the cross-section by combining the shape functions and degree of freedom results of the elements. The proposed fitting method is then applied for analyzing the blast resistance of steel structures. The potential application of the proposed method is demonstrated by evaluating the rotations, shear deformations, and moment–curvature relationships of the fitted cross-sections. |
| format | Article |
| id | doaj-art-8d337908cf1241548cea85a0d79db799 |
| institution | DOAJ |
| issn | 2075-5309 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Buildings |
| spelling | doaj-art-8d337908cf1241548cea85a0d79db7992025-08-20T02:59:14ZengMDPI AGBuildings2075-53092025-02-0115579710.3390/buildings15050797Planar Cross-Sectional Fitting of Structural Members to Numerical Simulation Results Obtained from Finite Element Models with Solid or Shell ElementsXuan Zhang0Shifa Xia1Huanchen Li2Fengwei Shi3En-Feng Deng4Meng Li5State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, ChinaState Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, ChinaState Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, ChinaCollege of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao 266590, ChinaSchool of Civil Engineering, Zhengzhou University, Zhengzhou 450001, ChinaState Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, ChinaModeling complex conditions involving extensive engineering structures with large numbers of beams and columns often requires a mixture of analytical modeling based on beam theory and numerical simulations involving finite element models composed of solid or shell elements. However, high levels of deformation in the planar configuration of cross-sections arising under extreme external loads, such as intensive earthquakes, explosions, and hurricanes, greatly complicates the task of fitting the numerical simulation results to the planar cross-sections required by beam theory. The present work addresses this issue by proposing a fitting method based on a least squares approximation method. The fitting problem is first transformed into a process of solving a cubic equation whose coefficients are integrals over the simulated cross-section. The solution of the cubic equation is defined using explicit formulae developed for calculating the integrals over the surfaces of single solid or shell elements lying within the cross-section by combining the shape functions and degree of freedom results of the elements. The proposed fitting method is then applied for analyzing the blast resistance of steel structures. The potential application of the proposed method is demonstrated by evaluating the rotations, shear deformations, and moment–curvature relationships of the fitted cross-sections.https://www.mdpi.com/2075-5309/15/5/797beam theorycross-section fittingleast squares approximationblast resistancesteel structure |
| spellingShingle | Xuan Zhang Shifa Xia Huanchen Li Fengwei Shi En-Feng Deng Meng Li Planar Cross-Sectional Fitting of Structural Members to Numerical Simulation Results Obtained from Finite Element Models with Solid or Shell Elements Buildings beam theory cross-section fitting least squares approximation blast resistance steel structure |
| title | Planar Cross-Sectional Fitting of Structural Members to Numerical Simulation Results Obtained from Finite Element Models with Solid or Shell Elements |
| title_full | Planar Cross-Sectional Fitting of Structural Members to Numerical Simulation Results Obtained from Finite Element Models with Solid or Shell Elements |
| title_fullStr | Planar Cross-Sectional Fitting of Structural Members to Numerical Simulation Results Obtained from Finite Element Models with Solid or Shell Elements |
| title_full_unstemmed | Planar Cross-Sectional Fitting of Structural Members to Numerical Simulation Results Obtained from Finite Element Models with Solid or Shell Elements |
| title_short | Planar Cross-Sectional Fitting of Structural Members to Numerical Simulation Results Obtained from Finite Element Models with Solid or Shell Elements |
| title_sort | planar cross sectional fitting of structural members to numerical simulation results obtained from finite element models with solid or shell elements |
| topic | beam theory cross-section fitting least squares approximation blast resistance steel structure |
| url | https://www.mdpi.com/2075-5309/15/5/797 |
| work_keys_str_mv | AT xuanzhang planarcrosssectionalfittingofstructuralmemberstonumericalsimulationresultsobtainedfromfiniteelementmodelswithsolidorshellelements AT shifaxia planarcrosssectionalfittingofstructuralmemberstonumericalsimulationresultsobtainedfromfiniteelementmodelswithsolidorshellelements AT huanchenli planarcrosssectionalfittingofstructuralmemberstonumericalsimulationresultsobtainedfromfiniteelementmodelswithsolidorshellelements AT fengweishi planarcrosssectionalfittingofstructuralmemberstonumericalsimulationresultsobtainedfromfiniteelementmodelswithsolidorshellelements AT enfengdeng planarcrosssectionalfittingofstructuralmemberstonumericalsimulationresultsobtainedfromfiniteelementmodelswithsolidorshellelements AT mengli planarcrosssectionalfittingofstructuralmemberstonumericalsimulationresultsobtainedfromfiniteelementmodelswithsolidorshellelements |