In-plane nonlinear postbuckling and buckling analysis of Lee’s frame using absolute nodal coordinate formulation
In this study, four absolute nodal coordinate formulation (ANCF)-based approaches are utilized in order to predict the buckling load of Lee’s frame under concentrated load. The first approach employs the standard two-dimensional shear deformable ANCF beam element based on the general continuum mecha...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-09-01
|
| Series: | Curved and Layered Structures |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/cls-2022-0212 |
| _version_ | 1797688831338610688 |
|---|---|
| author | Shaukat Abdur Rahman Lan Peng Wang Jia Wang Tengfei Lu Nianli |
| author_facet | Shaukat Abdur Rahman Lan Peng Wang Jia Wang Tengfei Lu Nianli |
| author_sort | Shaukat Abdur Rahman |
| collection | DOAJ |
| description | In this study, four absolute nodal coordinate formulation (ANCF)-based approaches are utilized in order to predict the buckling load of Lee’s frame under concentrated load. The first approach employs the standard two-dimensional shear deformable ANCF beam element based on the general continuum mechanics (GCM). The second approach adopts the standard ANCF beam element modified by the locking alleviation technique known as the strain-split method. The third approach has the standard ANCF beam element with strain energy modified by the enhanced continuum mechanics formulation. The fourth approach utilizes the higher-order ANCF beam element based on the GCM. Two buckling load estimation methods are used, i.e., by tracing the nonlinear equilibrium path of the load–displacement space using the arc-length method and applying the energy criterion, which requires tracking eigenvalues through the dichotomy scheme. Lee’s frame with different boundary conditions including pinned–pinned, fixed-pinned, pinned-fixed, and fixed–fixed are studied. The complex nonlinear responses in the form of snap-through, snap-back, and looping phenomena during nonlinear postbuckling analysis are simulated. The critical buckling loads and buckling mode shapes obtained through the energy criterion-based buckling method are obtained. After the comparison, higher-order beam element is found to be more accurate, stable, and consistent among the studied approaches. |
| first_indexed | 2024-03-12T01:36:22Z |
| format | Article |
| id | doaj.art-874500add90241f791d3c8d4013461b5 |
| institution | Directory Open Access Journal |
| issn | 2353-7396 |
| language | English |
| last_indexed | 2024-03-12T01:36:22Z |
| publishDate | 2023-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Curved and Layered Structures |
| spelling | doaj.art-874500add90241f791d3c8d4013461b52023-09-11T06:59:27ZengDe GruyterCurved and Layered Structures2353-73962023-09-011013394810.1515/cls-2022-0212In-plane nonlinear postbuckling and buckling analysis of Lee’s frame using absolute nodal coordinate formulationShaukat Abdur Rahman0Lan Peng1Wang Jia2Wang Tengfei3Lu Nianli4Department of Mechanical Engineering, University of Management and Technology, Sialkot Campus, Lahore, 51041, PakistanSchool of Mechanical and Electrical Engineering, Xi’an University of Architecture and Technology, Xi’an, Shanxi, 710055, ChinaSchool of Mechanical Engineering, Shenyang University of Technology, No. 111, Shenliao West Road, Shenyang, 110870, ChinaState Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, West Xianning Road 28, Xi’an, 710049, ChinaSchool of Mechatronics Engineering, Harbin Institute of Technology, Harbin, ChinaIn this study, four absolute nodal coordinate formulation (ANCF)-based approaches are utilized in order to predict the buckling load of Lee’s frame under concentrated load. The first approach employs the standard two-dimensional shear deformable ANCF beam element based on the general continuum mechanics (GCM). The second approach adopts the standard ANCF beam element modified by the locking alleviation technique known as the strain-split method. The third approach has the standard ANCF beam element with strain energy modified by the enhanced continuum mechanics formulation. The fourth approach utilizes the higher-order ANCF beam element based on the GCM. Two buckling load estimation methods are used, i.e., by tracing the nonlinear equilibrium path of the load–displacement space using the arc-length method and applying the energy criterion, which requires tracking eigenvalues through the dichotomy scheme. Lee’s frame with different boundary conditions including pinned–pinned, fixed-pinned, pinned-fixed, and fixed–fixed are studied. The complex nonlinear responses in the form of snap-through, snap-back, and looping phenomena during nonlinear postbuckling analysis are simulated. The critical buckling loads and buckling mode shapes obtained through the energy criterion-based buckling method are obtained. After the comparison, higher-order beam element is found to be more accurate, stable, and consistent among the studied approaches.https://doi.org/10.1515/cls-2022-0212absolute nodal coordinate formulationbuckling analysisnonlinear postbuckling analysisarc-length methodlee’s frame |
| spellingShingle | Shaukat Abdur Rahman Lan Peng Wang Jia Wang Tengfei Lu Nianli In-plane nonlinear postbuckling and buckling analysis of Lee’s frame using absolute nodal coordinate formulation Curved and Layered Structures absolute nodal coordinate formulation buckling analysis nonlinear postbuckling analysis arc-length method lee’s frame |
| title | In-plane nonlinear postbuckling and buckling analysis of Lee’s frame using absolute nodal coordinate formulation |
| title_full | In-plane nonlinear postbuckling and buckling analysis of Lee’s frame using absolute nodal coordinate formulation |
| title_fullStr | In-plane nonlinear postbuckling and buckling analysis of Lee’s frame using absolute nodal coordinate formulation |
| title_full_unstemmed | In-plane nonlinear postbuckling and buckling analysis of Lee’s frame using absolute nodal coordinate formulation |
| title_short | In-plane nonlinear postbuckling and buckling analysis of Lee’s frame using absolute nodal coordinate formulation |
| title_sort | in plane nonlinear postbuckling and buckling analysis of lee s frame using absolute nodal coordinate formulation |
| topic | absolute nodal coordinate formulation buckling analysis nonlinear postbuckling analysis arc-length method lee’s frame |
| url | https://doi.org/10.1515/cls-2022-0212 |
| work_keys_str_mv | AT shaukatabdurrahman inplanenonlinearpostbucklingandbucklinganalysisofleesframeusingabsolutenodalcoordinateformulation AT lanpeng inplanenonlinearpostbucklingandbucklinganalysisofleesframeusingabsolutenodalcoordinateformulation AT wangjia inplanenonlinearpostbucklingandbucklinganalysisofleesframeusingabsolutenodalcoordinateformulation AT wangtengfei inplanenonlinearpostbucklingandbucklinganalysisofleesframeusingabsolutenodalcoordinateformulation AT lunianli inplanenonlinearpostbucklingandbucklinganalysisofleesframeusingabsolutenodalcoordinateformulation |