Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution Patterns
A finite element analysis (FEA) model was developed for Euler and Timoshenko curved beam elements by incorporating trigonometric displacement distribution patterns. Local polar coordinate stiffness matrices were derived based on force-displacement relations and static equilibrium conditions. By empl...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Buildings |
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| Online Access: | https://www.mdpi.com/2075-5309/13/9/2239 |
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| author | Hengtao Cao Daihai Chen Yunsen Zhang Hexiang Wang Huai Chen |
| author_facet | Hengtao Cao Daihai Chen Yunsen Zhang Hexiang Wang Huai Chen |
| author_sort | Hengtao Cao |
| collection | DOAJ |
| description | A finite element analysis (FEA) model was developed for Euler and Timoshenko curved beam elements by incorporating trigonometric displacement distribution patterns. Local polar coordinate stiffness matrices were derived based on force-displacement relations and static equilibrium conditions. By employing the kinetic energy theorem and triangular displacement functions, an expression for the consistent mass matrix of a curved beam element was obtained. A coordinate transformation matrix for the curved beam element was established by relating the local polar coordinate system to the global polar coordinate system. Calculation programs were implemented in the Fortran language to evaluate the static–dynamic performance and natural frequency characteristics of curved beam bridges. The obtained results were then compared with those obtained using ANSYS solid models and “replace curve with straight” beam element models. The comparison demonstrated a strong agreement between the results of the Euler and Timoshenko curved beam element models and those of the ANSYS solid models. However, discrepancies were observed when comparing with the results of the “replace curve with straight” beam element model, particularly in terms of lateral static displacement. This discrepancy suggests that the characteristic matrix derived in this study accurately represents the stiffness and mass distribution of the curved beam, making it suitable for mechanical performance analysis of curved beam bridges. It should be noted that the “replace curve with straight” method overlooks the initial curvature and the bending–torsion coupling effects of a curved beam, resulting in calculation deviations. On the other hand, the use of curved beam elements in numerical analysis provides a simple and practical approach, which facilitates further research in areas such as vehicle–bridge coupling vibrations and seismic analysis of curved beam bridges. |
| first_indexed | 2024-03-10T22:58:28Z |
| format | Article |
| id | doaj.art-8a785b0b0e674e8784594d4e74a7cd4a |
| institution | Directory Open Access Journal |
| issn | 2075-5309 |
| language | English |
| last_indexed | 2024-03-10T22:58:28Z |
| publishDate | 2023-09-01 |
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| record_format | Article |
| series | Buildings |
| spelling | doaj.art-8a785b0b0e674e8784594d4e74a7cd4a2023-11-19T09:51:19ZengMDPI AGBuildings2075-53092023-09-01139223910.3390/buildings13092239Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution PatternsHengtao Cao0Daihai Chen1Yunsen Zhang2Hexiang Wang3Huai Chen4School of Civil Engineering, Zhengzhou University, Zhengzhou 450001, ChinaSchool of Civil Engineering, Zhengzhou University, Zhengzhou 450001, ChinaSchool of Civil Engineering, Zhengzhou University, Zhengzhou 450001, ChinaSchool of Civil Engineering, Zhengzhou University, Zhengzhou 450001, ChinaSchool of Civil Engineering, Zhengzhou University, Zhengzhou 450001, ChinaA finite element analysis (FEA) model was developed for Euler and Timoshenko curved beam elements by incorporating trigonometric displacement distribution patterns. Local polar coordinate stiffness matrices were derived based on force-displacement relations and static equilibrium conditions. By employing the kinetic energy theorem and triangular displacement functions, an expression for the consistent mass matrix of a curved beam element was obtained. A coordinate transformation matrix for the curved beam element was established by relating the local polar coordinate system to the global polar coordinate system. Calculation programs were implemented in the Fortran language to evaluate the static–dynamic performance and natural frequency characteristics of curved beam bridges. The obtained results were then compared with those obtained using ANSYS solid models and “replace curve with straight” beam element models. The comparison demonstrated a strong agreement between the results of the Euler and Timoshenko curved beam element models and those of the ANSYS solid models. However, discrepancies were observed when comparing with the results of the “replace curve with straight” beam element model, particularly in terms of lateral static displacement. This discrepancy suggests that the characteristic matrix derived in this study accurately represents the stiffness and mass distribution of the curved beam, making it suitable for mechanical performance analysis of curved beam bridges. It should be noted that the “replace curve with straight” method overlooks the initial curvature and the bending–torsion coupling effects of a curved beam, resulting in calculation deviations. On the other hand, the use of curved beam elements in numerical analysis provides a simple and practical approach, which facilitates further research in areas such as vehicle–bridge coupling vibrations and seismic analysis of curved beam bridges.https://www.mdpi.com/2075-5309/13/9/2239curved beam elementtrigonometric displacement distribution patternselement stiffness matrixelement mass matrixcoordinate transformation matrix |
| spellingShingle | Hengtao Cao Daihai Chen Yunsen Zhang Hexiang Wang Huai Chen Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution Patterns Buildings curved beam element trigonometric displacement distribution patterns element stiffness matrix element mass matrix coordinate transformation matrix |
| title | Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution Patterns |
| title_full | Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution Patterns |
| title_fullStr | Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution Patterns |
| title_full_unstemmed | Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution Patterns |
| title_short | Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution Patterns |
| title_sort | finite element analysis of curved beam elements employing trigonometric displacement distribution patterns |
| topic | curved beam element trigonometric displacement distribution patterns element stiffness matrix element mass matrix coordinate transformation matrix |
| url | https://www.mdpi.com/2075-5309/13/9/2239 |
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