A Variable-Length Rational Finite Element Based on the Absolute Nodal Coordinate Formulation
The variable-length arbitrary Lagrange–Euler absolute nodal coordinate formulation (ALE-ANCF) finite element, which employs nonrational interpolating polynomials, cannot exactly describe rational cubic Bezier curves such as conic and circular curves. The rational absolute nodal coordinate formulatio...
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| Format: | Article |
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MDPI AG
2022-02-01
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| Series: | Machines |
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| Online Access: | https://www.mdpi.com/2075-1702/10/3/174 |
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| author | Zhishen Ding Bin Ouyang |
| author_facet | Zhishen Ding Bin Ouyang |
| author_sort | Zhishen Ding |
| collection | DOAJ |
| description | The variable-length arbitrary Lagrange–Euler absolute nodal coordinate formulation (ALE-ANCF) finite element, which employs nonrational interpolating polynomials, cannot exactly describe rational cubic Bezier curves such as conic and circular curves. The rational absolute nodal coordinate formulation (RANCF) finite element, whose reference length (undeformed length) is constant, can exactly represent rational cubic Bezier curves. A new variable-length finite element called the ALE-RANCF finite element, which is capable of accurately describing rational cubic Bezier curves, is proposed and was formed by combining the desirable features of the ALE-ANCF and RANCF finite elements. To control the reference length of the ALE-RANCF element within a suitable range, element segmentation and merging schemes are proposed. It is demonstrated that the exact geometry and mechanics are maintained after the ALE-RANCF element is divided into two shorter ones, and compared with the ALE-ANCF elements, there are smaller deviations and oscillations after two ALE-RANCF elements are merged into a longer one. Numerical examples are presented, and the feasibility and advantages of the ALE-RANCF finite element are demonstrated. |
| first_indexed | 2024-03-09T13:32:59Z |
| format | Article |
| id | doaj.art-430616c0910d4d0b8f950af8acf28c9b |
| institution | Directory Open Access Journal |
| issn | 2075-1702 |
| language | English |
| last_indexed | 2024-03-09T13:32:59Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Machines |
| spelling | doaj.art-430616c0910d4d0b8f950af8acf28c9b2023-11-30T21:15:52ZengMDPI AGMachines2075-17022022-02-0110317410.3390/machines10030174A Variable-Length Rational Finite Element Based on the Absolute Nodal Coordinate FormulationZhishen Ding0Bin Ouyang1National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan 430000, ChinaNational Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan 430000, ChinaThe variable-length arbitrary Lagrange–Euler absolute nodal coordinate formulation (ALE-ANCF) finite element, which employs nonrational interpolating polynomials, cannot exactly describe rational cubic Bezier curves such as conic and circular curves. The rational absolute nodal coordinate formulation (RANCF) finite element, whose reference length (undeformed length) is constant, can exactly represent rational cubic Bezier curves. A new variable-length finite element called the ALE-RANCF finite element, which is capable of accurately describing rational cubic Bezier curves, is proposed and was formed by combining the desirable features of the ALE-ANCF and RANCF finite elements. To control the reference length of the ALE-RANCF element within a suitable range, element segmentation and merging schemes are proposed. It is demonstrated that the exact geometry and mechanics are maintained after the ALE-RANCF element is divided into two shorter ones, and compared with the ALE-ANCF elements, there are smaller deviations and oscillations after two ALE-RANCF elements are merged into a longer one. Numerical examples are presented, and the feasibility and advantages of the ALE-RANCF finite element are demonstrated.https://www.mdpi.com/2075-1702/10/3/174arbitrary Lagrange–Eulerrational finite elementabsolute nodal coordinate formulationvariable-length finite elementsliding joint |
| spellingShingle | Zhishen Ding Bin Ouyang A Variable-Length Rational Finite Element Based on the Absolute Nodal Coordinate Formulation Machines arbitrary Lagrange–Euler rational finite element absolute nodal coordinate formulation variable-length finite element sliding joint |
| title | A Variable-Length Rational Finite Element Based on the Absolute Nodal Coordinate Formulation |
| title_full | A Variable-Length Rational Finite Element Based on the Absolute Nodal Coordinate Formulation |
| title_fullStr | A Variable-Length Rational Finite Element Based on the Absolute Nodal Coordinate Formulation |
| title_full_unstemmed | A Variable-Length Rational Finite Element Based on the Absolute Nodal Coordinate Formulation |
| title_short | A Variable-Length Rational Finite Element Based on the Absolute Nodal Coordinate Formulation |
| title_sort | variable length rational finite element based on the absolute nodal coordinate formulation |
| topic | arbitrary Lagrange–Euler rational finite element absolute nodal coordinate formulation variable-length finite element sliding joint |
| url | https://www.mdpi.com/2075-1702/10/3/174 |
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