Static analysis of elastic cable structures under mechanical load using discrete catenary theory
In this paper, the nonlinear mechanical response of elastic cable structures under mechanical load is studied based on the discrete catenary theory. A cable net is discretized into multiple nodes and edges in our numerical approach, which is followed by an analytical formulation of the elastic energ...
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| Format: | Article |
| Language: | English |
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KeAi Communications Co. Ltd.
2023-11-01
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| Series: | Fundamental Research |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S266732582200139X |
| _version_ | 1827635964205334528 |
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| author | Weicheng Huang Dongze He Dezhong Tong Yuzhen Chen Xiaonan Huang Longhui Qin Qingguo Fei |
| author_facet | Weicheng Huang Dongze He Dezhong Tong Yuzhen Chen Xiaonan Huang Longhui Qin Qingguo Fei |
| author_sort | Weicheng Huang |
| collection | DOAJ |
| description | In this paper, the nonlinear mechanical response of elastic cable structures under mechanical load is studied based on the discrete catenary theory. A cable net is discretized into multiple nodes and edges in our numerical approach, which is followed by an analytical formulation of the elastic energy and the associated Hessian matrix to realize the dynamic simulation. A fully implicit framework is proposed based on the discrete differential geometry (DDG) theory. The equilibrium configuration of a target object is derived by adding damping force into the system, known as the dynamic relaxation method. The mechanical response of a single suspended cable is investigated and compared with the analytical solution for cross-validation. A more intricate scenario is further discussed in detail, where a structure consisting of multiple slender cables is connected through joints. Utilizing the robustness and efficiency of our discrete numerical framework, a systematic parameter sweep is performed to quantify the force displacement relationships of nets with the different number of cables and different directions of fibers. Finally, an empirical scaling law is provided to account for the rigidity of elastic cable net in terms of its geometric properties, material characteristics, component numbers, and cable orientations. Our results would provide new insight in revealing the connections between flexible structures and tensegrity structures, and could motivate innovative designs in both mechanical and civil engineered equipment. |
| first_indexed | 2024-03-09T15:34:40Z |
| format | Article |
| id | doaj.art-03324fa278444829951b9f709c9390fc |
| institution | Directory Open Access Journal |
| issn | 2667-3258 |
| language | English |
| last_indexed | 2024-03-09T15:34:40Z |
| publishDate | 2023-11-01 |
| publisher | KeAi Communications Co. Ltd. |
| record_format | Article |
| series | Fundamental Research |
| spelling | doaj.art-03324fa278444829951b9f709c9390fc2023-11-26T05:14:27ZengKeAi Communications Co. Ltd.Fundamental Research2667-32582023-11-0136967973Static analysis of elastic cable structures under mechanical load using discrete catenary theoryWeicheng Huang0Dongze He1Dezhong Tong2Yuzhen Chen3Xiaonan Huang4Longhui Qin5Qingguo Fei6School of Mechanical Engineering, Southeast University, Nanjing 211189, China; Jiangsu Engineering Research Center of Aerospace Machinery, Southeast University, Nanjing 211189, ChinaSchool of Mechanical Engineering, Southeast University, Nanjing 211189, China; Jiangsu Engineering Research Center of Aerospace Machinery, Southeast University, Nanjing 211189, ChinaDepartment of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USACorresponding authors.; Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USADepartment of Mechanical Engineering and Materials Science, Yale University, New Haven, CT 06511, USA; Corresponding authors.School of Mechanical Engineering, Southeast University, Nanjing 211189, China; Corresponding authors.School of Mechanical Engineering, Southeast University, Nanjing 211189, China; Jiangsu Engineering Research Center of Aerospace Machinery, Southeast University, Nanjing 211189, China; Corresponding authors.In this paper, the nonlinear mechanical response of elastic cable structures under mechanical load is studied based on the discrete catenary theory. A cable net is discretized into multiple nodes and edges in our numerical approach, which is followed by an analytical formulation of the elastic energy and the associated Hessian matrix to realize the dynamic simulation. A fully implicit framework is proposed based on the discrete differential geometry (DDG) theory. The equilibrium configuration of a target object is derived by adding damping force into the system, known as the dynamic relaxation method. The mechanical response of a single suspended cable is investigated and compared with the analytical solution for cross-validation. A more intricate scenario is further discussed in detail, where a structure consisting of multiple slender cables is connected through joints. Utilizing the robustness and efficiency of our discrete numerical framework, a systematic parameter sweep is performed to quantify the force displacement relationships of nets with the different number of cables and different directions of fibers. Finally, an empirical scaling law is provided to account for the rigidity of elastic cable net in terms of its geometric properties, material characteristics, component numbers, and cable orientations. Our results would provide new insight in revealing the connections between flexible structures and tensegrity structures, and could motivate innovative designs in both mechanical and civil engineered equipment.http://www.sciencedirect.com/science/article/pii/S266732582200139XCable structuresRigiditySolid mechanicsComputational mechanicsNumerical simulationNonlinearity |
| spellingShingle | Weicheng Huang Dongze He Dezhong Tong Yuzhen Chen Xiaonan Huang Longhui Qin Qingguo Fei Static analysis of elastic cable structures under mechanical load using discrete catenary theory Fundamental Research Cable structures Rigidity Solid mechanics Computational mechanics Numerical simulation Nonlinearity |
| title | Static analysis of elastic cable structures under mechanical load using discrete catenary theory |
| title_full | Static analysis of elastic cable structures under mechanical load using discrete catenary theory |
| title_fullStr | Static analysis of elastic cable structures under mechanical load using discrete catenary theory |
| title_full_unstemmed | Static analysis of elastic cable structures under mechanical load using discrete catenary theory |
| title_short | Static analysis of elastic cable structures under mechanical load using discrete catenary theory |
| title_sort | static analysis of elastic cable structures under mechanical load using discrete catenary theory |
| topic | Cable structures Rigidity Solid mechanics Computational mechanics Numerical simulation Nonlinearity |
| url | http://www.sciencedirect.com/science/article/pii/S266732582200139X |
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