An explicit nonlinear model for large spatial deflections of symmetric slender beams

Chen, Yuhan1,2; Yao, Shilong2; Liu, Li3,4; Meng, Max Q. -H.2

2024-12-01

10.1016/j.ijnonlinmec.2024.104910

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS   影响因子和分区

0020-7462

1878-5638

Flexible slender beams are commonly used in compliant mechanisms and continuum robots. However, the modeling of these beams can be complicated due to the geometric nonlinearity becoming significant at large elastic deflections. This paper presents an explicit nonlinear model for large spatial deflections of a slender beam with uniform, symmetrical sections subjected to general end-loading. The elongation, bending, torsion, and shear deformations of the beams are modeled based on Timoshenko's assumptions and Cosserat rod theory. Subsequently, the nonlinear governing differential equations for the beam are derived from the quaternion representation of the rotation matrix. The explicit load-displacement relations of the beam are obtained using the improved Adomian decomposition method. This method is superior to the classical Adomian decomposition method in terms of convergence rate and domain. The convergence and superiority of the method are also rigorously demonstrated. Simulations are provided to verify the one-, two-, and three-dimensional deflections of beams. Real-world experiments have also been performed to validate our method's effectiveness with two different beam configurations. The results indicate that the proposed method accurately estimates large spatial deflections of flexible beams.

Large spatial deflection Symmetric beams Compliant mechanism Quaternion Adomian polynomials

SCI

英语

通讯

Shenzhen Key Laboratory of Robotics Perception and Intelligence[ZDSYS2020081017 1800001] ; Fundamental Research Funds for the Central Universities[DUT24RC (3) 099] ; Hong Kong RGC GRF["14220622","14204321"]

Mechanics

Mechanics

WOS:001322223300001

PERGAMON-ELSEVIER SCIENCE LTD

Web of Science

1.Dalian Univ Technol, Inst Robot & Intelligent Syst, Dalian 116024, Liaoning, Peoples R China
2.Southern Univ Sci & Technol, Dept Elect & Elect Engn, Shenzhen 518055, Guangdong, Peoples R China
3.Great Bay Univ, Sch Engn, Dongguan 523000, Guangdong, Peoples R China
4.Chinese Univ Hong Kong, Dept Elect Engn, Hong Kong 999077, Peoples R China

Chen, Yuhan,Yao, Shilong,Liu, Li,et al. An explicit nonlinear model for large spatial deflections of symmetric slender beams[J]. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS,2024,167.

Chen, Yuhan,Yao, Shilong,Liu, Li,&Meng, Max Q. -H..(2024).An explicit nonlinear model for large spatial deflections of symmetric slender beams.INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS,167.

Chen, Yuhan,et al."An explicit nonlinear model for large spatial deflections of symmetric slender beams".INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 167(2024).