A Nonlinear Mechanical Model for Extensible Slender Rods

MA Gang; SUN Li-ping; AI Shang-mao; WANG Hong-wei

doi:10.3879/j.issn.1000-0887.2015.04.004

Volume 36 Issue 4

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MA Gang, SUN Li-ping, AI Shang-mao, WANG Hong-wei. A Nonlinear Mechanical Model for Extensible Slender Rods[J]. Applied Mathematics and Mechanics, 2015, 36(4): 371-377. doi: 10.3879/j.issn.1000-0887.2015.04.004

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A Nonlinear Mechanical Model for Extensible Slender Rods

doi: 10.3879/j.issn.1000-0887.2015.04.004

College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, P.R.China

Funds: The National Natural Science Foundation of China;The National Basic Research Program of China (973 Program)

Received Date: 2014-09-24
Rev Recd Date: 2014-12-01
Publish Date: 2015-04-15

Abstract

Abstract

The polyester mooring line is a flexible rod liable to axial extension and bending deformation. Due to its large axial deformation in tension, the polyester line’s deformed configurations shall be distinguished from the undeformed ones, and the slender rod model based on the small extension hypothesis shall be improved in view of its nonnegligible length change. The global coordinates and slopes were used to replace the rotation angles in the Euler-Bernoulli beam to deal with the geometrically nonlinear problem of large spatial rotation based on Garrett’s slender rod theory. Then the point-to-point mapping method was proposed to correlate the 2 configurations before and after axial extension in the slender rod theory, with 2 element nodes, 1 intermediate point and 3 quadratic polynomial combined to derive the differential equations of motion for the slender rod element in tension. Through comparison between the numerical results and the analytical solution of an extensible cantilever beam example, convergence and accuracy of the proposed model are proved.
- axial extension,
- slender rod,
- nonlinear,
- polyester line,
- large rotation

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References(15)

References

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