TY - JOUR
T1 - Mathematical modeling of linearly-elastic non-prestrained cables based on a local reference frame
AU - Tang, H. B.
AU - Han, Y.
AU - Fu, H.
AU - Xu, B. G.
N1 - Funding Information:
This work was supported by National Key Research and Development Program of China (No. 2018YFB1105304 ) and China Postdoctoral Science Foundation (No. 2013M542306 ). The authors greatly appreciate the financial support for this work.
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2021/3
Y1 - 2021/3
N2 - Cables are widely used and serve different purposes in engineering. This paper aims to formulate a general dynamic model on extensible non-prestrained cables under external forces. In terms of the Hamilton's principle, the governing equation and boundary conditions are achieved according to the variation of action integral. Meanwhile, the local reference frame of the cable curve is illustrated which is composed of four vectors. In the presented model, it is shown that the external force along the binormal direction could not be balanced by the internal tensile force of the cable itself. And the curved cable will result in an elastic force in the normal direction which is in a linear relationship with the curvature of the cable. Further, this approach is applied to cables under uniformly distributed loads or self-weights. The contours and internal tensile forces of the cables are figured out by means of numerical methods. The developed model is evaluated by means of experimental data in published literature. The good agreement between the numerical and experimental results shows that the presented method is feasible in theory.
AB - Cables are widely used and serve different purposes in engineering. This paper aims to formulate a general dynamic model on extensible non-prestrained cables under external forces. In terms of the Hamilton's principle, the governing equation and boundary conditions are achieved according to the variation of action integral. Meanwhile, the local reference frame of the cable curve is illustrated which is composed of four vectors. In the presented model, it is shown that the external force along the binormal direction could not be balanced by the internal tensile force of the cable itself. And the curved cable will result in an elastic force in the normal direction which is in a linear relationship with the curvature of the cable. Further, this approach is applied to cables under uniformly distributed loads or self-weights. The contours and internal tensile forces of the cables are figured out by means of numerical methods. The developed model is evaluated by means of experimental data in published literature. The good agreement between the numerical and experimental results shows that the presented method is feasible in theory.
KW - Extensible non-prestrained cable
KW - Local reference frame
KW - Mathematical modeling
KW - The Hamilton's principle
UR - http://www.scopus.com/inward/record.url?scp=85092921072&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2020.10.008
DO - 10.1016/j.apm.2020.10.008
M3 - Journal article
AN - SCOPUS:85092921072
SN - 0307-904X
VL - 91
SP - 695
EP - 708
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
ER -