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# Finite Element Nonlinear Analysis for Catenary Structure Considering Elastic Deformation

B.W. Kim1, H.G. Sung1, S.Y. Hong1, H.J. Jung2
KORDI/MOERI, Daejeon, Korea
KAIST, Daejeon, Korea

Computer Modeling in Engineering & Sciences 2010, 63(1), 29-46. https://doi.org/10.3970/cmes.2010.063.029

### Abstract

This paper numerically investigates the behavior of sag and tension of inclined catenary structure considering elastic deformation. Equilibrium equation for computing elastic catenary is formulated by employing finite element method (FEM). Minimum potential energy principle and the Lagrange multiplier method are used in the formulation to derive equilibrium equation with constraint condition for catenary length. Since stiffness and loading forces of catenary are dependent on its own geometry, the equilibrium equation is nonlinear. Using the iterative scheme such as fixed point iteration or bisection, equilibrium position and tension are found. Based on the formulation, a Fortran solver is developed in this study. With the solver, numerical analyses for example catenary structures are carried out. From the numerical examples, the sag and tension of catenary only which ignores elastic deformation are compared with those of elastic catenary of which elastic deformation is considered. By analyzing elastic catenary for various axial stiffness conditions, the asymptotic behaviors of sag and tension are examined. Inclined catenary structures with various slopes are also analyzed to study the effect of catenary slope on sag and tension.

### Keywords

Catenary, Elastic deformation, FEM, Length constraint, Sag, Tension, Catenary slope.

Kim, B., Sung, H., Hong, S., Jung, H. (2010). Finite Element Nonlinear Analysis for Catenary Structure Considering Elastic Deformation. CMES-Computer Modeling in Engineering & Sciences, 63(1), 29–46. This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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