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Mechanics in Engineering ›› 2020, Vol. 42 ›› Issue (1): 85-91.doi: 10.6052/1000-0879-19-176

• Research on Education • Previous Articles     Next Articles

FROM FINITENESS TO INFINITY: DERIVING THE CATENARY EQUATION AND THE BEAM DISPLACEMENT EQUATION BASED ON THE DISCRETE STATIC EQUILIBRIUM MODEL

LUO Wenying1)   

  1. School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
  • Received:2019-05-05 Published:2020-03-13

Abstract: The catenary problem is a very classical mechanical problem. There are many methods to derive the catenary equation from static equilibrium methods to variational principles. This paper establishes and solves the catenary equation based on the discrete static equilibrium model. Furthermore, this paper establishes a discrete static equilibrium model with torsion spring, then derives and solves the beam displacement equation. In the end, the beam displacement equations with different parameters are solved to obtain the gradual solution, and the existence of various equilibrium states is analyzed.

Key words: static equilibrium, catenary curve, beam

CLC Number: 

  • O312