Relative Displacement Method for Track-Structure Interaction

Algorithm 1

𝜎_rail,𝑛=const

𝑢₁=const

𝑁_rail,0=0

While 𝜎_rail,𝑛−𝜎_rail,𝑛≠0 do

   For 𝑖=1 to 𝑛 do:

     𝜎_rail,𝑖=𝑁_{rail,𝑖−1}−𝐹_long,𝑖−𝐹_ballast𝑢_𝑖𝐴_rail

     𝜎_deck,𝑖=𝑁_{deck,𝑖−1}−𝐹_pier,𝑖+𝐹_ballast𝑢_𝑖𝐴_deck

     𝜀_rail,𝑖=𝜎_rail,𝑖𝐸_rail+𝜀^′_rail,𝑖

     𝜀_deck,𝑖=𝜎_deck,𝑖𝐸_deck+𝜀^′_deck,𝑖

     𝑢_𝑖+1=𝑢_𝑖+𝜀_rail,𝑖−𝜀_deck,𝑖⋅𝐿

   End For

   change 𝑢₁ to minimise 𝜎_rail,𝑛−𝜎_rail,𝑛

End While