PSI - Issue 14

Saurabh Zajam et al. / Procedia Structural Integrity 14 (2019) 712–719 Saurabh Zajam et al./ Structural Integrity Procedia 00 (2018) 000–000

714

3

  0, w t  w l t    , 0, xx w t    , , 0 xx w l t    , 0

0

(2) (3) (4)

0

(5) Boundary conditions (2) and (3) corresponds to zero transverse displacement at both ends, and boundary conditions (4) and (5) corresponds to zero moment at both ends. Here, we also have two initial conditions:   , 0 0 w x  (6)   , , 0 0 t w x  (7) Initial condition (6) implies that there no initial deflection at any section of pipe, and initial condition (7) signifies that there is no initial velocity in transverse direction at any section of pipe. The solution of this equation gives response of the system. The detailed solution is presented by Hagedorn and DasGupta (2007) as follows:

2

   

   

j v

 

3

2

1

Fl

j v 

j vt 

j x 

 

  

  

j

(8)

( , )

sin

sin

sin

w x t 

t





j 

4

EI

l

l

l

l



 

  

2 Al v

2



1 2 2 j j

j



 

2

EI



1.2 Finite Element Approach The Finite Element model of the healthy pipe with moving load is developed in ANSYS 17 workbench to obtain the acceleration response of the system. The model is setup by coupling modal analysis module and transient structural analysis module in ANSYS. Since the damping in steel is very less (damping coefficient less than 0.01), structural damping is neglected while solving analytically as well as in ANSYS model. Simply supported ends and fixed ends are used in future analysis. Eight nodded linear hexahedron solid elements are used for meshing pipe. 1.3 Comparison of transient acceleration obtained from analytical and FEM approach The midpoint acceleration for moving load of 500N with velocity of 0.5 m/s is shown in figure 2. The FEM results are consistent with the analytical results for healthy pipe system. Hence, we can use this FEM model for damaged pipe system too.

(a) Analytical solution for 0.5 m/ s (b) FEM solution (ANSYS) for 0.5 m/s Figure 2: Acceleration of midpoint of pipe in vertical direction obtained analytically and by FE (ANSYS) for 500N load moving