PSI - Issue 52

J.C. Wen et al. / Procedia Structural Integrity 52 (2024) 625–646 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

643 19

/ a 

1 10 −

2 10 −

3 10 −

4 10 −

5 10 −

I 0 / K

1.9428

1.8407

1.8341

1.8332

1.8331

a  

M

Fig. 5. Normalized stress intensity factors in homogeneous plate vs the number of Chebyshev polynomial.

R

Fig. 6. Normalized stress intensity factors in homogeneous plate vs the different integral paths with a circle of radius R .

5.2. Chen's problem

For the problem with dynamic loadings, we consider a rectangular plate of width 2 b and length 2 h with a centrally located crack of length 2 a as shown in Fig. 4. Chen (1975) investigated it firstly by using FEM with the homogenous media. A dynamic load with step function 0 ( ) H t  is applied on the top and bottom perpendicularly to the crack surface, here ( ) H t is the Heaviside function. The dimensional parameters are selected as / 2 h w = and / 0.24 a w = . The velocity of the longitudinal wave is defined as   1/2 1 0 0 (1 )/ (1 )(1 2) c E     = − + − . The initial conditions are zeros in the domain at 0 t = . Following the suggestions from Durbin and Wen et al, the number of sample points in Laplace space is 1 26 K + = and 5/ T  = , where observation time is 0 20 T t = with the time unit

0 t h c = . Comparisons of the dynamic stress intensity factors solution by Chen (1975) are shown in Fig. 11 for homogenous. 1 /

a   with different paths ( R ) and FEM

0 ( ) / I K t