PSI - Issue 13

Yinghao Dong et al. / Procedia Structural Integrity 13 (2018) 1714–1719 Yinghao Dong, Xiaofan He, Yuhai Li / Structural Integrity Procedia 00 (2018) 000–000 Yinghao Dong, Xiaofan He, Yuhai Li / Structural Integrity Procedia 00 (2018) 000–000 Yinghao Dong, Xiaofan He, Yuhai Li / Structural Integrity Procedia 00 (2018) 000–000

5 5 5

1718

Table 1. Values of I n , i , j , k and J n , i , j , k ( n = 0 , 1 , 2 , i = 1 , 2 , 3 , 4 , j = 0 , 1 , 2 , k = 1 , 2 , 3). Table 1. Values of I n , i , j , k and J n , i , j , k ( n = 0 , 1 , 2 , i = 1 , 2 , 3 , 4 , j = 0 , 1 , 2 , k = 1 , 2 , 3). Table 1. Values of I n , i , j , k and J n , i , j , k ( n = 0 , 1 , 2 , i = 1 , 2 , 3 , 4 , j = 0 , 1 , 2 , k = 1 , 2 , 3). n i j I n , i , j , 1 I n , i , j , 2 I n , i , j , 3

J n , i , j , 1 J n , i , j , 1 J n , i , j , 1

J n , i , j , 2 J n , i , j , 2 J n , i , j , 2

J n , i , j , 3 J n , i , j , 3 J n , i , j , 3

n i n i

j j

I n , i , j , 1 I n , i , j , 1

I n , i , j , 2 I n , i , j , 2

I n , i , j , 3 I n , i , j , 3

1 0 6.05281e-01 4.06136e-01 6.59152e + 00 2.93491e + 00 3.66789e + 01 -8.70259e + 00 1 1.25257e + 00 -4.46256e-01 8.20739e + 00 -1.73401e + 00 -3.42936e + 01 -8.61888e + 00 2 -3.76915e-01 1.69790e-01 9.32044e + 00 5.31129e-01 8.38157e + 00 -8.67557e + 00 2 0 7.07008e-01 -4.68669e-01 6.36744e + 00 -1.24403e + 00 -2.62991e + 01 -8.35147e + 00 1 -9.74474e-01 4.88485e-01 8.07768e + 00 1.44289e + 00 2.38236e + 01 -8.14457e + 00 2 3.28320e-01 -1.66086e-01 9.38853e + 00 -4.64606e-01 -5.43668e + 00 -8.01931e + 00 3 0 8.68342e-01 -4.95713e-01 6.27353e + 00 -1.51251e + 00 -3.43834e + 01 -8.61775e + 00 1 -1.28031e + 00 5.00052e-01 8.04576e + 00 1.75898e + 00 3.26345e + 01 -8.76110e + 00 2 3.80868e-01 -1.77189e-01 9.28950e + 00 -5.69665e-01 -8.70497e + 00 -9.54143e + 00 4 0 -3.13214e-01 2.17121e-01 6.41704e + 00 4.62811e-01 1.01036e + 01 -8.59297e + 00 1 3.67050e-01 -2.14159e-01 8.23605e + 00 -5.64346e-01 -1.04316e + 01 -9.19628e + 00 2 -1.25638e-01 6.73135e-02 9.67030e + 00 1.84080e-01 3.33767e + 00 -1.11001e + 01 1 0 -2.50171e-01 -3.96516e-01 7.10748e + 00 -2.81305e + 00 -4.84470e + 01 -8.83822e + 00 1 -1.33987e + 00 4.46840e-01 8.67229e + 00 2.27110e + 00 4.79366e + 01 -8.63392e + 00 2 4.18358e-01 -1.73315e-01 9.72928e + 00 -7.70018e-01 -1.22294e + 01 -8.50150e + 00 2 0 -7.42390e-01 4.62930e-01 6.85702e + 00 1.48868e + 00 3.66938e + 01 -8.52923e + 00 1 1.08826e + 00 -4.92058e-01 8.53302e + 00 -1.92243e + 00 -3.54173e + 01 -8.22128e + 00 2 -3.66074e-01 1.71341e-01 9.78790e + 00 6.85622e-01 8.62271e + 00 -7.94291e + 00 3 0 -9.00307e-01 4.91724e-01 6.74311e + 00 1.75076e + 00 4.53266e + 01 -8.76335e + 00 1 1.39047e + 00 -5.02684e-01 8.49829e + 00 -2.25991e + 00 -4.57049e + 01 -8.79190e + 00 2 -4.21678e-01 1.80878e-01 9.70042e + 00 8.11740e-01 1.25804e + 01 -9.27726e + 00 4 0 3.44789e-01 -2.20305e-01 6.87238e + 00 -5.67731e-01 -1.44240e + 01 -8.84043e + 00 1 -4.08347e-01 2.17927e-01 8.69586e + 00 7.52573e-01 1.58118e + 01 -9.28990e + 00 2 1.37552e-01 -6.98056e-02 1.00893e + 01 -2.69322e-01 -5.06242e + 00 -1.06020e + 01 1 0 4.87391e-02 5.15703e-02 8.38799e + 00 5.05530e-01 7.12799e + 00 -7.86947e + 00 1 2.25248e-01 -6.37934e-02 9.76265e + 00 -4.69506e-01 -6.70677e + 00 -7.51528e + 00 2 -7.58474e-02 2.58712e-02 1.06866e + 01 1.65378e-01 1.64778e + 00 -7.30128e + 00 2 0 9.44616e-02 -5.97423e-02 8.15883e + 00 -2.87345e-01 -4.96333e + 00 -7.19481e + 00 1 -1.68997e-01 6.87304e-02 9.68384e + 00 3.92187e-01 4.42199e + 00 -6.60329e + 00 2 6.34465e-02 -2.50056e-02 1.08186e + 01 -1.45462e-01 -9.83411e-01 -5.98815e + 00 3 0 1.34242e-01 -7.00061e-02 7.79662e + 00 -3.45052e-01 -6.40361e + 00 -7.73084e + 00 1 -2.32925e-01 7.42654e-02 9.49935e + 00 4.80564e-01 6.11051e + 00 -7.74295e + 00 2 7.44675e-02 -2.71376e-02 1.06448e + 01 -1.83973e-01 -1.65794e + 00 -8.57786e + 00 4 0 -4.22885e-02 2.69554e-02 8.33553e + 00 1.19618e-01 1.98448e + 00 -7.78115e + 00 1 5.39847e-02 -2.81318e-02 1.00725e + 01 -1.71183e-01 -2.18579e + 00 -8.57245e + 00 2 -2.05840e-02 9.41426e-03 1.13529e + 01 6.23358e-02 7.33594e-01 -1.06071e + 01 1 0 6.05281e-01 4.06136e-01 6.59152e + 00 2.93491e + 00 3.66789e + 01 -8.70259e + 00 1 1.2 57 + 0 -4.46256e-01 8.20739e -1.73401e + -3.42936e + 01 61888 2 -3.76915e- 1 1.69790 9.32044e 5 31129 -01 8.38157 0 7557e 2 0 7.07008 - -4.68669e-01 6 67 -1 24403 + 00 -2.62991 1 3514 1 -9.74474 -01 .8 485 8 07 68 .4 289 00 .38236 1445 2 3.28320e-01 -1.660 6 9 38853 -4.64606e- 1 -5.43668e 0 8 01931e 3 0 8 6 42 4 95713 6 273 1.51251 + 0 3 834 1 6 775 1 -1.28031e + 00 5.00052 8 04576 .75898 00 .26345 76110 2 3 80868 -01 -1.77189e-01 9 28950 -5.69665e- 1 -8.70497e + 00 9.54143e 0 4 0 -3.13214e-01 2.1 21 6 41704 4. 2811 - 1.01036 1 8 9297 1 .67050 - -2.14159e-01 8 236 5 -5.64346e-01 -1.04316e + 01 9.19628e 0 2 -1.25638 - 6.73 35 2 9 67030 1.8 080 - 3.33767 0 1 1001 1 1 0 -2.50171e-01 -3.96516e-01 7.10748e + 00 -2.81305e + 00 -4.84470e + 01 -8.83822e + 00 1 1.33987 + 0 4.4 840 8 67229 .27110 00 .79366 6 39 2 4 18358 -01 -1.73315e-01 9 729 8 -7. 0018e-01 -1.22294e + 01 -8.50150e 2 0 -7.42 90 -01 4.62930 6 85702 1.48868e + 0 3.66938 2923 + 00 1 1.08826e + 0 -4.92058e-01 8 533 -1.92243e + -3.54173e + 01 2 1 8 2 -3.66074e-01 1.71341 9.78790 6 85622 -01 8.622 1 0 -7.94291e + 00 3 0 9 00307 4 9 724 6 4311 1.7 076 + 0 4 53 66 1 8 76335 1 1.39047e + 0 -5.02684e-01 8 49829 -2.25991e + -4.57049e + 01 - 79190 + 0 2 -4.216 8e- 1 1.80878 9.70042e + 00 8 11740 -01 1.25804 9 27726e 0 4 0 3.44789 -2.20305e-01 6 87238 -5.67731e-01 -1.44240e + 01 8.84043 1 -4.08347e-01 .17927 8 69586 7.52573 .58118 9 28990 2 1.37552 -6.98056 - 2 1 00893 1 -2.69322 - -5.06242 0 1 0602 1 1 0 4.87391e-02 5.15703e-02 8.38799e + 00 5.05530e-01 7.12799e + 00 -7.86947e + 00 1 2 25248 1 -6.37934e-02 9 76265 -4.69506e-01 -6.70677e + 00 51528 2 -7.58474e-02 2.58712 1.06866 + 01 1. 5378 1.647 8 -7.30128e 2 0 9.44616 -5.97423e-02 8 15 83 0 -2.87345e-01 -4.96333e + 00 19481 1 -1.68997e-01 6.8 304 9 683 4 3.92187 .42199 00 -6.60329e + 00 2 6.34465e-02 -2.50056 - 1 0 1 6 1 -1.45462 - -9.83411e- 1 5 98815 3 0 1 242 1 7 0 61 7 79662 0 3 05 6.4036 + 0 7 73084e + 00 1 -2.32925e-01 .42654 9 4 935 4.80564 .1105 4295 2 7.4467 2 -2.71376e-02 1 06448 1 -1.83973e-01 -1.65794e + 00 8 57786e + 00 4 0 -4.22885e-02 .69554 8 33553 0 .19618 .98448 7 78115 1 5.39 47 -2.81318e-02 1 00725 1 -1.71183e-01 -2.18579e + 8 5724 00 2 -2.05 0 - 9.4 426 3 135 9 6.23358 2 7 33 94 -01 1 06071 1 1 0 6.05281e-01 4.06136e-01 6.59152e + 00 2.93491e + 00 3.66789e + 01 -8.70259e + 00 1 1.25257e + 00 -4.46256e-01 8.20739e + 00 -1.73401e + 00 -3.42936e + 01 -8.61888e + 00 2 -3.76915e-01 1.69790e-01 9.32044e + 00 5.31129e-01 8.38157e + 00 -8.67557e + 00 2 0 7.07008e-01 -4.68669e-01 6.36744e + 00 -1.24403e + 00 -2.62991e + 01 -8.35147e + 00 1 -9.74474e-01 4.88485e-01 8.07768e + 00 1.44289e + 00 2.38236e + 01 -8.14457e + 00 2 3.28320e-01 -1.66086e-01 9.38853e + 00 -4.64606e-01 -5.43668e + 00 -8.01931e + 00 3 0 8.68342e-01 -4.95713e-01 6.27353e + 00 -1.51251e + 00 -3.43834e + 01 -8.61775e + 00 1 -1.28031e + 00 5.00052e-01 8.04576e + 00 1.75898e + 00 3.26345e + 01 -8.76110e + 00 2 3.80868e-01 -1.77189e-01 9.28950e + 00 -5.69665e-01 -8.70497e + 00 -9.54143e + 00 4 0 -3.13214e-01 2.17121e-01 6.41704e + 00 4.62811e-01 1.01036e + 01 -8.59297e + 00 1 3.67050e-01 -2.14159e-01 8.23605e + 00 -5.64346e-01 -1.04316e + 01 -9.19628e + 00 2 -1.25638e-01 6.73135e-02 9.67030e + 00 1.84080e-01 3.33767e + 00 -1.11001e + 01 1 0 -2.50171e-01 -3.96516e-01 7.10748e + 00 -2.81305e + 00 -4.84470e + 01 -8.83822e + 00 1 -1.33987e + 00 4.46840e-01 8.67229e + 00 2.27110e + 00 4.79366e + 01 -8.63392e + 00 2 4.18358e-01 -1.73315e-01 9.72928e + 00 -7.70018e-01 -1.22294e + 01 -8.50150e + 00 2 0 -7.42390e-01 4.62930e-01 6.85702e + 00 1.48868e + 00 3.66938e + 01 -8.52923e + 00 1 1.08826e + 00 -4.92058e-01 8.53302e + 00 -1.92243e + 00 -3.54173e + 01 -8.22128e + 00 2 -3.66074e-01 1.71341e-01 9.78790e + 00 6.85622e-01 8.62271e + 00 -7.94291e + 00 3 0 -9.00307e-01 4.91724e-01 6.74311e + 00 1.75076e + 00 4.53266e + 01 -8.76335e + 00 1 1.39047e + 00 -5.02684e-01 8.49829e + 00 -2.25991e + 00 -4.57049e + 01 -8.79190e + 00 2 -4.21678e-01 1.80878e-01 9.70042e + 00 8.11740e-01 1.25804e + 01 -9.27726e + 00 4 0 3.44789e-01 -2.20305e-01 6.87238e + 00 -5.67731e-01 -1.44240e + 01 -8.84043e + 00 1 -4.08347e-01 2.17927e-01 8.69586e + 00 7.52573e-01 1.58118e + 01 -9.28990e + 00 2 1.37552e-01 -6.98056e-02 1.00893e + 01 -2.69322e-01 -5.06242e + 00 -1.06020e + 01 1 0 4.87391e-02 5.15703e-02 8.38799e + 00 5.05530e-01 7.12799e + 00 -7.86947e + 00 1 2.25248e-01 -6.37934e-02 9.76265e + 00 -4.69506e-01 -6.70677e + 00 -7.51528e + 00 2 -7.58474e-02 2.58712e-02 1.06866e + 01 1.65378e-01 1.64778e + 00 -7.30128e + 00 2 0 9.44616e-02 -5.97423e-02 8.15883e + 00 -2.87345e-01 -4.96333e + 00 -7.19481e + 00 1 -1.68997e-01 6.87304e-02 9.68384e + 00 3.92187e-01 4.42199e + 00 -6.60329e + 00 2 6.34465e-02 -2.50056e-02 1.08186e + 01 -1.45462e-01 -9.83411e-01 -5.98815e + 00 3 0 1.34242e-01 -7.00061e-02 7.79662e + 00 -3.45052e-01 -6.40361e + 00 -7.73084e + 00 1 -2.32925e-01 7.42654e-02 9.49935e + 00 4.80564e-01 6.11051e + 00 -7.74295e + 00 2 7.44675e-02 -2.71376e-02 1.06448e + 01 -1.83973e-01 -1.65794e + 00 -8.57786e + 00 4 0 -4.22885e-02 2.69554e-02 8.33553e + 00 1.19618e-01 1.98448e + 00 -7.78115e + 00 1 5.39847e-02 -2.81318e-02 1.00725e + 01 -1.71183e-01 -2.18579e + 00 -8.57245e + 00 2 -2.05840e-02 9.41426e-03 1.13529e + 01 6.23358e-02 7.33594e-01 -1.06071e + 01

0 0 0

1 1 1

2 2 2

(a) (a) (a)

(b) (b) (b)

Fig. 3. Variation of the maximum error in Eq. (2) with t / W , c / a and a / t ; (a) t / W = 0 . 125 and (b) t / W = 0 . 45; 1 . 0 ≤ c / a ≤ 5 . 0 and a / ( lt ) ≤ 0 . 8. Fig. 3. Variation of the maximum error in Eq. (2) with t / W , c / a and a / t ; (a) t / W = 0 . 125 and (b) t / W = 0 . 45; 1 . 0 ≤ c / a ≤ 5 . 0 and a / ( lt ) ≤ 0 . 8. Fig. 3. Variation of the maximum error in Eq. (2) with t / W , c / a and a / t ; (a) t / W = 0 . 125 and (b) t / W = 0 . 45; 1 . 0 ≤ c / a ≤ 5 . 0 and a / ( lt ) ≤ 0 . 8.