PSI - Issue 5

Behzad V. Farahani et al. / Procedia Structural Integrity 5 (2017) 584–591 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2017) 000 – 000

589

6

relative error is determined as = ‖ ̅− ‖ .

(a)

(b)

Fig. 1. A Mindlin plate: (a) geometry and degrees of freedom demonstration and (b) a regular 10-by-10 nodal distribution.

0,0043

-0,01 0 0,01 0,02 0,03 0,04 0,05 0,06

0,0042

w max

0,0041

Error

Exact RBF

0,0040

0

1000

2000

3000

0

1000

2000

3000

Number of nodes

Number of nodes

(a) (b) Fig. 2. Obtained RBF results in terms of total number of nodes if = 2⁄√ , (a) maximum transverse displacement and (b) relative error. Considering the present optimal shape parameter, Equation (20) and selecting a regular distribution consisting of 361 nodes ( = 24 ), Fig. 3-a shows the maximum transverse displacement variation obtained from RBF analysis assuming several distinct values ( ∈ [1.5,5] ) in comparison with the exact solution. Besides, the relative error correlated with the several k values was evaluated as seen in Fig. 3-b.

0,00428

0,004

0,003

0,00427

0,002

w max

0,00426

Error

0,001

Exact RBF

0

0,00425

0

2

4

6

0

2

4

6

k

k

(a) (b) Fig. 3. RBF results when = 24 and the optimal shape parameter is present, (a) ̅ versus k and (b) the relative error correlated with k . Choosing a definite k value, k = 1.75, the maximum transverse displacement was computed for distinct mesh