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
Made with FlippingBook - Online catalogs