108
J. Chen et al.
l
Symmetrica
l
Symmetrica
Fixed
Fixed
y
α 2 =
x
α 1 =
Indicator
Fig. 10. Model and irregular mesh for the square plate
Table 1. ˜
w with different d /l for the square plate
1 × 10 −3
1 × 10 −4
1 × 10 −5
1 × 10 −6
1 × 10 −7
1 × 10 −8
4 × 4
0.1510
0.1504
0.1504
0.1504
0.1504
0.1497
8 × 8
0.1509
0.1505
0.1505
0.1505
0.1505
0.1499
16 × 16
0.1509
0.1505
0.1505
0.1505
0.1505
0.1500
Table 2. Condition number of matrix K with different d /l for the square plate
1 × 10 −4
1 × 10 −5
1 × 10 −6
1 × 10 −7
4 × 4
1.2048 × 10 12
1.1820 × 10 13
1.1157 × 10 14
1.2211 × 10 15
8 × 8
7.8388 × 10 14
7.7621 × 10 15
7.8440 × 10 16
7.8536 × 10 17
16 × 16
4.9574 × 10 15
4.9576 × 10 16
4.9590 × 10 17
4.9624 × 10 18
Table 3 lists ˜
w with different H /L, which shows that the SEIA is locking free to the
thin limit of engineering structures (H /L = 1 × 10 −4 ). The SEIA provides satisfactory
results for thick/thin plates and is insensitive to element distortion, such as the irregular
mesh in Fig. 10.