Forces and Moments Calculation
Integration Points Throughout the Thickness
Coefficients | w1 | w2 | w3 |
---|---|---|---|
Radioss | 0.250 | 0.500 | 0.250 |
Simpson | 0.166 | 0.666 | 0.166 |
Coefficients | w1 | w2 | w3 |
---|---|---|---|
Radioss | -0.083 | 0. | 0.083 |
Simpson | -0.083 | 0. | 0.083 |
Number of Points | Position | Weight |
---|---|---|
1 | ±0.0000 | 2.0000 |
2 | ±0.5774 | 1.0000 |
3 | 0.0000 ±0.7746 |
0.8889 0.5556 |
4 | ±0.8611 ±0.3400 |
0.6521 0.3479 |
5 | ±0.9062 ±0.5385 0.0000 |
0.2369 0.4786 0.5689 |
6 | ±0.9325 ±0.6612 ±0.2386 |
0.1713 0.3608 0.4679 |
7 | ±0.9491 ±0.7415 ±0.4058 0.0000 |
0.1295 0.2797 0.3818 0.4180 |
8 | ±0.9603 ±0.7967 ±0.5255 ±0.1834 |
0.1012 0.2224 0.3137 0.3627 |
9 | ±0.9681 ±0.8360 ±0.6134 ±0.3243 0.0000 |
0.0813 0.1806 0.2606 0.3123 0.3302 |
10 | ±0.9739 ±0.8650 ±0.6794 ±0.4334 ±0.1489 |
0.0667 0.1495 0.2191 0.2693 0.2955 |
Number of Points | Position | Weight for Membrane wN |
Weight for Bending wM |
---|---|---|---|
1 | 0.0000 | 1.0000 | 0.0000 |
2 | ±0.5000 | 0.5000 | ±0.0833 |
3 | ±0.5000 0.0000 |
0.2500 0.5000 |
±0.0833 0.0000 |
4 | ±0.5000 ±0.1667 |
0.1667 0.3333 |
±0.0648 ±0.0556 |
5 | ±0.5000 ±0.2500 0.0000 |
0.1250 0.2500 0.2500 |
±0.0521 ±0.0625 0.0000 |
6 | ±0.5000 ±0.3000 ±0.1000 |
0.1000 0.2000 0.2000 |
±0.0433 ±0.0600 ±0.0200 |
7 | ±0.500 ±0.3333 ±0.1667 0.0000 |
0.0833 0.1667 0.1667 0.1667 |
±0.0370 ±0.0556 ±0.0278 0.0000 |
8 | ±0.5000 ±0.3750 ±0.2500 ±0.1250 |
0.0714 0.1429 0.1429 0.1429 |
±0.0323 ±0.0510 ±0.0306 ±0.0102 |
9 | ±0.5000 ±0.3750 ±0.2500 ±0.1250 0.0000 |
0.0625 0.1250 0.1250 0.1250 0.1250 |
±0.086 ±0.0469 ±0.0313 ±0.0156 0.0000 |
10 | ±0.5000 ±0.3889 ±0.2778 ±0.1667 ±0.0555 |
0.0556 0.1111 0.1111 0.1111 0.1111 |
±0.0257 ±0.0432 ±0.0309 ±0.0185 ±0.0062 |
For shell elements, integration points through the thickness are almost Lobatto points.
Global Plasticity Algorithm
Where, and are scalar material characteristic constants, function of plastic deformation. They can be identified by the material hardening law in pure traction and pure bending.
If no hardening law in pure bending is used, is simply computed by varying between 1.0 and 1.5.
Where, is the plastic module. The derivative of function in 式 7 is discontinuous when =0. This can be treated when small steps are used by putting s=0 as explained in 2.