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Ex​amples

Annulus Quarter

For better presentation this example can be broken into 6 main parts.
Part 1. Geometry Definition
Problem type: 3D-Plane stress
(a) Initial mesh.
(b) Fine mesh.
Table 1. ​​​Control point number per axis and polynomial degree definition.
Table 2. Geometry.
(a) Initial mesh.
(b) Fine mesh.
Table 3. control point variables (cartesian coordinates and weights of control points).​​
Part 2. Meshing
Knot value vectors (initial mesh):
Knot value vectors (fine mesh):
Part 3. Material
The material is steel with:
Part 4. Boundary Conditions
(a) Initial mesh.
(b) Fine mesh.
Table 4. Boundary conditions. The “1” indicates supported degree of freedom.
Part 5. Loading Conditions
(a) Initial mesh.
(b) Fine mesh.
Table 5. Loading conditions.
Part 6. Post-Processing

BSPLine Basis Function

NURBS Shape Function

Index Space

(a) Initial mesh.
(b) Fine mesh.
Figure 3. Index space.​​​

Parameter Space

(a) Initial mesh.
(b) Fine mesh.
Figure 4. Parameter space.​​​

Physical Space

(a) Initial mesh.
(b) Fine mesh.
Figure 5. Physical space.​​​

Stiffness Matrix

(a) Initial mesh.
(b) Fine mesh.
Table 6. Stiffness matrix.​​​
Figure 6. Stiffness matrix.​​​

PseudoDisplacement

(a) Initial mesh.
(b) Fine mesh.
Table 7. PseudoDisplacement.​​​

Displacement Field

(a) Initial mesh.
(b) Fine mesh.
Table 8. Gauss point displacement.
Figure 7. Contour. Displacement field.​​​

Strain Field

(a) Initial mesh.
(b) Fine mesh.
Table 9. Gauss point strain.
Figure 8. Contour. Strain field.​​​

Stress FIeld

(a) Initial mesh.
(b) Fine mesh.
Table 10. Gauss point stress.
(a) Initial mesh.
(b) Fine mesh.
Table 11. Norm.
Figure 9. Contour. Stress field.​​​
​​Example 8. The quarter of the annulus . 3D NURBS model.