Product: ABAQUS/Standard
B21 B21H B22 B22H B23 B23H B31 B31H B31OS B31OSH B32 B32H B32OS B32OSH B33 B33H
PIPE21 PIPE21H PIPE22 PIPE22H PIPE31 PIPE31H PIPE32 PIPE32H
Linear elastic, Young's modulus = 30 × 106, Poisson's ratio = 0.3.
Boundary conditions:
End A is clamped.
Loading:
25.0 at end B.
Initial curvature is defined by specifying the direction cosines of the normals at the two ends.
Gauss integration is used for the shell cross-section for the S4R elements.
Reference results are generated from models consisting of 20 B33 cubic beam elements. (Since only one element is used for modeling, if the direction cosines of the normals are not used, the solution will correspond to straight beam theory.) The reference tests use SECTION=RECT, SECTION=I, or SECTION=PIPE. These sections correspond to regular beams and shells, open section beams, and pipes, respectively.
Regular beams and shells (see erefrrs7.inp):
Displacements, curved beam solution
2.1735 × 10–5, 
1.4570 × 10–4.
Displacements, straight beam solution
1.6667 × 10–5, 0.0.
Open section beam elements (see erefois7.inp):
Displacements, curved beam solution
3.1946 × 10–4, 1.0962 × 10–3.
Displacements, straight beam solution
2.8153 × 10–4, 0.0.
Pipe elements (see erefpps7.inp):
Displacements, curved beam solution
2.9461 × 10–5, 4.5078 × 10–5.
Displacements, straight beam solution
2.7922 × 10–5, 0.0.
Table 1.3.11–1 Regular beams and shells.
| Element Type |  |  | Remarks |
|---|---|---|---|
| B21 (1-element mesh) | 1.6667 × 10–5 | 0.0 | Straight* |
| B21 (Refined mesh) | 2.1715 × 10–5 | 1.4343 × 10–4 | Curved |
| B21H (1-element mesh) | 1.6667 × 10–5 | 0.0 | Straight* |
| B21H (Refined mesh) | 2.1665 × 10–5 | 1.4343 × 10–4 | Curved |
| B22 | 2.1085 × 10–5 | 1.4686 × 10–4 | Curved |
| B22H | 2.1085 × 10–5 | 1.4686 × 10–4 | Curved |
| B23 | 2.0873 × 10–5 | 1.4549 × 10–4 | Curved |
| B23H | 2.0873 × 10–5 | 1.4549 × 10–4 | Curved |
| B31 (1-element mesh) | 1.6667 × 10–5 | 0.0 | Straight* |
| B31 (Refined mesh) | 2.1715 × 10–5 | 1.4343 × 10–4 | Curved |
| B31H (1-element mesh) | 1.6667 × 10–5 | 0.0 | Straight |
| B31H (Refined mesh) | 2.1715 × 10–5 | 1.4343 × 10–4 | Curved |
| B32 | 2.1084 × 10–5 | 1.4686 × 10–4 | Curved |
| B32H | 2.1084 × 10–5 | 1.4686 × 10–4 | Curved |
| B33 | 2.0873 × 10–5 | 1.4548 × 10–4 | Curved |
| B33H | 2.0873 × 10–5 | 1.4548 × 10–4 | Curved |
| S4 (1-element mesh) | 1.6292 × 10–5 | 0.0 | Straight* |
| S4 (Refined mesh) | 2.1607 × 10–5 | 1.4314 × 10–4 | Curved |
| S4R (1-element mesh) | 1.6666 × 10–5 | 0.0 | Straight* |
| S4R (Refined mesh) | 2.1661 × 10–5 | 1.4340 × 10–4 | Curved |
| S4R5 (1-element mesh) | 1.6666 × 10–5 | 0.0 | Straight* |
| S4R5 (Refined mesh) | 2.1667 × 10–5 | 1.4344 × 10–4 | Curved |
| S8R | 2.1036 × 10–5 | 1.4508 × 10–4 | Curved |
| S8R5 | 2.1001 × 10–5 | 1.4638 × 10–4 | Curved |
| S9R5 | 2.1001 × 10–5 | 1.4638 × 10–4 | Curved |
| STRI3 | 1.6667 × 10–5 | 0.0 | Straight |
STRI65  | 2.0750 × 10–5 | 1.4331 × 10–4 | Curved |
| SC6R | 2.1673 × 10–5 | 1.425 × 10–4 | Curved |
| SC8R | 2.156 × 10–5 | 1.2402 × 10–4 | Curved |
| SC8R | 1.6608 × 10–5 | 2.5028 × 10–4 | Straight |
| SC8R** | 2.1491 × 10–5 | 1.4175 × 10–4 | Curved |
| SC8R** | 1.6276 × 10–5 | 2.4271 × 10–4 | Straight |
Table 1.3.11–2 Open section beam elements.
| Element Type | | | Remarks |
|---|---|---|---|
| B31OS (1-element mesh) | 2.8153 × 10–4 | 0.0 | Straight* |
| B31OS (Refined mesh) | 3.2287 × 10–4 | 1.0790 × 10–3 | Curved |
| B31OSH (1-element mesh) | 2.8153 × 10–4 | 0.0 | Straight* |
| B31OSH (Refined mesh) | 3.2287 × 10–4 | 1.0790 × 10–3 | Curved |
| B32OS (1-element mesh) | 3.1787 × 10–4 | 1.1048 × 10–3 | Curved |
| B32OSH (Refined mesh) | 3.1787 × 10–4 | 1.1048 × 10–3 | Curved |
| Element Type | | | Remarks |
|---|---|---|---|
| PIPE21 (1-element mesh) | 2.7922 × 10–5 | 0.0 | Straight* |
| PIPE21 (Refined mesh) | 2.9768 × 10–5 | 4.4373 × 10–5 | Curved |
| PIPE21H (1-element mesh) | 2.7922 × 10–5 | 0.0 | Straight* |
| PIPE21H (Refined mesh) | 2.9768 × 10–5 | 4.4373 × 10–5 | Curved |
| PIPE22 (1-element mesh) | 2.9572 × 10–5 | 4.5435 × 10–5 | Curved |
| PIPE22H (1-element mesh) | 2.9572 × 10–5 | 4.5435 × 10–5 | Curved |
| PIPE31 (1-element mesh) | 2.7922 × 10–5 | 0.0 | Straight* |
| PIPE31 (Refined mesh) | 2.9768 × 10–5 | 4.4373 × 10–5 | Curved |
| PIPE31H (1-element mesh) | 2.7922 × 10–5 | 0.0 | Straight* |
| PIPE31H (Refined mesh) | 2.9768 × 10–5 | 4.4373 × 10–5 | Curved |
| PIPE32 (1-element mesh) | 2.9572 × 10–5 | 4.5435 × 10–5 | Curved |
| PIPE32H (1-element mesh) | 2.9572 × 10–5 | 4.5435 × 10–5 | Curved |
Due to the lack of symmetry for triangular meshes, the displacements at the nodes that are at point B may differ slightly. The maximum values are documented here.** These results are obtained using enhanced hourglass control.B21 elements.
B21H elements.
B22 elements.
B22H elements.
B23 elements.
B23H elements.
B31 elements.
B31H elements.
B31OS elements.
B31OSH elements.
B32 elements.
B32H elements.
B32OS elements.
B32OSH elements.
B33 elements.
B33H elements.
PIPE21 elements.
PIPE21H elements.
PIPE22 elements.
PIPE22H elements.
PIPE31 elements.
PIPE31H elements.
PIPE32 elements.
PIPE32H elements.
S4 elements.
S4R elements.
S4R5 elements.
S8R elements.
S8R5 elements.
S9R5 elements.
STRI3 elements.
STRI65 elements.
SC8R elements.
SC8R elements with enhanced hourglass control.
B21 elements.
B21H elements.
B31 elements.
B31H elements.
B31OS elements.
B31OSH elements.
PIPE21 elements.
PIPE21H elements.
PIPE31 elements.
PIPE31H elements.
S4 elements.
S4R elements.
S4R5 elements.
SC6R elements.
SC8R elements.
SC8R elements with enhanced hourglass control.