1.2: Cantilever Beam under Different Loading¶
Geometry and Boundary Conditions¶
The beam has a cross section of 0.2 × 0.1 m² (yz plane) and a length of 6.0 m (x-axis).
One end of the beam is fixed, while a unit load is applied to the other end in x, y, and z directions, respectively, as well as a unit twisting load around the x axis.
Material¶
Isotropic material with:
E = 10 MPa
ν = 0.3
Results¶
Reference results from [1]
Displacement in the Direction of the Load (Linear Elements)¶
Load Type (measurement direction) |
Theory [1] |
Intact Direct Solver [%Error] |
Intact Iterative Solver [%Error] |
Time (s) to solve with <1% error |
|---|---|---|---|---|
Extension (x) |
3.00E-05 |
3.00E-05 [0.06%] |
3.00E-05 [0.06%] |
Direct: 4.0 / Iterative: 34 |
In-plane Shear (y) |
0.1081 |
0.1076 [0.42%] |
0.1078 [0.29%] |
Direct: 4.0 / Iterative: 5.3 |
Out-of-Plane Shear (z) |
0.4321 |
0.4261 [1.39%] |
0.4285 [0.84%] |
Direct: 12.6 / Iterative: 36 |
Twist (y) |
3.41E-03 |
3.37E-03 [1.07%] |
3.38E-03 [0.773%] |
Direct: 13.2 / Iterative: 34 |
Displacement in the Direction of the Load (Quadratic Elements)¶
Load Type (measurement direction) |
Theory [1] |
Intact Direct Solver [%Error] |
Intact Iterative Solver [%Error] |
Time (s) to solve with <1% error |
|---|---|---|---|---|
Extension (x) |
3.00E-05 |
3.00E-05 [0.04%] |
3.00E-05 [0.04%] |
Direct: 1.3 / Iterative: 2.0 |
In-plane Shear (y) |
0.1081 |
0.1080 [0.08%] |
0.1080 [0.08%] |
Direct: 1.3 / Iterative: 2.5 |
Out-of-Plane Shear (z) |
0.4321 |
0.4315 [0.13%] |
0.4315 [0.13%] |
Direct: 1.3 / Iterative: 2.4 |
Twist (y) |
3.41E-03 |
3.39E-03 [0.460%] |
3.39E-03 [0.46%] |
Direct: 9.9 / Iterative: 55 |