2. Benchmark solutions#
2.1. Calculation method used for reference solutions#
2.1.1. Modeling A#
The equation for non-linear behavior is known as well as the load while moving, the solution is calculated analytically.
The law of behavior’s response in effort is:
INST |
DX [mm] |
Force [N] |
||
1.000E-01 |
1.1755705046E+00 |
3.6359182479E+02 |
||
1.500E-01 |
1.6180339887E+00 |
3.9812608291E+02 |
||
2.000E-01 |
1.9021130326E+00 |
4.1019465908E+02 |
||
2.500E-01 |
2.0000000000E+00 |
4.1334696516E+02 |
||
3.000E-01 |
1.9021130326E+00 |
3.7419217820E+02 |
||
3.500E-01 |
1.6180339887E+00 |
2.6056056066E+02 |
||
4.000E-01 |
1.1755705046E+00 |
8.3575166995E+01 |
||
4.500E-01 |
6.1803398875E-01 |
-1.3943943934E+02 |
||
5.500E-01 |
-6.1803398875E-01 |
-4.2538927701E+02 |
||
6.000E-01 |
-1.1755705046E+00 |
-4.3218671109E+02 |
||
6.500E-01 |
-1.6180339887E+00 |
-4.3565267662E+02 |
||
7.000E-01 |
-1.9021130326E+00 |
-4.3733359687E+02 |
||
7.500E-01 |
-2.0000000000E+00 |
-4.3783890390E+02 |
||
8.000E-01 |
-1.9021130326E+00 |
-3.9868411694E+02 |
||
8.500E-01 |
-1.6180339887E+00 |
-2.8505249940E+02 |
||
9.000E-01 |
-1.1755705046E+00 |
-1.0806710573E+02 |
||
9.500E-01 |
-6.1803398875E-01 |
1.1494750060E+02 |
-6.180339887575E-01 |
-6.1803398875E-01 |
1.050E+00 |
6.1803398875E-01 |
6.1803398875E-01 |
4.3970639868E+02 |
|
1.100E+00 |
1.1755705046E+00 |
4.4151193260E+02 |
||
1.150E+00 |
1.6180339887E+00 |
4.4260216756E+02 |
||
1.200E+00 |
1.9021130326E+00 |
4.4318572288E+02 |
||
1.250E+00 |
2.0000000000E+00 |
4.4336937364E+02 |
||
1.300E+00 |
1.9021130326E+00 |
4.0421458667E+02 |
1.9021130326E+00 |
|
1.350E+00 |
1.6180339887E+00 |
2.9058296914E+02 |
||
1.400E+00 |
1.1755705046E+00 |
1.1359757547E+02 |
||
1.450E+00 |
6.1803398875E-01 |
-1.0941703086E+02 |
-1.0941703086E+02 |
The internal variables of the law of behavior are also calculated and will be tested.
Variable name |
||
V1 |
|
Axial force in the local coordinate system |
V4 |
|
Axial displacement in the local coordinate system |
V7 |
|
Dissipation |
V8 |
|
Cumulative anelastic displacement |
V9 |
|
Anelastic displacement |
The internal variables of the law of behavior:
INST |
V1 |
V4 |
V4 |
V7 |
V9 |
V8 |
1.000E-01 |
3.63592E+02 |
1.17557E+00 |
8.68431E+01 |
2.66591E-01 |
2.66591E-01 |
2.66591E-01 |
1.500E-01 |
3.98126E+02 |
1.61803E+00 |
2.23467E+02 |
6.22719E-01 |
6.22719E-01 |
6.22719E-01 |
2.000E-01 |
4.10195E+02 |
1.90211E+00 |
3.26206E+02 |
8.76626E-01 |
8.76626E-01 |
8.76626E-01 |
2.500E-01 |
4.13347E+02 |
2.00000E+00 |
3.63271E+02 |
9.66633E-01 |
9.66633E-01 |
9.66633E-01 |
3.000E-01 |
3.74192E+02 |
1.90211E+00 |
3.63271E+02 |
9.66633E-01 |
9.66633E-01 |
9.66633E-01 |
3.500E-01 |
2.60561E+02 |
1.61803E+00 |
3.63271E+02 |
9.66633E-01 |
9.66633E-01 |
9.66633E-01 |
4.000E-01 |
8.35752E+01 |
1.17557E+00 |
3.63271E+02 |
9.66633E-01 |
9.66633E-01 |
9.66633E-01 |
4.500E-01 |
-1.39439E+02 |
6.18034E-01 |
3.63271E+02 |
9.66633E-01 |
9.66633E-01 |
9.66633E-01 |
5.500E-01 |
-4.25389E+02 |
-6.18034E-01 |
5.82185E+02 |
4.45439E-01 |
4.45439E-01 |
1.48783E+00 |
6.000E-01 |
-4.32187E+02 |
-1.17557E+00 |
8.14129E+02 |
-9.51037E-02 |
-9.51037E-02 |
2.02837E+00 |
6.500E-01 |
-4.35653E+02 |
-1.61803E+00 |
1.00241E+03 |
-5.28902E-01 |
-5.28902E-01 |
2.46217E+00 |
7.000E-01 |
-4.37334E+02 |
-1.90211E+00 |
1.12458E+03 |
-8.08779E-01 |
-8.08779E-01 |
2.74204E+00 |
7.500E-01 |
-4.37839E+02 |
-2.00000E+00 |
1.16686E+03 |
-9.05403E-01 |
2.83867E+00 |
2.83867E+00 |
8.000E-01 |
-3.98684E+02 |
-1.90211E+00 |
1.16686E+03 |
-9.05403E-01 |
-9.05403E-01 |
2.83867E+00 |
8.500E-01 |
-2.85052E+02 |
-1.61803E+00 |
1.16686E+03 |
-9.05403E-01 |
-9.05403E-01 |
2.83867E+00 |
9.000E-01 |
-1.08067E+02 |
-1.17557E+00 |
1.16686E+03 |
-9.05403E-01 |
-9.05403E-01 |
2.83867E+00 |
9.500E-01 |
1.14948E+02 |
-6.18034E-01 |
1.16686E+03 |
-9.05403E-01 |
2.83867E+00 |
2.83867E+00 |
1.050E+00 |
4.39706E+02 |
6.18034E-01 |
1.35299E+03 |
-4.81232E-01 |
3.26284E+00 |
3.26284E+00 |
1.100E+00 |
4.41512E+02 |
1.17557E+00 |
1.59669E+03 |
7.17907E-02 |
3.81586E+00 |
3.81586E+00 |
1.150E+00 |
4.42602E+02 |
1.61803E+00 |
1.79109E+03 |
5.11529E-01 |
4.25560E+00 |
4.25560E+00 |
1.200E+00 |
4.43186E+02 |
1.90211E+00 |
1.91626E+03 |
7.94149E-01 |
4.53822E+00 |
4.53822E+00 |
1.250E+00 |
4.43369E+02 |
2.00000E+00 |
2.00000E+00 |
1.95945E+03 |
8.91577E-01 |
4.63565E+00 |
1.300E+00 |
4.04215E+02 |
1.90211E+00 |
1.95945E+03 |
8.91577E-01 |
4.63565E+00 |
4.63565E+00 |
1.350E+00 |
2.90583E+02 |
1.61803E+00 |
1.95945E+03 |
8.91577E-01 |
4.63565E+00 |
4.63565E+00 |
1.400E+00 |
1.13598E+02 |
1.17557E+00 |
1.95945E+03 |
8.91577E-01 |
8.91577E-01 |
4.63565E+00 |
1.450E+00 |
-1.09417E+02 |
6.18034E-01 |
1.95945E+03 |
8.91577E-01 |
8.91577E-01 |
4.63565E+00 |
2.1.2. B and C models#
Non-regression test cases
2.2. Uncertainty about the solution#
2.2.1. Modeling A#
None, the reference solution is accurate.
2.2.2. B and C models#
Not applicable