3. Modeling A#
3.1. Characteristics of modeling#
The beam consists of a single mesh.
The modeling used for the beam is that of Euler-Bernoulli (POU_D_E).
The \(A\) end is embedded:
The velocities and accelerations are obtained in the following manner in harmony:
\(v(B)=i\mathrm{\omega }u(B)\)
\(a(B)=-{\mathrm{\omega }}^{2}u(B)\)
3.2. Characteristics of the mesh#
Number of knots: 2
Number of meshes and types: 1 mesh of type SEG 2
The characteristic points of the mesh are as follows:
3.3. Quantities tested (real/imaginary shape)#
Problem 1: Traction
Point/Size |
Reference value |
Reference type |
Precision (%) |
|||
displacement |
B |
DX |
(5.318 10—5, 0. ) |
“ANALYTIQUE” |
0.05 |
|
speed |
B |
DX |
(0., 3.341 10—3) |
“ANALYTIQUE” |
0.05 |
|
acceleration |
B |
DX |
(—2.099 10—1, 0. ) |
“ANALYTIQUE” |
0.05 |
|
generalized effort |
B |
N |
N |
(3000., 0. ) |
“ANALYTIQUE” |
0.05 |
Problem 2: flexion
Point/Size |
Reference value |
Reference type |
Precision (%) |
||
displacement |
B |
DY |
(1.828 10—2, 0. ) |
“ANALYTIQUE” |
0.05 |
DRZ |
(1.82 10—2, 0. ) |
“ANALYTIQUE” |
0.05 |
||
speed |
B |
DY |
(0., 1.1489) |
“ANALYTIQUE” |
0.05 |
DRZ |
(0., 1.1438) |
“ANALYTIQUE” |
0.05 |
||
acceleration |
B |
DY |
(—72.19, 0. ) |
“ANALYTIQUE” |
0.05 |
DRZ |
(—71.86, 0. ) |
“ANALYTIQUE” |
0.05 |
||
generalized effort |
B |
VY |
(3000., 0. ) |
“ANALYTIQUE” |
0.05 |
Problem 3: traction + dampening
Point/Size |
Reference value |
Reference type |
Precision (%) |
|||
displacement |
B |
DX |
(5.296 10—5, —3.363 10—6) |
“ANALYTIQUE” |
DX |
0.05 |
speed |
B |
DX |
(2.113 10—4, 3.327 10—3) |
“ANALYTIQUE” |
0.05 |
|
acceleration |
B |
DX |
(—2.091 10—1, 1.327 10—2) |
“ANALYTIQUE” |
0.05 |
|
generalized effort |
B |
N |
N |
(2.9879103, —1.897 102) |
“ANALYTIQUE” |
0.05 |
Problem 4: flexure + dampening