3. Modeling A

3.1. Characteristics of modeling

We use Timoshenko’s right beam element: POU_D_T

Problem 1:

Cutting:	beam \(\mathrm{AB}\): 40 meshes SEG2
Boundary conditions: In all the knots in \(A\): in \(B\):	DDL_IMPO =( GROUP_NO = “AB”, DZ=0., DRX =0, DRY =0.) (NOEUD =”A”, DX=0., D=0.) (NOEUD =”B”, DY=0.)

Problem 2:

Cutting:	beam \(\mathrm{AB}\): 40 meshes SEG2 2 rigid elements \(\mathrm{AC}\), \(\mathrm{BC}\): 2 meshes SEG2
Boundary conditions: In all the knots in \(C\): in \(D\):	DDL_IMPO = (TOUT =” OUI “, DZ=0., DRX =0, DRY =0.) (NOEUD =”C”, DX=0., DY=0.) (NOEUD =”D”, DY=0.)

Node names:

Point \(A\) = \(\mathrm{N100}\) Point \(B\) = \(\mathrm{N200}\)

Point \(C\) = \(\mathrm{N300}\) Point \(D\) = \(\mathrm{N400}\)

3.2. Characteristics of the mesh

Number of knots:	43
Number of meshes and types:	42 SEG2

3.3. notes

Definition of rigid beams \(\mathrm{AC}\) and \(\mathrm{BD}\):

• Section: \(\mathrm{Hy}=0.2\), \(\mathrm{Hz}=0.2\).

• Material: \(E={2.10}^{16}\), \(\rho =0\).

3.4. Tested sizes and results

Frequency ( \(\mathrm{Hz}\) )

Clean Mode	Reference	Aster	Tolerance
Problem 1
flexure 1	431.555	431.8916	0.2%
traction 1	1265.924	1266.0056	0.2%
flexure 2	1498.295	1500.7635	0.2%
flexure 3	2870.661	2873.5344	0.2%
traction 2	3797.773	3799.9692	0.2%
flexure 4	4377.837	4370.8206	0.2%

Clean Mode	Reference	Aster	Tolerance
Problem 2
1	392.8	394.4774	0.5%
coupling 2	922.2	922.6072	0.1%
flexure 3	1592.0	1638.2311	3%
traction 4	2629.2	2778.7000	5.8%
compression 5	3126.2	3261.6699	4.5%

We calculate the kinetic energy of the first beam element connected to point \(A\) of problem 1:

Option	Component	Reference ( NON_REGRESSION )	Aster	% difference
ECIN_ELEM	TOTALE	51366.0	51366.027	1%

3.5. notes

Calculations made by:

Problem 1:

CALC_MODES

OPTION =” AJUSTE “ CALC_FREQ =_F (FREQ =( 430., 4500.))

Problem 2:

CALC_MODES

OPTION =” AJUSTE “ CALC_FREQ =_F (FREQ =( 380., 300.))

Contents of the results file:

Problem 1:

6 first natural frequencies, eigenvectors and modal parameters.

Problem 1:

5 first natural frequencies, eigenvectors and modal parameters.